Exam 1 ndash Econ 304 ndash Chuderewicz ndash Spring 2017

Name ______________KEY________________ Last 4 (PSU ID) __________

Section Please Check

Section 001 - 010 Sparks 1010 am ______________

Section 002 - 121 Sparks 1115 am ______________

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 = 230

Test time = 120 minutes

Approximately one minute for every two points

To help with time management if spreading time evenly

Question 1 = 50 points 25 minutes

Question 2 = 50 points 25 minutes

Question 31 = 40 points 20 minutes

Question 32 = 40 points 20 minutes

Question 5 = 50 points 25 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 $200K and expected future income of $200K He has zero in current wealth and zero in expected wealth

Dagwoodrsquos behavior is consistent with the life-cycle theory of consumption as his preferences are to perfectly smooth consumption Given that Dagwood faces a real interest rate of 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))(200 + 0) + 200 + 0] (2 + (05))

C = 200

(10 points for a completely labeled graph ndash be sure to label the no lending no borrowing points =

NLNB) Use space above

b)(5 points) Dagwood works in an industry that is becoming obsolete and thus quits his job and goes back to school (college) As a result he has to take a part time job so his current income is now $100K The good news that is expected future income has risen to $350K given his new degree Resolve for Dagwoods optimal consumption bundle and label as point CB

C = [(1 + (05))(100 + 0) + 350 + 0] (2 + (05))

2

C = 222

c) (5 points) Janet Yellen and the Fed are not happy with the state of the economy and worry about an impending recession As a result the Fed lowers rates so that the new real rate is negative 5 Recalculate the optimal bundle for Dagwood and add this point to your graph and label as point CB

C = [(1 + (-05))(100 + 0) + 350 + 0] (2 + (-05))

C = 228

d) (10 points) Did the Fed policy work as in stimulating the economy as measured by the change in Dagwoods current consumption That is did Dagwoods consumption rise Why or why not Explain using the income and substitution effects Please use actual numbers to support your answer

YES Since Dagwood is a borrower he cares most about his PV of futures resources since he is financing consumption today by borrowing from the future When r goes down PV = (yf + af) (1 + r) rises and therefore Dagwood is richer and should spread the gain and consume more in both periods - this is the income effect With numbers PV = 350 (1 + (05)) = 33333 vs PV = 350 (1 + (-05)) = 36842

The substitution effect works in the same direction - when r goes down so does the price of current consumption = 1+r 1 The price of current consumption goes from 105 units of future consumption to 95 units of future consumption - since the price of current consumption has gone down Dagwood should substitute away from future consumption towards current consumption

e) (15 points total) In the space below draw two savings functions for Dagwood The first savings function is for the initial conditions before Dagwood quits his job (when his current income equals future income = $200K) Label as point A where r = 05 and point B when r = -05

Now draw another savings function representing the conditions after Dagwood quit his job where his current income is $100K and his expected future income is $350K Label as point C where r = 05 and then point D where r = -05 Please put only the relevant shift variables in parentheses next to each savings function Please show work for each of the four points (A B C D)

3

10 points for correct and completely labeled graph

2 (50 points total) You own a golf resort and you need to determine how many golf carts 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 golf cart costs 200 rounds of golf (this is your output) and the rate of depreciation is 7 (007)

The real interest rate is 3 (03)

And the expected marginal product of capital is given by MPKf = 275 ndash 5K

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

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

expressed in (Show work)

uc = [(03 + 07) 200] (1 - 20) = 25 rounds of golf

b) (5 points) How many golf carts should you buy to maximize profits Show work

25 = 275 - 5KK = 50

4

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

Now conditions change The following two shocks occur simultaneously

i) the price of golf carts rises to 240 rounds of golf

ii) the expected marginal product of capital changes and is now MPKf = 300 ndash 5K

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

uc = [(03 + 07) 240] (1 - 20) = 30

30 = 300 - 5K K = 54

d) (10 points) Given the two shocks as above explain the intuition underlying the change in the profit maximizing level of carts (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)

K = 50 uc = 30 MPK = 300 - 5(50) = 50 since uc= 30 is LESS than MPK=50 we need to BUY 4 golf carts to get back to profit maximization where uc = MPK = 30 when K=54 - for every cart we buy MPK falls by 5 when we buy 4 MPK falls by 4 x 5 = 20from 50 to 30 = uc

e) (5 points) Suppose that the Federal Reserve had a goal to get the capital stock the number of golf carts purchased to equal 52 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

