Exam 1 ndash Econ 304 ndash Chuderewicz ndash Spring 2015

Name ____________KEY__________________ Last 4 (PSU ID) __________

Section Please Check

Sparks ______________

Keller ______________

PLEASE PUT THE FIRST TWO LETTERS OF YOUR LAST NAME ON TOP RIGHT HAND CORNER OF THIS COVER SHEET ndash ONLY NON-PROGRAMMABLE CALCULATORS ALLOWED THANKS AND GOOD LUCK

Total Points for exam = 240

Test time = 120 minutes

One minute for every two points

To help with time management if spreading time evenly

Question 1 = 55 points 28 minutes

Question 2 = 50 points 25 minutes

Question 31 = 35 points 17 minutes

Question 32 = 45 points 22 minutes

Question 4 = 55 points 27 minutes

1

Please answer all questions You must show all work or points will be taken off

1 (50 points total) Suppose we have Dagwood who has a current income of $600K and expected future income of $300K He has zero in current wealth and zero in expected wealth

Dagwoodrsquos behavior is consistent with the life-cycle theory of consumption For one he perfectly smoothes consumption and two since he is in his peak earning years he is saving now so that he can maintain his current level of consumption in the future Given that Dagwood faces a real interest rate of negative 5 (- 0 05) Please answer the following questions

a) (5 points) Calculate Dagwoodrsquos optimal consumption bundle showing all work Then draw a completely labeled graph (the two period consumption model) depicting this initial optimal consumption bundle as point CA

C = [(1 + r)(y + a) + yf + af] (2 + r)

C = [(1 + (-05))(600 + 0) + 300 + 0] (2 + (-05))

C = 44615

(10 points for a completely labeled graph ndash be sure to label the no lending no borrowing point(s) = NLNB and the slope of the budget constraint(s))

2

b) (5 points) Janet Yellen and the Fed are finally happy with the way the economy is headed and to be honest is now fearful of overheating As such the Fed tightens and the real rate of interest rises to 5 (005) Recalculate the optimal bundle for Dagwood and add this point to your graph and label as point CB

C = [(1 + (05))(600 + 0) + 300 + 0] (2 + (05))

C = 4537

c) (10 points) Did the Fed policy of raising interest rates work in term of lowering current consumption consistent with preventing overheating Explain being sure to discuss exactly how the substitution and income effects play a role here Be sure to define what the income and substitution effects are and how they play a role in Dagwoodrsquos decision to alter his previously optimal bundle (we are comparing part a) to part b)) Also comment on whether these income and substitution effects work in the same or opposite direction (ie is it a tug of war or do they work in the same direction) in this particular case

NO - Dagwood is a saver and cares most about his FV = (1 + r) (y + a) so that when r rises so does their future value of present resources and since they are effectively richer and that they are a consumption smoother they will spread the gain and consume more in both periods ndash with numbers FV= (1 + (-05) (600) = 570 vs (1 + 05) (600) = 630not what the Fed had in mind in terms of preventing overheating

According to the substitution effect when r rises the price of present consumption in terms of future consumption goes up so they should substitute away from current consumption towards future consumption ndash consistent with preventing overheating ndash more formally the price of (one unit) current consumption went from 95 units of future consumption to 105 units of future consumption

Pcc = 1+r1helliphellip when r rises so does the price of current consumption in terms of future consumption

d) (5 points) Now Dagwood goes to the doctor and finds out that he is not as healthy as he thought (too many eating binges) The doctor tells him that he is fine now but next period he is likely to be ill and that if you had anything in life that you really wanted to do (as in leisure) you should do it now As a result Dagwoods preferences change so that he prefers to consume like our friend Homer that is Dagwood prefers to consume twice as much today relative to next period Resolve for

3

Dagwoods optimal consumption bundle given these new preferences and label as point CC (this is of course after the Fed raised rates to 5)

C = [(1 + r)(y + a) + yf + af] (3 + 2r)

C = [(1 + (05))(600 + 0) + 300 + 0] (3 + 2(05))

cf = 300 c = 600

e) ( 5 points) Janet Yellen and the Fed are again really happy with incoming economic data and are very much worried about overheating and raise real rates again to equal 10 (10) Given his change in preferences as above in part d) recalculate the optimal bundle for Dagwood and add this point to your graph and label as point CD

C = [(1 + r)(y + a) + yf + af] (3 + 2r)

C = [(1 + (10))(600 + 0) + 300 + 0] (3 + 2(10))

cf = 300 c = 600

f) (5 points) Did the Fed policy of raising interest rates work in term of lowering current consumption consistent with preventing overheating Explain being sure to discuss exactly how the substitution and income effects play a role here

No since Dagwood is consuming at his NLNB point he doesnt care about his FV of current resources nor does he care about his PV of his future resources - he lives paycheck to paycheck (neither a saver nor a borrower) thus there is no income effect - there is also no substitution effect so the policy of a higher interest rate to cool the economy did not work

4

g) (5 points) In the space below derive and draw Dagwoods savings function (this is after Dagwood went to the doctor ie use the information from parts d) and e) only

h) (5 points) Given your results from part d) and e) above what are the implications as to the power of monetary policy with regard to influencing consumption Assume that there are many consumers in the economy just like Dagwood after he went to the doctor Please explain

Absolutely No power

5

2 (50 points total) You own a fleet of offshore fishing boats and you need to determine how many fishing poles you need to buy to maximize profits Please answer the following questions given the information below Please be sure to SHOW all work

A brand new fishing pole cost 2000 fishing hours (this is your output) and the rate of depreciation is 5 (005)

The real interest rate is 5 (05)

And the expected marginal product of capital is given by MPKf = 400 ndash 10K

There is a tax on capital so tao (τ) = 20 (20)

a) What is the (tax adjusted) user cost of capital and what is this user cost expressed in (Show work) (5 points)

uc = [(05 + 05) 2000] (1 - 20) = 250 fishing hours

b) How many fishing poles should you buy to maximize profits Show work (5 points)

250 = 400 - 10KK = 15

Draw a ucK graph depicting the state of affairs and label this initial profit maximizing condition as point A

A correctly drawn and completely labeled diagram is worth 10 points

6

Now conditions change The following two shocks occur simultaneously

i) the US $ depreciates and since you buy your poles from abroad the poles become more expensive and now cost 2400 fishing hours

ii) the expected marginal product of capital changes and is now MPKf = 420 ndash 5K

c) Resolve for K and show as point B on your ucK diagram ( 5 points)

uc = [(05 + 05) 2400] (1 - 20) = 300

300 = 420 - 5K K = 24

d) Given the two shocks as above explain the intuition underlying the change in the profit maximizing level of fishing poles (ie why does the firm change its behavior) making sure you refer to the firmrsquos profit maximizing condition (write it out) Be specific and write this like you were a professional economist Be sure to compare the actual user cost to the actual MPKf after the shocks holding K constant at its level from part b) (10 points)

K = 15 uc = 300 MPK = 420 - 5(15) = 345 since uc=300 is LESS than MPK=345 the firm needs to buy 9 fishing poles to get back to profit maximization where uc = MPK = 300 when K=24

e) Suppose that the Federal Reserve had a goal to get the capital stock (the number of fishing poles purchased) back to its initial level as in part b Given the two shocks as above what would they have to do to the real rate of interest to achieve their objective Please show all work and I am looking for a specific number (ie r = ) Please add this development to your diagram as point C (5 points)

What is MPK when K = 15 MPK = 420 - 5(15) = 345 so the Fed needs to get the uc = 345 345 = [(r + 05) 2400] (1 - 20) r = 065

7

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables (with the appropriate values as in τ = 20 etc) noted next to the function in parentheses) depicting the initial equilibrium as point A (simply draw a negatively sloped ID curve going through point A) Label the initial level of desired investment as Id

A Note importantly that we do not have numbers for desired investment but thatrsquos ok we are focusing on the change in desired investment Then show as point B the level of desired investment after the change in the price of capital and the change in the expected MPK Finally show how the Fed policy maps to your investment diagram and label as point C with the corresponding level of investment labeled as Id

C

A completely labeled and correct diagram is worth 10 points (make sure you include the relevant shift variables in parentheses or points will be taken off)

8

3 PART 1 (35 points total for this part) This problem is broken into two parts that are totally connected to each other In this first part of the question you apply Chapter 3 (labor mkt etc) material and in PART 2 you get to use Chapter 4 (goods market equilibrium) material Please take all calculations to two decimal places where appropriate except with real interest rate calculations (PART 2) where you need to take the calculation to three decimal places if appropriate PLEASE SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

P roduction function Y = AKN ndash N22Marginal product of labor MPN = AK ndash N

where the initial values of A = 8 and K = 10

The initial labor supply curve is given as NS = 20 + 9w

a) (10 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 10 - (20 + 9w)

w= 6 N = 74 Y = 3182

In the space below draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph Be sure to label everything including these initial equilibrium points as point A

9

(10 points for completely labeled and correct diagrams)

10

We now have numerous changes to our economic conditions (all is not constant) Think of all these changes happening together that is we go from one state of economic affairs to a different state of economic affairs Below are the changes

The labor supply changes and is now NS = 30 + 9w A goes up from 8 to 9

b) (5 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 9 x 10 - (30 + 9w)

w= 6 N = 84 Y = 4032

c) (10 points) Why exactly did the firm change their behavior To answer calculate the MPN and w at the same N and compare Then explain what the firm does and why and what the worker does and why This question is worth 10 points so please be specific and complete

N = 74 MPN = 9 x 10 - 74 = 16 The wage needed to attract 74 workers is 74 = 30 + 9w w = 4888 so N = 74 the MPN = 16 w = 488 The firm will hire more workers since MPN gt w at N = 74 As they hire workers the MPN falls and in order to hire more workers they need to increase the price of leisure what we call the real wage This process will continue until we return to the profit maximizing condition where at N = 84 w = MPN = 6

11

3 PART 2 (NEW GRADER ndash 45 points total for PART 2)

Before we start this problem put the initial Y as computed in part a) here _____3182__

And the new Y (after the change in conditions) here ___4032___

Initial conditions in the goods market

Cd = 1001 + 50(Y-T) ndash 500rId = 590 ndash 500rG = 100T= 100

d) (10 points) Given the initial conditions solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment

S = 3182 - [1001 + 5(3182 - 100) - 500 r ] - 100S = 540 + 500r

540 + 500r = 590 ndash 500r

r = 05S = 565 = I

Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

12

10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function)

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

Please answer all questions You must show all work or points will be taken off

1 (50 points total) Suppose we have Dagwood who has a current income of $600K and expected future income of $300K He has zero in current wealth and zero in expected wealth

Dagwoodrsquos behavior is consistent with the life-cycle theory of consumption For one he perfectly smoothes consumption and two since he is in his peak earning years he is saving now so that he can maintain his current level of consumption in the future Given that Dagwood faces a real interest rate of negative 5 (- 0 05) Please answer the following questions

a) (5 points) Calculate Dagwoodrsquos optimal consumption bundle showing all work Then draw a completely labeled graph (the two period consumption model) depicting this initial optimal consumption bundle as point CA

C = [(1 + r)(y + a) + yf + af] (2 + r)

C = [(1 + (-05))(600 + 0) + 300 + 0] (2 + (-05))

C = 44615

(10 points for a completely labeled graph ndash be sure to label the no lending no borrowing point(s) = NLNB and the slope of the budget constraint(s))

2

b) (5 points) Janet Yellen and the Fed are finally happy with the way the economy is headed and to be honest is now fearful of overheating As such the Fed tightens and the real rate of interest rises to 5 (005) Recalculate the optimal bundle for Dagwood and add this point to your graph and label as point CB

C = [(1 + (05))(600 + 0) + 300 + 0] (2 + (05))

C = 4537

c) (10 points) Did the Fed policy of raising interest rates work in term of lowering current consumption consistent with preventing overheating Explain being sure to discuss exactly how the substitution and income effects play a role here Be sure to define what the income and substitution effects are and how they play a role in Dagwoodrsquos decision to alter his previously optimal bundle (we are comparing part a) to part b)) Also comment on whether these income and substitution effects work in the same or opposite direction (ie is it a tug of war or do they work in the same direction) in this particular case

NO - Dagwood is a saver and cares most about his FV = (1 + r) (y + a) so that when r rises so does their future value of present resources and since they are effectively richer and that they are a consumption smoother they will spread the gain and consume more in both periods ndash with numbers FV= (1 + (-05) (600) = 570 vs (1 + 05) (600) = 630not what the Fed had in mind in terms of preventing overheating

According to the substitution effect when r rises the price of present consumption in terms of future consumption goes up so they should substitute away from current consumption towards future consumption ndash consistent with preventing overheating ndash more formally the price of (one unit) current consumption went from 95 units of future consumption to 105 units of future consumption

Pcc = 1+r1helliphellip when r rises so does the price of current consumption in terms of future consumption

d) (5 points) Now Dagwood goes to the doctor and finds out that he is not as healthy as he thought (too many eating binges) The doctor tells him that he is fine now but next period he is likely to be ill and that if you had anything in life that you really wanted to do (as in leisure) you should do it now As a result Dagwoods preferences change so that he prefers to consume like our friend Homer that is Dagwood prefers to consume twice as much today relative to next period Resolve for

3

Dagwoods optimal consumption bundle given these new preferences and label as point CC (this is of course after the Fed raised rates to 5)

C = [(1 + r)(y + a) + yf + af] (3 + 2r)

C = [(1 + (05))(600 + 0) + 300 + 0] (3 + 2(05))

cf = 300 c = 600

e) ( 5 points) Janet Yellen and the Fed are again really happy with incoming economic data and are very much worried about overheating and raise real rates again to equal 10 (10) Given his change in preferences as above in part d) recalculate the optimal bundle for Dagwood and add this point to your graph and label as point CD

C = [(1 + r)(y + a) + yf + af] (3 + 2r)

C = [(1 + (10))(600 + 0) + 300 + 0] (3 + 2(10))

cf = 300 c = 600

f) (5 points) Did the Fed policy of raising interest rates work in term of lowering current consumption consistent with preventing overheating Explain being sure to discuss exactly how the substitution and income effects play a role here

No since Dagwood is consuming at his NLNB point he doesnt care about his FV of current resources nor does he care about his PV of his future resources - he lives paycheck to paycheck (neither a saver nor a borrower) thus there is no income effect - there is also no substitution effect so the policy of a higher interest rate to cool the economy did not work

4

g) (5 points) In the space below derive and draw Dagwoods savings function (this is after Dagwood went to the doctor ie use the information from parts d) and e) only

h) (5 points) Given your results from part d) and e) above what are the implications as to the power of monetary policy with regard to influencing consumption Assume that there are many consumers in the economy just like Dagwood after he went to the doctor Please explain

Absolutely No power

5

2 (50 points total) You own a fleet of offshore fishing boats and you need to determine how many fishing poles you need to buy to maximize profits Please answer the following questions given the information below Please be sure to SHOW all work

A brand new fishing pole cost 2000 fishing hours (this is your output) and the rate of depreciation is 5 (005)

The real interest rate is 5 (05)

And the expected marginal product of capital is given by MPKf = 400 ndash 10K

There is a tax on capital so tao (τ) = 20 (20)

a) What is the (tax adjusted) user cost of capital and what is this user cost expressed in (Show work) (5 points)

uc = [(05 + 05) 2000] (1 - 20) = 250 fishing hours

b) How many fishing poles should you buy to maximize profits Show work (5 points)

250 = 400 - 10KK = 15

Draw a ucK graph depicting the state of affairs and label this initial profit maximizing condition as point A