What is MPK when K = 52 MPK = 300 - 5(52) = 40 so the Fed needs to get the uc = 40 40 = [(r + 07) 240] (1 - 20)[40 x (1 - 20)] 240 - 07 r = 0633

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables) 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 after the two shocks 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)

6

3 PART 1 (40 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 SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

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

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

The initial labor supply curve is given as NS = 14 + 4w

a) (5 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 8 - [14 + 4w]

5w = 50 w = 10 N = 54 Y = 1998

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

(15 points for completely labeled and correct diagrams)

7

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 = 6 + 4w K goes down from 8 to 7

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons Be sure to explain your answer

5 CHOICES 1) HIGHER EXPECTED INCOME2) HIGHER WEALTH3) TIGHTER IMMIGRATION LAWS4) LESS PARTICIPATION5) DEMOGRAPHICS - AGING POPULATION - LESS PEOPLE ENTERING LABOR FORCE

c) (5 points) Given the change in NS and K 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 = 8 x 7 - [6 + 4w]

5w = 50 w = 10 N = 46 Y = 1518

d) (10 points) Explain exactly why the profit maximizing level of labor has changed given the change in NS

and K Be very specific with your answer as in using numbers Begin your answer with At the same level of labor input N = (what it was at point A) the firm is no longer

N = 54w = 12 and MPN = 2 (MPN = 8 x 7 - 54) SO wgtMPN fire people - if you fire 8 people the MPN will rise to = 10as you fire people you can pay a lower wage - if you layoff 4 people wage falls by one layoff 8 people wage falls by 2 from 12 to 10back at profit max where w = 10 = MPN when N = 46

8

3 PART 2 (40 points total for PART 2)

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

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

Initial conditions in the goods market

Cd = 299 + 50(Y-T) ndash 500rId = 330 ndash 500rG = 500T= 200

e) (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 = 1998 - [299 + 50(1998 - 200) ndash 500r] - 500

S = 300 + 500r

300 + 500r = 330 ndash 500r

r = 03 S = I = 315 Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

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

9

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN THE CONSUMPTION FUNCTION

The new consumption function is Cd = 49 + 50(Y-T) ndash 500r

f) (5 points) What could cause such a change in the consumption function Please give two specific and well supported reasons Be sure to explain your answer

4 POSSIBILITIES

LOWER WEALTH (a)LOWER EXPECTED INCOME (yf)LOWER EXPECTED WEALTH (af)LOWER CONSUMER CONFIDENCE (CC)

g) (10 points) Given these changes ie changes in Y from part 1 and the change in the consumption function 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 = 1518 - [49 + 50(1518 - 200) ndash 500r] - 500

S = 310 + 500r

310 + 500r = 330 ndash 500r

r = 02 S = I = 320

h) (5 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be a specific as possible with regard to the changes in the consumption function and the change in labor supply (please refer to each for full credit)

YES FOR THE MOST PART - THE CONSUMPTION FUNCTION SHIFTED DOWN CONSISTENT WITH LOSSES IN WEALTH ($14 TRILLION WORTH WAS LOST IN THE GREAT RECESSION) - LOWER CC EXPECTED WEALTH EXPECTED INCOME - ALL PERFECTLY CONSISTENT WITH GREAT RECESSION

LABOR SUPPLY - YES IF YOU THINK ABOUT LESS PARTICIPATION SINCE JOB MARKET CONDITIONS WERE SO BAD BUT NO IF YOU THINK OF THE LOSS OF WEALTH THIS WOULD RESULT IN HIGHER LABOR SUPPLY NOT LOWER LABOR SUPPLY AS IN PROBLEM

10

4 (50 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 05(Y-T) ndash 300rw

Id = 430 ndash 200rw

Y = 2300T = 300G =500

China Initial Conditions

CdF = 600 + 5(YF ndash TF) ndash 300rw

IdF = 310 ndash 200rw

YF = 2000TF = 400GF = 300

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

S = 2300 - [400 + 5(2300 - 300) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [600 + 5(2000 - 400) - 300 r ] - 300

S = 300 + 300r

[400 + 300r] - [430 - 200r] + [300 + 300r] - [310 - 200r] = 0

-40 + 1000r = 0 r = 04

11

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

USA

S = 400 + 300(04) = 412I = 430 - 200(04) = 422

NX = -10

CHINA

S = 300 + 300(04) = 312I = 310 - 200(04) = 302

NX = + 10

c) (5 points) 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 in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater than the income we generate Y Absorption in the US is 2310 Y = 2300 Absorption in China is 1990 Y =2000 China is the saver - USA is spending beyond its means

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

15 points for correct and completely labeled diagrams

We now have a change in conditions The Investment function changes for the US and is now

Id = 450 ndash 200rw

12

d) (5 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)

[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0

-60 + 1000r = 0 r = 06

USA

S = 400 + 300(06) = 418I = 450 - 200(06) = 438

NX = -20

CHINA

S = 300 + 300(06) = 318I = 310 - 200(06) = 298

NX = +20

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 Also what happened to investment in both countries and why Again be specific

NO the US has not gone to AA their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10

Investment in the US rose by 16 given the positive shock to the investment function At same r investment would have risen by 20 but r has to go up to finance this investment - when r goes up by 02 4 units of investment are crowded out in the US20 minus 4 = 16

Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US at the same K uc gt MPK China needs to sell machines to get back to profit maximization Since I = K - Kt + dKtwhen K falls so does I

13

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 $200K and expected future income of $200K He has zero in current wealth and zero in expected wealth

Dagwoodrsquos behavior is consistent with the life-cycle theory of consumption as his preferences are to perfectly smooth consumption Given that Dagwood faces a real interest rate of 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))(200 + 0) + 200 + 0] (2 + (05))

C = 200

(10 points for a completely labeled graph ndash be sure to label the no lending no borrowing points =

NLNB) Use space above

b)(5 points) Dagwood works in an industry that is becoming obsolete and thus quits his job and goes back to school (college) As a result he has to take a part time job so his current income is now $100K The good news that is expected future income has risen to $350K given his new degree Resolve for Dagwoods optimal consumption bundle and label as point CB

C = [(1 + (05))(100 + 0) + 350 + 0] (2 + (05))

2

C = 222

c) (5 points) Janet Yellen and the Fed are not happy with the state of the economy and worry about an impending recession As a result the Fed lowers rates so that the new real rate is negative 5 Recalculate the optimal bundle for Dagwood and add this point to your graph and label as point CB

C = [(1 + (-05))(100 + 0) + 350 + 0] (2 + (-05))

C = 228

d) (10 points) Did the Fed policy work as in stimulating the economy as measured by the change in Dagwoods current consumption That is did Dagwoods consumption rise Why or why not Explain using the income and substitution effects Please use actual numbers to support your answer

YES Since Dagwood is a borrower he cares most about his PV of futures resources since he is financing consumption today by borrowing from the future When r goes down PV = (yf + af) (1 + r) rises and therefore Dagwood is richer and should spread the gain and consume more in both periods - this is the income effect With numbers PV = 350 (1 + (05)) = 33333 vs PV = 350 (1 + (-05)) = 36842

The substitution effect works in the same direction - when r goes down so does the price of current consumption = 1+r 1 The price of current consumption goes from 105 units of future consumption to 95 units of future consumption - since the price of current consumption has gone down Dagwood should substitute away from future consumption towards current consumption

e) (15 points total) In the space below draw two savings functions for Dagwood The first savings function is for the initial conditions before Dagwood quits his job (when his current income equals future income = $200K) Label as point A where r = 05 and point B when r = -05

Now draw another savings function representing the conditions after Dagwood quit his job where his current income is $100K and his expected future income is $350K Label as point C where r = 05 and then point D where r = -05 Please put only the relevant shift variables in parentheses next to each savings function Please show work for each of the four points (A B C D)

3

10 points for correct and completely labeled graph

2 (50 points total) You own a golf resort and you need to determine how many golf carts 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 golf cart costs 200 rounds of golf (this is your output) and the rate of depreciation is 7 (007)

The real interest rate is 3 (03)

And the expected marginal product of capital is given by MPKf = 275 ndash 5K

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

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

expressed in (Show work)

uc = [(03 + 07) 200] (1 - 20) = 25 rounds of golf

b) (5 points) How many golf carts should you buy to maximize profits Show work

25 = 275 - 5KK = 50

4

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

Now conditions change The following two shocks occur simultaneously

i) the price of golf carts rises to 240 rounds of golf

ii) the expected marginal product of capital changes and is now MPKf = 300 ndash 5K

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

uc = [(03 + 07) 240] (1 - 20) = 30

30 = 300 - 5K K = 54

d) (10 points) Given the two shocks as above explain the intuition underlying the change in the profit maximizing level of carts (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)