A correctly drawn and completely labeled diagram is worth 10 points

6

Now conditions change The following two shocks occur simultaneously

i) the US $ depreciates and since you buy your poles from abroad the poles become more expensive and now cost 2400 fishing hours

ii) the expected marginal product of capital changes and is now MPKf = 420 ndash 5K

c) Resolve for K and show as point B on your ucK diagram ( 5 points)

uc = [(05 + 05) 2400] (1 - 20) = 300

300 = 420 - 5K K = 24

d) Given the two shocks as above explain the intuition underlying the change in the profit maximizing level of fishing poles (ie why does the firm change its behavior) making sure you refer to the firmrsquos profit maximizing condition (write it out) Be specific and write this like you were a professional economist Be sure to compare the actual user cost to the actual MPKf after the shocks holding K constant at its level from part b) (10 points)

K = 15 uc = 300 MPK = 420 - 5(15) = 345 since uc=300 is LESS than MPK=345 the firm needs to buy 9 fishing poles to get back to profit maximization where uc = MPK = 300 when K=24

e) Suppose that the Federal Reserve had a goal to get the capital stock (the number of fishing poles purchased) back to its initial level as in part b Given the two shocks as above what would they have to do to the real rate of interest to achieve their objective Please show all work and I am looking for a specific number (ie r = ) Please add this development to your diagram as point C (5 points)

What is MPK when K = 15 MPK = 420 - 5(15) = 345 so the Fed needs to get the uc = 345 345 = [(r + 05) 2400] (1 - 20) r = 065

7

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables (with the appropriate values as in τ = 20 etc) noted next to the function in parentheses) depicting the initial equilibrium as point A (simply draw a negatively sloped ID curve going through point A) Label the initial level of desired investment as Id

A Note importantly that we do not have numbers for desired investment but thatrsquos ok we are focusing on the change in desired investment Then show as point B the level of desired investment after the change in the price of capital and the change in the expected MPK Finally show how the Fed policy maps to your investment diagram and label as point C with the corresponding level of investment labeled as Id

C

A completely labeled and correct diagram is worth 10 points (make sure you include the relevant shift variables in parentheses or points will be taken off)

8

3 PART 1 (35 points total for this part) This problem is broken into two parts that are totally connected to each other In this first part of the question you apply Chapter 3 (labor mkt etc) material and in PART 2 you get to use Chapter 4 (goods market equilibrium) material Please take all calculations to two decimal places where appropriate except with real interest rate calculations (PART 2) where you need to take the calculation to three decimal places if appropriate PLEASE SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

P roduction function Y = AKN ndash N22Marginal product of labor MPN = AK ndash N

where the initial values of A = 8 and K = 10

The initial labor supply curve is given as NS = 20 + 9w

a) (10 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 10 - (20 + 9w)

w= 6 N = 74 Y = 3182

In the space below draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph Be sure to label everything including these initial equilibrium points as point A

9

(10 points for completely labeled and correct diagrams)

10

We now have numerous changes to our economic conditions (all is not constant) Think of all these changes happening together that is we go from one state of economic affairs to a different state of economic affairs Below are the changes

The labor supply changes and is now NS = 30 + 9w A goes up from 8 to 9

b) (5 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 9 x 10 - (30 + 9w)

w= 6 N = 84 Y = 4032

c) (10 points) Why exactly did the firm change their behavior To answer calculate the MPN and w at the same N and compare Then explain what the firm does and why and what the worker does and why This question is worth 10 points so please be specific and complete

N = 74 MPN = 9 x 10 - 74 = 16 The wage needed to attract 74 workers is 74 = 30 + 9w w = 4888 so N = 74 the MPN = 16 w = 488 The firm will hire more workers since MPN gt w at N = 74 As they hire workers the MPN falls and in order to hire more workers they need to increase the price of leisure what we call the real wage This process will continue until we return to the profit maximizing condition where at N = 84 w = MPN = 6

11

3 PART 2 (NEW GRADER ndash 45 points total for PART 2)

Before we start this problem put the initial Y as computed in part a) here _____3182__

And the new Y (after the change in conditions) here ___4032___

Initial conditions in the goods market

Cd = 1001 + 50(Y-T) ndash 500rId = 590 ndash 500rG = 100T= 100

d) (10 points) Given the initial conditions solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment

S = 3182 - [1001 + 5(3182 - 100) - 500 r ] - 100S = 540 + 500r

540 + 500r = 590 ndash 500r

r = 05S = 565 = I

Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

12

10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function)

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

b) (5 points) Janet Yellen and the Fed are finally happy with the way the economy is headed and to be honest is now fearful of overheating As such the Fed tightens and the real rate of interest rises to 5 (005) Recalculate the optimal bundle for Dagwood and add this point to your graph and label as point CB

C = [(1 + (05))(600 + 0) + 300 + 0] (2 + (05))

C = 4537

c) (10 points) Did the Fed policy of raising interest rates work in term of lowering current consumption consistent with preventing overheating Explain being sure to discuss exactly how the substitution and income effects play a role here Be sure to define what the income and substitution effects are and how they play a role in Dagwoodrsquos decision to alter his previously optimal bundle (we are comparing part a) to part b)) Also comment on whether these income and substitution effects work in the same or opposite direction (ie is it a tug of war or do they work in the same direction) in this particular case

NO - Dagwood is a saver and cares most about his FV = (1 + r) (y + a) so that when r rises so does their future value of present resources and since they are effectively richer and that they are a consumption smoother they will spread the gain and consume more in both periods ndash with numbers FV= (1 + (-05) (600) = 570 vs (1 + 05) (600) = 630not what the Fed had in mind in terms of preventing overheating

According to the substitution effect when r rises the price of present consumption in terms of future consumption goes up so they should substitute away from current consumption towards future consumption ndash consistent with preventing overheating ndash more formally the price of (one unit) current consumption went from 95 units of future consumption to 105 units of future consumption

Pcc = 1+r1helliphellip when r rises so does the price of current consumption in terms of future consumption

d) (5 points) Now Dagwood goes to the doctor and finds out that he is not as healthy as he thought (too many eating binges) The doctor tells him that he is fine now but next period he is likely to be ill and that if you had anything in life that you really wanted to do (as in leisure) you should do it now As a result Dagwoods preferences change so that he prefers to consume like our friend Homer that is Dagwood prefers to consume twice as much today relative to next period Resolve for

3

Dagwoods optimal consumption bundle given these new preferences and label as point CC (this is of course after the Fed raised rates to 5)

C = [(1 + r)(y + a) + yf + af] (3 + 2r)

C = [(1 + (05))(600 + 0) + 300 + 0] (3 + 2(05))

cf = 300 c = 600

e) ( 5 points) Janet Yellen and the Fed are again really happy with incoming economic data and are very much worried about overheating and raise real rates again to equal 10 (10) Given his change in preferences as above in part d) recalculate the optimal bundle for Dagwood and add this point to your graph and label as point CD

C = [(1 + r)(y + a) + yf + af] (3 + 2r)

C = [(1 + (10))(600 + 0) + 300 + 0] (3 + 2(10))

cf = 300 c = 600

f) (5 points) Did the Fed policy of raising interest rates work in term of lowering current consumption consistent with preventing overheating Explain being sure to discuss exactly how the substitution and income effects play a role here

No since Dagwood is consuming at his NLNB point he doesnt care about his FV of current resources nor does he care about his PV of his future resources - he lives paycheck to paycheck (neither a saver nor a borrower) thus there is no income effect - there is also no substitution effect so the policy of a higher interest rate to cool the economy did not work

4

g) (5 points) In the space below derive and draw Dagwoods savings function (this is after Dagwood went to the doctor ie use the information from parts d) and e) only

h) (5 points) Given your results from part d) and e) above what are the implications as to the power of monetary policy with regard to influencing consumption Assume that there are many consumers in the economy just like Dagwood after he went to the doctor Please explain