K = 50 uc = 30 MPK = 300 - 5(50) = 50 since uc= 30 is LESS than MPK=50 we need to BUY 4 golf carts to get back to profit maximization where uc = MPK = 30 when K=54 - for every cart we buy MPK falls by 5 when we buy 4 MPK falls by 4 x 5 = 20from 50 to 30 = uc

e) (5 points) Suppose that the Federal Reserve had a goal to get the capital stock the number of golf carts purchased to equal 52 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

What is MPK when K = 52 MPK = 300 - 5(52) = 40 so the Fed needs to get the uc = 40 40 = [(r + 07) 240] (1 - 20)[40 x (1 - 20)] 240 - 07 r = 0633

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables) 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 after the two shocks 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)

6

3 PART 1 (40 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 SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

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

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

The initial labor supply curve is given as NS = 14 + 4w

a) (5 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 8 - [14 + 4w]

5w = 50 w = 10 N = 54 Y = 1998

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

(15 points for completely labeled and correct diagrams)

7

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 = 6 + 4w K goes down from 8 to 7

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons Be sure to explain your answer

5 CHOICES 1) HIGHER EXPECTED INCOME2) HIGHER WEALTH3) TIGHTER IMMIGRATION LAWS4) LESS PARTICIPATION5) DEMOGRAPHICS - AGING POPULATION - LESS PEOPLE ENTERING LABOR FORCE

c) (5 points) Given the change in NS and K 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 = 8 x 7 - [6 + 4w]

5w = 50 w = 10 N = 46 Y = 1518

d) (10 points) Explain exactly why the profit maximizing level of labor has changed given the change in NS

and K Be very specific with your answer as in using numbers Begin your answer with At the same level of labor input N = (what it was at point A) the firm is no longer

N = 54w = 12 and MPN = 2 (MPN = 8 x 7 - 54) SO wgtMPN fire people - if you fire 8 people the MPN will rise to = 10as you fire people you can pay a lower wage - if you layoff 4 people wage falls by one layoff 8 people wage falls by 2 from 12 to 10back at profit max where w = 10 = MPN when N = 46

8

3 PART 2 (40 points total for PART 2)

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

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

Initial conditions in the goods market

Cd = 299 + 50(Y-T) ndash 500rId = 330 ndash 500rG = 500T= 200

e) (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 = 1998 - [299 + 50(1998 - 200) ndash 500r] - 500

S = 300 + 500r

300 + 500r = 330 ndash 500r

r = 03 S = I = 315 Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

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

9

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN THE CONSUMPTION FUNCTION

The new consumption function is Cd = 49 + 50(Y-T) ndash 500r

f) (5 points) What could cause such a change in the consumption function Please give two specific and well supported reasons Be sure to explain your answer

4 POSSIBILITIES

LOWER WEALTH (a)LOWER EXPECTED INCOME (yf)LOWER EXPECTED WEALTH (af)LOWER CONSUMER CONFIDENCE (CC)

g) (10 points) Given these changes ie changes in Y from part 1 and the change in the consumption function 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 = 1518 - [49 + 50(1518 - 200) ndash 500r] - 500

S = 310 + 500r

310 + 500r = 330 ndash 500r

r = 02 S = I = 320

h) (5 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be a specific as possible with regard to the changes in the consumption function and the change in labor supply (please refer to each for full credit)

YES FOR THE MOST PART - THE CONSUMPTION FUNCTION SHIFTED DOWN CONSISTENT WITH LOSSES IN WEALTH ($14 TRILLION WORTH WAS LOST IN THE GREAT RECESSION) - LOWER CC EXPECTED WEALTH EXPECTED INCOME - ALL PERFECTLY CONSISTENT WITH GREAT RECESSION

LABOR SUPPLY - YES IF YOU THINK ABOUT LESS PARTICIPATION SINCE JOB MARKET CONDITIONS WERE SO BAD BUT NO IF YOU THINK OF THE LOSS OF WEALTH THIS WOULD RESULT IN HIGHER LABOR SUPPLY NOT LOWER LABOR SUPPLY AS IN PROBLEM

10

4 (50 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 05(Y-T) ndash 300rw

Id = 430 ndash 200rw

Y = 2300T = 300G =500

China Initial Conditions

CdF = 600 + 5(YF ndash TF) ndash 300rw

IdF = 310 ndash 200rw

YF = 2000TF = 400GF = 300

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

S = 2300 - [400 + 5(2300 - 300) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [600 + 5(2000 - 400) - 300 r ] - 300

S = 300 + 300r

[400 + 300r] - [430 - 200r] + [300 + 300r] - [310 - 200r] = 0

-40 + 1000r = 0 r = 04

11

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

USA

S = 400 + 300(04) = 412I = 430 - 200(04) = 422

NX = -10

CHINA

S = 300 + 300(04) = 312I = 310 - 200(04) = 302

NX = + 10

c) (5 points) 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 in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater than the income we generate Y Absorption in the US is 2310 Y = 2300 Absorption in China is 1990 Y =2000 China is the saver - USA is spending beyond its means

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

15 points for correct and completely labeled diagrams

We now have a change in conditions The Investment function changes for the US and is now

Id = 450 ndash 200rw

12

d) (5 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)

[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0

-60 + 1000r = 0 r = 06

USA

S = 400 + 300(06) = 418I = 450 - 200(06) = 438

NX = -20

CHINA

S = 300 + 300(06) = 318I = 310 - 200(06) = 298

NX = +20

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 Also what happened to investment in both countries and why Again be specific

NO the US has not gone to AA their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10

Investment in the US rose by 16 given the positive shock to the investment function At same r investment would have risen by 20 but r has to go up to finance this investment - when r goes up by 02 4 units of investment are crowded out in the US20 minus 4 = 16

Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US at the same K uc gt MPK China needs to sell machines to get back to profit maximization Since I = K - Kt + dKtwhen K falls so does I

13

C = 222

c) (5 points) Janet Yellen and the Fed are not happy with the state of the economy and worry about an impending recession As a result the Fed lowers rates so that the new real rate is negative 5 Recalculate the optimal bundle for Dagwood and add this point to your graph and label as point CB

C = [(1 + (-05))(100 + 0) + 350 + 0] (2 + (-05))

C = 228

d) (10 points) Did the Fed policy work as in stimulating the economy as measured by the change in Dagwoods current consumption That is did Dagwoods consumption rise Why or why not Explain using the income and substitution effects Please use actual numbers to support your answer

YES Since Dagwood is a borrower he cares most about his PV of futures resources since he is financing consumption today by borrowing from the future When r goes down PV = (yf + af) (1 + r) rises and therefore Dagwood is richer and should spread the gain and consume more in both periods - this is the income effect With numbers PV = 350 (1 + (05)) = 33333 vs PV = 350 (1 + (-05)) = 36842

The substitution effect works in the same direction - when r goes down so does the price of current consumption = 1+r 1 The price of current consumption goes from 105 units of future consumption to 95 units of future consumption - since the price of current consumption has gone down Dagwood should substitute away from future consumption towards current consumption

e) (15 points total) In the space below draw two savings functions for Dagwood The first savings function is for the initial conditions before Dagwood quits his job (when his current income equals future income = $200K) Label as point A where r = 05 and point B when r = -05

Now draw another savings function representing the conditions after Dagwood quit his job where his current income is $100K and his expected future income is $350K Label as point C where r = 05 and then point D where r = -05 Please put only the relevant shift variables in parentheses next to each savings function Please show work for each of the four points (A B C D)

3

10 points for correct and completely labeled graph

2 (50 points total) You own a golf resort and you need to determine how many golf carts 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 golf cart costs 200 rounds of golf (this is your output) and the rate of depreciation is 7 (007)

The real interest rate is 3 (03)

And the expected marginal product of capital is given by MPKf = 275 ndash 5K

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

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

expressed in (Show work)

uc = [(03 + 07) 200] (1 - 20) = 25 rounds of golf

b) (5 points) How many golf carts should you buy to maximize profits Show work

25 = 275 - 5KK = 50

4

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

Now conditions change The following two shocks occur simultaneously

i) the price of golf carts rises to 240 rounds of golf

ii) the expected marginal product of capital changes and is now MPKf = 300 ndash 5K

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

uc = [(03 + 07) 240] (1 - 20) = 30

30 = 300 - 5K K = 54

d) (10 points) Given the two shocks as above explain the intuition underlying the change in the profit maximizing level of carts (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)