Absolutely No power

5

2 (50 points total) You own a fleet of offshore fishing boats and you need to determine how many fishing poles you need to buy to maximize profits Please answer the following questions given the information below Please be sure to SHOW all work

A brand new fishing pole cost 2000 fishing hours (this is your output) and the rate of depreciation is 5 (005)

The real interest rate is 5 (05)

And the expected marginal product of capital is given by MPKf = 400 ndash 10K

There is a tax on capital so tao (τ) = 20 (20)

a) What is the (tax adjusted) user cost of capital and what is this user cost expressed in (Show work) (5 points)

uc = [(05 + 05) 2000] (1 - 20) = 250 fishing hours

b) How many fishing poles should you buy to maximize profits Show work (5 points)

250 = 400 - 10KK = 15

Draw a ucK graph depicting the state of affairs and label this initial profit maximizing condition as point A

A correctly drawn and completely labeled diagram is worth 10 points

6

Now conditions change The following two shocks occur simultaneously

i) the US $ depreciates and since you buy your poles from abroad the poles become more expensive and now cost 2400 fishing hours

ii) the expected marginal product of capital changes and is now MPKf = 420 ndash 5K

c) Resolve for K and show as point B on your ucK diagram ( 5 points)

uc = [(05 + 05) 2400] (1 - 20) = 300

300 = 420 - 5K K = 24

d) Given the two shocks as above explain the intuition underlying the change in the profit maximizing level of fishing poles (ie why does the firm change its behavior) making sure you refer to the firmrsquos profit maximizing condition (write it out) Be specific and write this like you were a professional economist Be sure to compare the actual user cost to the actual MPKf after the shocks holding K constant at its level from part b) (10 points)

K = 15 uc = 300 MPK = 420 - 5(15) = 345 since uc=300 is LESS than MPK=345 the firm needs to buy 9 fishing poles to get back to profit maximization where uc = MPK = 300 when K=24

e) Suppose that the Federal Reserve had a goal to get the capital stock (the number of fishing poles purchased) back to its initial level as in part b Given the two shocks as above what would they have to do to the real rate of interest to achieve their objective Please show all work and I am looking for a specific number (ie r = ) Please add this development to your diagram as point C (5 points)

What is MPK when K = 15 MPK = 420 - 5(15) = 345 so the Fed needs to get the uc = 345 345 = [(r + 05) 2400] (1 - 20) r = 065

7

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables (with the appropriate values as in τ = 20 etc) noted next to the function in parentheses) depicting the initial equilibrium as point A (simply draw a negatively sloped ID curve going through point A) Label the initial level of desired investment as Id

A Note importantly that we do not have numbers for desired investment but thatrsquos ok we are focusing on the change in desired investment Then show as point B the level of desired investment after the change in the price of capital and the change in the expected MPK Finally show how the Fed policy maps to your investment diagram and label as point C with the corresponding level of investment labeled as Id

C

A completely labeled and correct diagram is worth 10 points (make sure you include the relevant shift variables in parentheses or points will be taken off)

8

3 PART 1 (35 points total for this part) This problem is broken into two parts that are totally connected to each other In this first part of the question you apply Chapter 3 (labor mkt etc) material and in PART 2 you get to use Chapter 4 (goods market equilibrium) material Please take all calculations to two decimal places where appropriate except with real interest rate calculations (PART 2) where you need to take the calculation to three decimal places if appropriate PLEASE SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

P roduction function Y = AKN ndash N22Marginal product of labor MPN = AK ndash N

where the initial values of A = 8 and K = 10

The initial labor supply curve is given as NS = 20 + 9w

a) (10 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 10 - (20 + 9w)

w= 6 N = 74 Y = 3182

In the space below draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph Be sure to label everything including these initial equilibrium points as point A

9

(10 points for completely labeled and correct diagrams)

10

We now have numerous changes to our economic conditions (all is not constant) Think of all these changes happening together that is we go from one state of economic affairs to a different state of economic affairs Below are the changes

The labor supply changes and is now NS = 30 + 9w A goes up from 8 to 9

b) (5 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 9 x 10 - (30 + 9w)

w= 6 N = 84 Y = 4032

c) (10 points) Why exactly did the firm change their behavior To answer calculate the MPN and w at the same N and compare Then explain what the firm does and why and what the worker does and why This question is worth 10 points so please be specific and complete

N = 74 MPN = 9 x 10 - 74 = 16 The wage needed to attract 74 workers is 74 = 30 + 9w w = 4888 so N = 74 the MPN = 16 w = 488 The firm will hire more workers since MPN gt w at N = 74 As they hire workers the MPN falls and in order to hire more workers they need to increase the price of leisure what we call the real wage This process will continue until we return to the profit maximizing condition where at N = 84 w = MPN = 6

11

3 PART 2 (NEW GRADER ndash 45 points total for PART 2)

Before we start this problem put the initial Y as computed in part a) here _____3182__

And the new Y (after the change in conditions) here ___4032___

Initial conditions in the goods market

Cd = 1001 + 50(Y-T) ndash 500rId = 590 ndash 500rG = 100T= 100

d) (10 points) Given the initial conditions solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment

S = 3182 - [1001 + 5(3182 - 100) - 500 r ] - 100S = 540 + 500r

540 + 500r = 590 ndash 500r

r = 05S = 565 = I

Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

12

10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function)

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

Dagwoods optimal consumption bundle given these new preferences and label as point CC (this is of course after the Fed raised rates to 5)

C = [(1 + r)(y + a) + yf + af] (3 + 2r)

C = [(1 + (05))(600 + 0) + 300 + 0] (3 + 2(05))

cf = 300 c = 600

e) ( 5 points) Janet Yellen and the Fed are again really happy with incoming economic data and are very much worried about overheating and raise real rates again to equal 10 (10) Given his change in preferences as above in part d) recalculate the optimal bundle for Dagwood and add this point to your graph and label as point CD

C = [(1 + r)(y + a) + yf + af] (3 + 2r)

C = [(1 + (10))(600 + 0) + 300 + 0] (3 + 2(10))

cf = 300 c = 600

f) (5 points) Did the Fed policy of raising interest rates work in term of lowering current consumption consistent with preventing overheating Explain being sure to discuss exactly how the substitution and income effects play a role here

No since Dagwood is consuming at his NLNB point he doesnt care about his FV of current resources nor does he care about his PV of his future resources - he lives paycheck to paycheck (neither a saver nor a borrower) thus there is no income effect - there is also no substitution effect so the policy of a higher interest rate to cool the economy did not work

4

g) (5 points) In the space below derive and draw Dagwoods savings function (this is after Dagwood went to the doctor ie use the information from parts d) and e) only

h) (5 points) Given your results from part d) and e) above what are the implications as to the power of monetary policy with regard to influencing consumption Assume that there are many consumers in the economy just like Dagwood after he went to the doctor Please explain

Absolutely No power

5

2 (50 points total) You own a fleet of offshore fishing boats and you need to determine how many fishing poles you need to buy to maximize profits Please answer the following questions given the information below Please be sure to SHOW all work

A brand new fishing pole cost 2000 fishing hours (this is your output) and the rate of depreciation is 5 (005)

The real interest rate is 5 (05)

And the expected marginal product of capital is given by MPKf = 400 ndash 10K

There is a tax on capital so tao (τ) = 20 (20)

a) What is the (tax adjusted) user cost of capital and what is this user cost expressed in (Show work) (5 points)

uc = [(05 + 05) 2000] (1 - 20) = 250 fishing hours

b) How many fishing poles should you buy to maximize profits Show work (5 points)

250 = 400 - 10KK = 15

Draw a ucK graph depicting the state of affairs and label this initial profit maximizing condition as point A