K = 50 uc = 30 MPK = 300 - 5(50) = 50 since uc= 30 is LESS than MPK=50 we need to BUY 4 golf carts to get back to profit maximization where uc = MPK = 30 when K=54 - for every cart we buy MPK falls by 5 when we buy 4 MPK falls by 4 x 5 = 20from 50 to 30 = uc

e) (5 points) Suppose that the Federal Reserve had a goal to get the capital stock the number of golf carts purchased to equal 52 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

What is MPK when K = 52 MPK = 300 - 5(52) = 40 so the Fed needs to get the uc = 40 40 = [(r + 07) 240] (1 - 20)[40 x (1 - 20)] 240 - 07 r = 0633

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables) 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 after the two shocks 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)

6

3 PART 1 (40 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 SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

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

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

The initial labor supply curve is given as NS = 14 + 4w

a) (5 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 8 - [14 + 4w]

5w = 50 w = 10 N = 54 Y = 1998

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

(15 points for completely labeled and correct diagrams)

7

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 = 6 + 4w K goes down from 8 to 7

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons Be sure to explain your answer

5 CHOICES 1) HIGHER EXPECTED INCOME2) HIGHER WEALTH3) TIGHTER IMMIGRATION LAWS4) LESS PARTICIPATION5) DEMOGRAPHICS - AGING POPULATION - LESS PEOPLE ENTERING LABOR FORCE

c) (5 points) Given the change in NS and K 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 = 8 x 7 - [6 + 4w]

5w = 50 w = 10 N = 46 Y = 1518

d) (10 points) Explain exactly why the profit maximizing level of labor has changed given the change in NS

and K Be very specific with your answer as in using numbers Begin your answer with At the same level of labor input N = (what it was at point A) the firm is no longer

N = 54w = 12 and MPN = 2 (MPN = 8 x 7 - 54) SO wgtMPN fire people - if you fire 8 people the MPN will rise to = 10as you fire people you can pay a lower wage - if you layoff 4 people wage falls by one layoff 8 people wage falls by 2 from 12 to 10back at profit max where w = 10 = MPN when N = 46

8

3 PART 2 (40 points total for PART 2)

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

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

Initial conditions in the goods market

Cd = 299 + 50(Y-T) ndash 500rId = 330 ndash 500rG = 500T= 200

e) (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 = 1998 - [299 + 50(1998 - 200) ndash 500r] - 500

S = 300 + 500r

300 + 500r = 330 ndash 500r

r = 03 S = I = 315 Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

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

9

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN THE CONSUMPTION FUNCTION

The new consumption function is Cd = 49 + 50(Y-T) ndash 500r

f) (5 points) What could cause such a change in the consumption function Please give two specific and well supported reasons Be sure to explain your answer

4 POSSIBILITIES

LOWER WEALTH (a)LOWER EXPECTED INCOME (yf)LOWER EXPECTED WEALTH (af)LOWER CONSUMER CONFIDENCE (CC)

g) (10 points) Given these changes ie changes in Y from part 1 and the change in the consumption function 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 = 1518 - [49 + 50(1518 - 200) ndash 500r] - 500

S = 310 + 500r

310 + 500r = 330 ndash 500r

r = 02 S = I = 320

h) (5 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be a specific as possible with regard to the changes in the consumption function and the change in labor supply (please refer to each for full credit)

YES FOR THE MOST PART - THE CONSUMPTION FUNCTION SHIFTED DOWN CONSISTENT WITH LOSSES IN WEALTH ($14 TRILLION WORTH WAS LOST IN THE GREAT RECESSION) - LOWER CC EXPECTED WEALTH EXPECTED INCOME - ALL PERFECTLY CONSISTENT WITH GREAT RECESSION

LABOR SUPPLY - YES IF YOU THINK ABOUT LESS PARTICIPATION SINCE JOB MARKET CONDITIONS WERE SO BAD BUT NO IF YOU THINK OF THE LOSS OF WEALTH THIS WOULD RESULT IN HIGHER LABOR SUPPLY NOT LOWER LABOR SUPPLY AS IN PROBLEM

10

4 (50 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 05(Y-T) ndash 300rw

Id = 430 ndash 200rw

Y = 2300T = 300G =500

China Initial Conditions

CdF = 600 + 5(YF ndash TF) ndash 300rw

IdF = 310 ndash 200rw

YF = 2000TF = 400GF = 300

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

S = 2300 - [400 + 5(2300 - 300) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [600 + 5(2000 - 400) - 300 r ] - 300