A correctly drawn and completely labeled diagram is worth 10 points

6

Now conditions change The following two shocks occur simultaneously

i) the US $ depreciates and since you buy your poles from abroad the poles become more expensive and now cost 2400 fishing hours

ii) the expected marginal product of capital changes and is now MPKf = 420 ndash 5K

c) Resolve for K and show as point B on your ucK diagram ( 5 points)

uc = [(05 + 05) 2400] (1 - 20) = 300

300 = 420 - 5K K = 24

d) Given the two shocks as above explain the intuition underlying the change in the profit maximizing level of fishing poles (ie why does the firm change its behavior) making sure you refer to the firmrsquos profit maximizing condition (write it out) Be specific and write this like you were a professional economist Be sure to compare the actual user cost to the actual MPKf after the shocks holding K constant at its level from part b) (10 points)

K = 15 uc = 300 MPK = 420 - 5(15) = 345 since uc=300 is LESS than MPK=345 the firm needs to buy 9 fishing poles to get back to profit maximization where uc = MPK = 300 when K=24

e) Suppose that the Federal Reserve had a goal to get the capital stock (the number of fishing poles purchased) back to its initial level as in part b Given the two shocks as above what would they have to do to the real rate of interest to achieve their objective Please show all work and I am looking for a specific number (ie r = ) Please add this development to your diagram as point C (5 points)

What is MPK when K = 15 MPK = 420 - 5(15) = 345 so the Fed needs to get the uc = 345 345 = [(r + 05) 2400] (1 - 20) r = 065

7

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables (with the appropriate values as in τ = 20 etc) noted next to the function in parentheses) depicting the initial equilibrium as point A (simply draw a negatively sloped ID curve going through point A) Label the initial level of desired investment as Id

A Note importantly that we do not have numbers for desired investment but thatrsquos ok we are focusing on the change in desired investment Then show as point B the level of desired investment after the change in the price of capital and the change in the expected MPK Finally show how the Fed policy maps to your investment diagram and label as point C with the corresponding level of investment labeled as Id

C

A completely labeled and correct diagram is worth 10 points (make sure you include the relevant shift variables in parentheses or points will be taken off)

8

3 PART 1 (35 points total for this part) This problem is broken into two parts that are totally connected to each other In this first part of the question you apply Chapter 3 (labor mkt etc) material and in PART 2 you get to use Chapter 4 (goods market equilibrium) material Please take all calculations to two decimal places where appropriate except with real interest rate calculations (PART 2) where you need to take the calculation to three decimal places if appropriate PLEASE SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

P roduction function Y = AKN ndash N22Marginal product of labor MPN = AK ndash N

where the initial values of A = 8 and K = 10

The initial labor supply curve is given as NS = 20 + 9w

a) (10 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 10 - (20 + 9w)

w= 6 N = 74 Y = 3182

In the space below draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph Be sure to label everything including these initial equilibrium points as point A

9

(10 points for completely labeled and correct diagrams)

10

We now have numerous changes to our economic conditions (all is not constant) Think of all these changes happening together that is we go from one state of economic affairs to a different state of economic affairs Below are the changes

The labor supply changes and is now NS = 30 + 9w A goes up from 8 to 9

b) (5 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 9 x 10 - (30 + 9w)

w= 6 N = 84 Y = 4032

c) (10 points) Why exactly did the firm change their behavior To answer calculate the MPN and w at the same N and compare Then explain what the firm does and why and what the worker does and why This question is worth 10 points so please be specific and complete

N = 74 MPN = 9 x 10 - 74 = 16 The wage needed to attract 74 workers is 74 = 30 + 9w w = 4888 so N = 74 the MPN = 16 w = 488 The firm will hire more workers since MPN gt w at N = 74 As they hire workers the MPN falls and in order to hire more workers they need to increase the price of leisure what we call the real wage This process will continue until we return to the profit maximizing condition where at N = 84 w = MPN = 6

11

3 PART 2 (NEW GRADER ndash 45 points total for PART 2)

Before we start this problem put the initial Y as computed in part a) here _____3182__

And the new Y (after the change in conditions) here ___4032___

Initial conditions in the goods market

Cd = 1001 + 50(Y-T) ndash 500rId = 590 ndash 500rG = 100T= 100

d) (10 points) Given the initial conditions solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment

S = 3182 - [1001 + 5(3182 - 100) - 500 r ] - 100S = 540 + 500r

540 + 500r = 590 ndash 500r

r = 05S = 565 = I

Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

12

10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function)

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

g) (5 points) In the space below derive and draw Dagwoods savings function (this is after Dagwood went to the doctor ie use the information from parts d) and e) only

h) (5 points) Given your results from part d) and e) above what are the implications as to the power of monetary policy with regard to influencing consumption Assume that there are many consumers in the economy just like Dagwood after he went to the doctor Please explain

Absolutely No power

5

2 (50 points total) You own a fleet of offshore fishing boats and you need to determine how many fishing poles you need to buy to maximize profits Please answer the following questions given the information below Please be sure to SHOW all work

A brand new fishing pole cost 2000 fishing hours (this is your output) and the rate of depreciation is 5 (005)

The real interest rate is 5 (05)

And the expected marginal product of capital is given by MPKf = 400 ndash 10K

There is a tax on capital so tao (τ) = 20 (20)

a) What is the (tax adjusted) user cost of capital and what is this user cost expressed in (Show work) (5 points)

uc = [(05 + 05) 2000] (1 - 20) = 250 fishing hours

b) How many fishing poles should you buy to maximize profits Show work (5 points)

250 = 400 - 10KK = 15

Draw a ucK graph depicting the state of affairs and label this initial profit maximizing condition as point A

A correctly drawn and completely labeled diagram is worth 10 points

6

Now conditions change The following two shocks occur simultaneously

i) the US $ depreciates and since you buy your poles from abroad the poles become more expensive and now cost 2400 fishing hours

ii) the expected marginal product of capital changes and is now MPKf = 420 ndash 5K

c) Resolve for K and show as point B on your ucK diagram ( 5 points)

uc = [(05 + 05) 2400] (1 - 20) = 300

300 = 420 - 5K K = 24

d) Given the two shocks as above explain the intuition underlying the change in the profit maximizing level of fishing poles (ie why does the firm change its behavior) making sure you refer to the firmrsquos profit maximizing condition (write it out) Be specific and write this like you were a professional economist Be sure to compare the actual user cost to the actual MPKf after the shocks holding K constant at its level from part b) (10 points)

K = 15 uc = 300 MPK = 420 - 5(15) = 345 since uc=300 is LESS than MPK=345 the firm needs to buy 9 fishing poles to get back to profit maximization where uc = MPK = 300 when K=24

e) Suppose that the Federal Reserve had a goal to get the capital stock (the number of fishing poles purchased) back to its initial level as in part b Given the two shocks as above what would they have to do to the real rate of interest to achieve their objective Please show all work and I am looking for a specific number (ie r = ) Please add this development to your diagram as point C (5 points)

What is MPK when K = 15 MPK = 420 - 5(15) = 345 so the Fed needs to get the uc = 345 345 = [(r + 05) 2400] (1 - 20) r = 065

7

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables (with the appropriate values as in τ = 20 etc) noted next to the function in parentheses) depicting the initial equilibrium as point A (simply draw a negatively sloped ID curve going through point A) Label the initial level of desired investment as Id

A Note importantly that we do not have numbers for desired investment but thatrsquos ok we are focusing on the change in desired investment Then show as point B the level of desired investment after the change in the price of capital and the change in the expected MPK Finally show how the Fed policy maps to your investment diagram and label as point C with the corresponding level of investment labeled as Id

C

A completely labeled and correct diagram is worth 10 points (make sure you include the relevant shift variables in parentheses or points will be taken off)

8

3 PART 1 (35 points total for this part) This problem is broken into two parts that are totally connected to each other In this first part of the question you apply Chapter 3 (labor mkt etc) material and in PART 2 you get to use Chapter 4 (goods market equilibrium) material Please take all calculations to two decimal places where appropriate except with real interest rate calculations (PART 2) where you need to take the calculation to three decimal places if appropriate PLEASE SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

P roduction function Y = AKN ndash N22Marginal product of labor MPN = AK ndash N

where the initial values of A = 8 and K = 10

The initial labor supply curve is given as NS = 20 + 9w

a) (10 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 10 - (20 + 9w)

w= 6 N = 74 Y = 3182

In the space below draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph Be sure to label everything including these initial equilibrium points as point A

9

(10 points for completely labeled and correct diagrams)

10

We now have numerous changes to our economic conditions (all is not constant) Think of all these changes happening together that is we go from one state of economic affairs to a different state of economic affairs Below are the changes

The labor supply changes and is now NS = 30 + 9w A goes up from 8 to 9

b) (5 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 9 x 10 - (30 + 9w)

w= 6 N = 84 Y = 4032

c) (10 points) Why exactly did the firm change their behavior To answer calculate the MPN and w at the same N and compare Then explain what the firm does and why and what the worker does and why This question is worth 10 points so please be specific and complete

N = 74 MPN = 9 x 10 - 74 = 16 The wage needed to attract 74 workers is 74 = 30 + 9w w = 4888 so N = 74 the MPN = 16 w = 488 The firm will hire more workers since MPN gt w at N = 74 As they hire workers the MPN falls and in order to hire more workers they need to increase the price of leisure what we call the real wage This process will continue until we return to the profit maximizing condition where at N = 84 w = MPN = 6

11

3 PART 2 (NEW GRADER ndash 45 points total for PART 2)

Before we start this problem put the initial Y as computed in part a) here _____3182__

And the new Y (after the change in conditions) here ___4032___

Initial conditions in the goods market

Cd = 1001 + 50(Y-T) ndash 500rId = 590 ndash 500rG = 100T= 100

d) (10 points) Given the initial conditions solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment

S = 3182 - [1001 + 5(3182 - 100) - 500 r ] - 100S = 540 + 500r

540 + 500r = 590 ndash 500r

r = 05S = 565 = I

Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

12

10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function)

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

2 (50 points total) You own a fleet of offshore fishing boats and you need to determine how many fishing poles you need to buy to maximize profits Please answer the following questions given the information below Please be sure to SHOW all work

A brand new fishing pole cost 2000 fishing hours (this is your output) and the rate of depreciation is 5 (005)

The real interest rate is 5 (05)

And the expected marginal product of capital is given by MPKf = 400 ndash 10K

There is a tax on capital so tao (τ) = 20 (20)

a) What is the (tax adjusted) user cost of capital and what is this user cost expressed in (Show work) (5 points)

uc = [(05 + 05) 2000] (1 - 20) = 250 fishing hours

b) How many fishing poles should you buy to maximize profits Show work (5 points)

250 = 400 - 10KK = 15

Draw a ucK graph depicting the state of affairs and label this initial profit maximizing condition as point A

A correctly drawn and completely labeled diagram is worth 10 points

6

Now conditions change The following two shocks occur simultaneously

i) the US $ depreciates and since you buy your poles from abroad the poles become more expensive and now cost 2400 fishing hours

ii) the expected marginal product of capital changes and is now MPKf = 420 ndash 5K

c) Resolve for K and show as point B on your ucK diagram ( 5 points)

uc = [(05 + 05) 2400] (1 - 20) = 300

300 = 420 - 5K K = 24

d) Given the two shocks as above explain the intuition underlying the change in the profit maximizing level of fishing poles (ie why does the firm change its behavior) making sure you refer to the firmrsquos profit maximizing condition (write it out) Be specific and write this like you were a professional economist Be sure to compare the actual user cost to the actual MPKf after the shocks holding K constant at its level from part b) (10 points)

K = 15 uc = 300 MPK = 420 - 5(15) = 345 since uc=300 is LESS than MPK=345 the firm needs to buy 9 fishing poles to get back to profit maximization where uc = MPK = 300 when K=24

e) Suppose that the Federal Reserve had a goal to get the capital stock (the number of fishing poles purchased) back to its initial level as in part b Given the two shocks as above what would they have to do to the real rate of interest to achieve their objective Please show all work and I am looking for a specific number (ie r = ) Please add this development to your diagram as point C (5 points)

What is MPK when K = 15 MPK = 420 - 5(15) = 345 so the Fed needs to get the uc = 345 345 = [(r + 05) 2400] (1 - 20) r = 065

7

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables (with the appropriate values as in τ = 20 etc) noted next to the function in parentheses) depicting the initial equilibrium as point A (simply draw a negatively sloped ID curve going through point A) Label the initial level of desired investment as Id

A Note importantly that we do not have numbers for desired investment but thatrsquos ok we are focusing on the change in desired investment Then show as point B the level of desired investment after the change in the price of capital and the change in the expected MPK Finally show how the Fed policy maps to your investment diagram and label as point C with the corresponding level of investment labeled as Id

C

A completely labeled and correct diagram is worth 10 points (make sure you include the relevant shift variables in parentheses or points will be taken off)

8

3 PART 1 (35 points total for this part) This problem is broken into two parts that are totally connected to each other In this first part of the question you apply Chapter 3 (labor mkt etc) material and in PART 2 you get to use Chapter 4 (goods market equilibrium) material Please take all calculations to two decimal places where appropriate except with real interest rate calculations (PART 2) where you need to take the calculation to three decimal places if appropriate PLEASE SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

P roduction function Y = AKN ndash N22Marginal product of labor MPN = AK ndash N

where the initial values of A = 8 and K = 10

The initial labor supply curve is given as NS = 20 + 9w

a) (10 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 10 - (20 + 9w)

w= 6 N = 74 Y = 3182

In the space below draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph Be sure to label everything including these initial equilibrium points as point A

9

(10 points for completely labeled and correct diagrams)

10

We now have numerous changes to our economic conditions (all is not constant) Think of all these changes happening together that is we go from one state of economic affairs to a different state of economic affairs Below are the changes

The labor supply changes and is now NS = 30 + 9w A goes up from 8 to 9

b) (5 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 9 x 10 - (30 + 9w)

w= 6 N = 84 Y = 4032

c) (10 points) Why exactly did the firm change their behavior To answer calculate the MPN and w at the same N and compare Then explain what the firm does and why and what the worker does and why This question is worth 10 points so please be specific and complete

N = 74 MPN = 9 x 10 - 74 = 16 The wage needed to attract 74 workers is 74 = 30 + 9w w = 4888 so N = 74 the MPN = 16 w = 488 The firm will hire more workers since MPN gt w at N = 74 As they hire workers the MPN falls and in order to hire more workers they need to increase the price of leisure what we call the real wage This process will continue until we return to the profit maximizing condition where at N = 84 w = MPN = 6

11

3 PART 2 (NEW GRADER ndash 45 points total for PART 2)

Before we start this problem put the initial Y as computed in part a) here _____3182__

And the new Y (after the change in conditions) here ___4032___

Initial conditions in the goods market

Cd = 1001 + 50(Y-T) ndash 500rId = 590 ndash 500rG = 100T= 100

d) (10 points) Given the initial conditions solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment

S = 3182 - [1001 + 5(3182 - 100) - 500 r ] - 100S = 540 + 500r

540 + 500r = 590 ndash 500r

r = 05S = 565 = I

Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

12

10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function)

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

Now conditions change The following two shocks occur simultaneously

i) the US $ depreciates and since you buy your poles from abroad the poles become more expensive and now cost 2400 fishing hours

ii) the expected marginal product of capital changes and is now MPKf = 420 ndash 5K

c) Resolve for K and show as point B on your ucK diagram ( 5 points)

uc = [(05 + 05) 2400] (1 - 20) = 300

300 = 420 - 5K K = 24

d) Given the two shocks as above explain the intuition underlying the change in the profit maximizing level of fishing poles (ie why does the firm change its behavior) making sure you refer to the firmrsquos profit maximizing condition (write it out) Be specific and write this like you were a professional economist Be sure to compare the actual user cost to the actual MPKf after the shocks holding K constant at its level from part b) (10 points)