S = 300 + 300r

[400 + 300r] - [430 - 200r] + [300 + 300r] - [310 - 200r] = 0

-40 + 1000r = 0 r = 04

11

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

USA

S = 400 + 300(04) = 412I = 430 - 200(04) = 422

NX = -10

CHINA

S = 300 + 300(04) = 312I = 310 - 200(04) = 302

NX = + 10

c) (5 points) 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 in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater than the income we generate Y Absorption in the US is 2310 Y = 2300 Absorption in China is 1990 Y =2000 China is the saver - USA is spending beyond its means

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

15 points for correct and completely labeled diagrams

We now have a change in conditions The Investment function changes for the US and is now

Id = 450 ndash 200rw

12

d) (5 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)

[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0

-60 + 1000r = 0 r = 06

USA

S = 400 + 300(06) = 418I = 450 - 200(06) = 438

NX = -20

CHINA

S = 300 + 300(06) = 318I = 310 - 200(06) = 298

NX = +20

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 Also what happened to investment in both countries and why Again be specific

NO the US has not gone to AA their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10

Investment in the US rose by 16 given the positive shock to the investment function At same r investment would have risen by 20 but r has to go up to finance this investment - when r goes up by 02 4 units of investment are crowded out in the US20 minus 4 = 16

Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US at the same K uc gt MPK China needs to sell machines to get back to profit maximization Since I = K - Kt + dKtwhen K falls so does I

13

10 points for correct and completely labeled graph

2 (50 points total) You own a golf resort and you need to determine how many golf carts 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 golf cart costs 200 rounds of golf (this is your output) and the rate of depreciation is 7 (007)

The real interest rate is 3 (03)

And the expected marginal product of capital is given by MPKf = 275 ndash 5K

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

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

expressed in (Show work)

uc = [(03 + 07) 200] (1 - 20) = 25 rounds of golf

b) (5 points) How many golf carts should you buy to maximize profits Show work

25 = 275 - 5KK = 50

4

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

Now conditions change The following two shocks occur simultaneously

i) the price of golf carts rises to 240 rounds of golf

ii) the expected marginal product of capital changes and is now MPKf = 300 ndash 5K

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

uc = [(03 + 07) 240] (1 - 20) = 30

30 = 300 - 5K K = 54

d) (10 points) Given the two shocks as above explain the intuition underlying the change in the profit maximizing level of carts (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)

K = 50 uc = 30 MPK = 300 - 5(50) = 50 since uc= 30 is LESS than MPK=50 we need to BUY 4 golf carts to get back to profit maximization where uc = MPK = 30 when K=54 - for every cart we buy MPK falls by 5 when we buy 4 MPK falls by 4 x 5 = 20from 50 to 30 = uc

e) (5 points) Suppose that the Federal Reserve had a goal to get the capital stock the number of golf carts purchased to equal 52 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

What is MPK when K = 52 MPK = 300 - 5(52) = 40 so the Fed needs to get the uc = 40 40 = [(r + 07) 240] (1 - 20)[40 x (1 - 20)] 240 - 07 r = 0633

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables) 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 after the two shocks 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)

6

3 PART 1 (40 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 SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

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

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

The initial labor supply curve is given as NS = 14 + 4w

a) (5 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 8 - [14 + 4w]

5w = 50 w = 10 N = 54 Y = 1998

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

(15 points for completely labeled and correct diagrams)

7

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 = 6 + 4w K goes down from 8 to 7

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons Be sure to explain your answer

5 CHOICES 1) HIGHER EXPECTED INCOME2) HIGHER WEALTH3) TIGHTER IMMIGRATION LAWS4) LESS PARTICIPATION5) DEMOGRAPHICS - AGING POPULATION - LESS PEOPLE ENTERING LABOR FORCE

c) (5 points) Given the change in NS and K 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 = 8 x 7 - [6 + 4w]

5w = 50 w = 10 N = 46 Y = 1518

d) (10 points) Explain exactly why the profit maximizing level of labor has changed given the change in NS

and K Be very specific with your answer as in using numbers Begin your answer with At the same level of labor input N = (what it was at point A) the firm is no longer

N = 54w = 12 and MPN = 2 (MPN = 8 x 7 - 54) SO wgtMPN fire people - if you fire 8 people the MPN will rise to = 10as you fire people you can pay a lower wage - if you layoff 4 people wage falls by one layoff 8 people wage falls by 2 from 12 to 10back at profit max where w = 10 = MPN when N = 46