K = 15 uc = 300 MPK = 420 - 5(15) = 345 since uc=300 is LESS than MPK=345 the firm needs to buy 9 fishing poles to get back to profit maximization where uc = MPK = 300 when K=24

e) Suppose that the Federal Reserve had a goal to get the capital stock (the number of fishing poles purchased) back to its initial level as in part b Given the two shocks as above what would they have to do to the real rate of interest to achieve their objective Please show all work and I am looking for a specific number (ie r = ) Please add this development to your diagram as point C (5 points)

What is MPK when K = 15 MPK = 420 - 5(15) = 345 so the Fed needs to get the uc = 345 345 = [(r + 05) 2400] (1 - 20) r = 065

7

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables (with the appropriate values as in τ = 20 etc) noted next to the function in parentheses) depicting the initial equilibrium as point A (simply draw a negatively sloped ID curve going through point A) Label the initial level of desired investment as Id

A Note importantly that we do not have numbers for desired investment but thatrsquos ok we are focusing on the change in desired investment Then show as point B the level of desired investment after the change in the price of capital and the change in the expected MPK Finally show how the Fed policy maps to your investment diagram and label as point C with the corresponding level of investment labeled as Id

C

A completely labeled and correct diagram is worth 10 points (make sure you include the relevant shift variables in parentheses or points will be taken off)

8

3 PART 1 (35 points total for this part) This problem is broken into two parts that are totally connected to each other In this first part of the question you apply Chapter 3 (labor mkt etc) material and in PART 2 you get to use Chapter 4 (goods market equilibrium) material Please take all calculations to two decimal places where appropriate except with real interest rate calculations (PART 2) where you need to take the calculation to three decimal places if appropriate PLEASE SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

P roduction function Y = AKN ndash N22Marginal product of labor MPN = AK ndash N

where the initial values of A = 8 and K = 10

The initial labor supply curve is given as NS = 20 + 9w

a) (10 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 10 - (20 + 9w)

w= 6 N = 74 Y = 3182

In the space below draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph Be sure to label everything including these initial equilibrium points as point A

9

(10 points for completely labeled and correct diagrams)

10

We now have numerous changes to our economic conditions (all is not constant) Think of all these changes happening together that is we go from one state of economic affairs to a different state of economic affairs Below are the changes

The labor supply changes and is now NS = 30 + 9w A goes up from 8 to 9

b) (5 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 9 x 10 - (30 + 9w)

w= 6 N = 84 Y = 4032

c) (10 points) Why exactly did the firm change their behavior To answer calculate the MPN and w at the same N and compare Then explain what the firm does and why and what the worker does and why This question is worth 10 points so please be specific and complete

N = 74 MPN = 9 x 10 - 74 = 16 The wage needed to attract 74 workers is 74 = 30 + 9w w = 4888 so N = 74 the MPN = 16 w = 488 The firm will hire more workers since MPN gt w at N = 74 As they hire workers the MPN falls and in order to hire more workers they need to increase the price of leisure what we call the real wage This process will continue until we return to the profit maximizing condition where at N = 84 w = MPN = 6

11

3 PART 2 (NEW GRADER ndash 45 points total for PART 2)

Before we start this problem put the initial Y as computed in part a) here _____3182__

And the new Y (after the change in conditions) here ___4032___

Initial conditions in the goods market

Cd = 1001 + 50(Y-T) ndash 500rId = 590 ndash 500rG = 100T= 100

d) (10 points) Given the initial conditions solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment

S = 3182 - [1001 + 5(3182 - 100) - 500 r ] - 100S = 540 + 500r

540 + 500r = 590 ndash 500r

r = 05S = 565 = I

Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

12

10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function)

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables (with the appropriate values as in τ = 20 etc) noted next to the function in parentheses) depicting the initial equilibrium as point A (simply draw a negatively sloped ID curve going through point A) Label the initial level of desired investment as Id

A Note importantly that we do not have numbers for desired investment but thatrsquos ok we are focusing on the change in desired investment Then show as point B the level of desired investment after the change in the price of capital and the change in the expected MPK Finally show how the Fed policy maps to your investment diagram and label as point C with the corresponding level of investment labeled as Id

C

A completely labeled and correct diagram is worth 10 points (make sure you include the relevant shift variables in parentheses or points will be taken off)

8

3 PART 1 (35 points total for this part) This problem is broken into two parts that are totally connected to each other In this first part of the question you apply Chapter 3 (labor mkt etc) material and in PART 2 you get to use Chapter 4 (goods market equilibrium) material Please take all calculations to two decimal places where appropriate except with real interest rate calculations (PART 2) where you need to take the calculation to three decimal places if appropriate PLEASE SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

P roduction function Y = AKN ndash N22Marginal product of labor MPN = AK ndash N

where the initial values of A = 8 and K = 10

The initial labor supply curve is given as NS = 20 + 9w

a) (10 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 10 - (20 + 9w)

w= 6 N = 74 Y = 3182

In the space below draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph Be sure to label everything including these initial equilibrium points as point A

9

(10 points for completely labeled and correct diagrams)

10

We now have numerous changes to our economic conditions (all is not constant) Think of all these changes happening together that is we go from one state of economic affairs to a different state of economic affairs Below are the changes

The labor supply changes and is now NS = 30 + 9w A goes up from 8 to 9

b) (5 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 9 x 10 - (30 + 9w)

w= 6 N = 84 Y = 4032

c) (10 points) Why exactly did the firm change their behavior To answer calculate the MPN and w at the same N and compare Then explain what the firm does and why and what the worker does and why This question is worth 10 points so please be specific and complete

N = 74 MPN = 9 x 10 - 74 = 16 The wage needed to attract 74 workers is 74 = 30 + 9w w = 4888 so N = 74 the MPN = 16 w = 488 The firm will hire more workers since MPN gt w at N = 74 As they hire workers the MPN falls and in order to hire more workers they need to increase the price of leisure what we call the real wage This process will continue until we return to the profit maximizing condition where at N = 84 w = MPN = 6

11

3 PART 2 (NEW GRADER ndash 45 points total for PART 2)

Before we start this problem put the initial Y as computed in part a) here _____3182__

And the new Y (after the change in conditions) here ___4032___

Initial conditions in the goods market

Cd = 1001 + 50(Y-T) ndash 500rId = 590 ndash 500rG = 100T= 100

d) (10 points) Given the initial conditions solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment

S = 3182 - [1001 + 5(3182 - 100) - 500 r ] - 100S = 540 + 500r

540 + 500r = 590 ndash 500r

r = 05S = 565 = I

Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

12

10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function)

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

3 PART 1 (35 points total for this part) This problem is broken into two parts that are totally connected to each other In this first part of the question you apply Chapter 3 (labor mkt etc) material and in PART 2 you get to use Chapter 4 (goods market equilibrium) material Please take all calculations to two decimal places where appropriate except with real interest rate calculations (PART 2) where you need to take the calculation to three decimal places if appropriate PLEASE SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

P roduction function Y = AKN ndash N22Marginal product of labor MPN = AK ndash N

where the initial values of A = 8 and K = 10

The initial labor supply curve is given as NS = 20 + 9w

a) (10 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 10 - (20 + 9w)

w= 6 N = 74 Y = 3182

In the space below draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph Be sure to label everything including these initial equilibrium points as point A

9

(10 points for completely labeled and correct diagrams)

10

We now have numerous changes to our economic conditions (all is not constant) Think of all these changes happening together that is we go from one state of economic affairs to a different state of economic affairs Below are the changes

The labor supply changes and is now NS = 30 + 9w A goes up from 8 to 9

b) (5 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 9 x 10 - (30 + 9w)

w= 6 N = 84 Y = 4032

c) (10 points) Why exactly did the firm change their behavior To answer calculate the MPN and w at the same N and compare Then explain what the firm does and why and what the worker does and why This question is worth 10 points so please be specific and complete

N = 74 MPN = 9 x 10 - 74 = 16 The wage needed to attract 74 workers is 74 = 30 + 9w w = 4888 so N = 74 the MPN = 16 w = 488 The firm will hire more workers since MPN gt w at N = 74 As they hire workers the MPN falls and in order to hire more workers they need to increase the price of leisure what we call the real wage This process will continue until we return to the profit maximizing condition where at N = 84 w = MPN = 6

11

3 PART 2 (NEW GRADER ndash 45 points total for PART 2)

Before we start this problem put the initial Y as computed in part a) here _____3182__

And the new Y (after the change in conditions) here ___4032___

Initial conditions in the goods market

Cd = 1001 + 50(Y-T) ndash 500rId = 590 ndash 500rG = 100T= 100

d) (10 points) Given the initial conditions solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment

S = 3182 - [1001 + 5(3182 - 100) - 500 r ] - 100S = 540 + 500r

540 + 500r = 590 ndash 500r

r = 05S = 565 = I

Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

12

10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function)

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

(10 points for completely labeled and correct diagrams)

10

We now have numerous changes to our economic conditions (all is not constant) Think of all these changes happening together that is we go from one state of economic affairs to a different state of economic affairs Below are the changes

The labor supply changes and is now NS = 30 + 9w A goes up from 8 to 9

b) (5 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 9 x 10 - (30 + 9w)

w= 6 N = 84 Y = 4032

c) (10 points) Why exactly did the firm change their behavior To answer calculate the MPN and w at the same N and compare Then explain what the firm does and why and what the worker does and why This question is worth 10 points so please be specific and complete

N = 74 MPN = 9 x 10 - 74 = 16 The wage needed to attract 74 workers is 74 = 30 + 9w w = 4888 so N = 74 the MPN = 16 w = 488 The firm will hire more workers since MPN gt w at N = 74 As they hire workers the MPN falls and in order to hire more workers they need to increase the price of leisure what we call the real wage This process will continue until we return to the profit maximizing condition where at N = 84 w = MPN = 6

11

3 PART 2 (NEW GRADER ndash 45 points total for PART 2)

Before we start this problem put the initial Y as computed in part a) here _____3182__

And the new Y (after the change in conditions) here ___4032___

Initial conditions in the goods market

Cd = 1001 + 50(Y-T) ndash 500rId = 590 ndash 500rG = 100T= 100

d) (10 points) Given the initial conditions solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment

S = 3182 - [1001 + 5(3182 - 100) - 500 r ] - 100S = 540 + 500r

540 + 500r = 590 ndash 500r

r = 05S = 565 = I

Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

12

10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function)

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

We now have numerous changes to our economic conditions (all is not constant) Think of all these changes happening together that is we go from one state of economic affairs to a different state of economic affairs Below are the changes

The labor supply changes and is now NS = 30 + 9w A goes up from 8 to 9

b) (5 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 9 x 10 - (30 + 9w)

w= 6 N = 84 Y = 4032

c) (10 points) Why exactly did the firm change their behavior To answer calculate the MPN and w at the same N and compare Then explain what the firm does and why and what the worker does and why This question is worth 10 points so please be specific and complete

N = 74 MPN = 9 x 10 - 74 = 16 The wage needed to attract 74 workers is 74 = 30 + 9w w = 4888 so N = 74 the MPN = 16 w = 488 The firm will hire more workers since MPN gt w at N = 74 As they hire workers the MPN falls and in order to hire more workers they need to increase the price of leisure what we call the real wage This process will continue until we return to the profit maximizing condition where at N = 84 w = MPN = 6

11

3 PART 2 (NEW GRADER ndash 45 points total for PART 2)

Before we start this problem put the initial Y as computed in part a) here _____3182__

And the new Y (after the change in conditions) here ___4032___

Initial conditions in the goods market

Cd = 1001 + 50(Y-T) ndash 500rId = 590 ndash 500rG = 100T= 100

d) (10 points) Given the initial conditions solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment

S = 3182 - [1001 + 5(3182 - 100) - 500 r ] - 100S = 540 + 500r

540 + 500r = 590 ndash 500r

r = 05S = 565 = I

Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

12

10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function)

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

3 PART 2 (NEW GRADER ndash 45 points total for PART 2)

Before we start this problem put the initial Y as computed in part a) here _____3182__

And the new Y (after the change in conditions) here ___4032___

Initial conditions in the goods market

Cd = 1001 + 50(Y-T) ndash 500rId = 590 ndash 500rG = 100T= 100

d) (10 points) Given the initial conditions solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment

S = 3182 - [1001 + 5(3182 - 100) - 500 r ] - 100S = 540 + 500r

540 + 500r = 590 ndash 500r

r = 05S = 565 = I

Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

12

10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function)

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function)

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN DESIRED INVESTMENT

The desired investment function changes and is now Id = 715 ndash 500r The consumption function is now Cd = 1301 + 50(Y-T) ndash 500r

e) (5 points) What could cause such a change in the desired investment function Please give three specific reasons

3 uc shifters

1) lower τ2) higher ITC3) lower Pk

2 mpk shifters

1) higher A2) higher AS (animal spirits)

f) (10 points) Given these changes (ie changes in A Y Id and C) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 4032 - [1301 + 5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 ndash 500r

r = 05

S = 690 = I

14

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem In the space below draw and use the two period consumption model and depict the movement from point A to point B Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph Explain why your graph changed the way it did Make sure you label your graph completely Now the discussion Are the results with regard to the change in income change in consumption and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery Please explain and be as specific as possible

Consumption at point A Cd = 1001 + 50(3182 - 100) ndash 500(05) = 2517 Consumption at point B Cd = 1301 + 50(4032 - 100) ndash 500(05) = 3242 The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1 income went up from 3182 to 4032 and 2 something shifted the Cd function as in a rise in a yf af or CC

Consistent with the economy being in the midst of a recovery Y went up - consumption function shifted up investment went up (most pro-cyclical variable out there)

15

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

4 (55 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 04(Y-T) ndash 200rw

Id = 420 ndash 200rw

Y = 2000T = 200G =500

China Initial Conditions

CdF = 480 + 4(YF ndash TF) ndash 300rw

IdF = 370 ndash 300rw

YF = 1600TF = 400GF = 300

a) What is the equilibrium interest rate that clears the international goods market Show all work (10 points)

USA

S = 2000 - [400 + 4(2000 - 200) - 200 r ] - 500

S = 380 + 200r

S = 1600 - [480 + 4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 r = 07

b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points)

USA

16

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

S = 380 + 200(07) = 394I = 420 - 200(07) = 406

NX = -12

CHINA

S = 340 + 300(07) = 361I = 370 - 300(07) = 349

NX = + 12

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption (specific with each component of absorption) in each country to its income Explain (5 points) The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106I = 406G= 500

C + I + G = 2012Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939I = 349G = 300

C + I + G = 1588Y = 1600

Draw two diagrams side by side with the US on the left and the China on right Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses

17

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

19

20

21

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by

IdF = 400 ndash 300rw

d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the lsquonewrsquo Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams (10 points)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 r = 10

e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA) Are your results consistent with the US going to AA Why or why not Explain and please be specific as to what happened to absorption in the US and why

USA

S = 380 + 200(10) = 400I = 420 - 200(10) = 400

NX = 0 (A TRADE BALANCE)

18

CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

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CHINA

S = 340 + 300(10) = 370I = 400 - 300(10) = 370

NX = 0 (A TRADE BALANCE)

YES THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12 NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION WHEN INVESTMENT IN CHINA WENT UP REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINAS INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30 RATES WENT UP BY 03C IN US WENT DOWN BY 03 X 200 = 6 AND I IN US WENT DOWN BY 03 X 200 = 6 SO ABSORPTION IN US FELL BY 12 EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA THE CHANGES WERE 9 AND 9 RESPECTIVELY (03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30 THIS IS HOW THE SHOCK WAS ABSORBED AFTER THE SHOCK OF 30ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES

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