8

3 PART 2 (40 points total for PART 2)

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

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

Initial conditions in the goods market

Cd = 299 + 50(Y-T) ndash 500rId = 330 ndash 500rG = 500T= 200

e) (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 = 1998 - [299 + 50(1998 - 200) ndash 500r] - 500

S = 300 + 500r

300 + 500r = 330 ndash 500r

r = 03 S = I = 315 Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

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

9

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN THE CONSUMPTION FUNCTION

The new consumption function is Cd = 49 + 50(Y-T) ndash 500r

f) (5 points) What could cause such a change in the consumption function Please give two specific and well supported reasons Be sure to explain your answer

4 POSSIBILITIES

LOWER WEALTH (a)LOWER EXPECTED INCOME (yf)LOWER EXPECTED WEALTH (af)LOWER CONSUMER CONFIDENCE (CC)

g) (10 points) Given these changes ie changes in Y from part 1 and the change in the consumption function 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 = 1518 - [49 + 50(1518 - 200) ndash 500r] - 500

S = 310 + 500r

310 + 500r = 330 ndash 500r

r = 02 S = I = 320

h) (5 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be a specific as possible with regard to the changes in the consumption function and the change in labor supply (please refer to each for full credit)

YES FOR THE MOST PART - THE CONSUMPTION FUNCTION SHIFTED DOWN CONSISTENT WITH LOSSES IN WEALTH ($14 TRILLION WORTH WAS LOST IN THE GREAT RECESSION) - LOWER CC EXPECTED WEALTH EXPECTED INCOME - ALL PERFECTLY CONSISTENT WITH GREAT RECESSION

LABOR SUPPLY - YES IF YOU THINK ABOUT LESS PARTICIPATION SINCE JOB MARKET CONDITIONS WERE SO BAD BUT NO IF YOU THINK OF THE LOSS OF WEALTH THIS WOULD RESULT IN HIGHER LABOR SUPPLY NOT LOWER LABOR SUPPLY AS IN PROBLEM

10

4 (50 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 05(Y-T) ndash 300rw

Id = 430 ndash 200rw

Y = 2300T = 300G =500

China Initial Conditions

CdF = 600 + 5(YF ndash TF) ndash 300rw

IdF = 310 ndash 200rw

YF = 2000TF = 400GF = 300

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

S = 2300 - [400 + 5(2300 - 300) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [600 + 5(2000 - 400) - 300 r ] - 300

S = 300 + 300r

[400 + 300r] - [430 - 200r] + [300 + 300r] - [310 - 200r] = 0

-40 + 1000r = 0 r = 04

11

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

USA

S = 400 + 300(04) = 412I = 430 - 200(04) = 422

NX = -10

CHINA

S = 300 + 300(04) = 312I = 310 - 200(04) = 302

NX = + 10

c) (5 points) 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 in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater than the income we generate Y Absorption in the US is 2310 Y = 2300 Absorption in China is 1990 Y =2000 China is the saver - USA is spending beyond its means

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

15 points for correct and completely labeled diagrams

We now have a change in conditions The Investment function changes for the US and is now

Id = 450 ndash 200rw

12

d) (5 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)

[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0

-60 + 1000r = 0 r = 06

USA

S = 400 + 300(06) = 418I = 450 - 200(06) = 438

NX = -20

CHINA

S = 300 + 300(06) = 318I = 310 - 200(06) = 298

NX = +20

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 Also what happened to investment in both countries and why Again be specific

NO the US has not gone to AA their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10

Investment in the US rose by 16 given the positive shock to the investment function At same r investment would have risen by 20 but r has to go up to finance this investment - when r goes up by 02 4 units of investment are crowded out in the US20 minus 4 = 16

Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US at the same K uc gt MPK China needs to sell machines to get back to profit maximization Since I = K - Kt + dKtwhen K falls so does I

13

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

Now conditions change The following two shocks occur simultaneously

i) the price of golf carts rises to 240 rounds of golf

ii) the expected marginal product of capital changes and is now MPKf = 300 ndash 5K

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

uc = [(03 + 07) 240] (1 - 20) = 30

30 = 300 - 5K K = 54

d) (10 points) Given the two shocks as above explain the intuition underlying the change in the profit maximizing level of carts (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)

K = 50 uc = 30 MPK = 300 - 5(50) = 50 since uc= 30 is LESS than MPK=50 we need to BUY 4 golf carts to get back to profit maximization where uc = MPK = 30 when K=54 - for every cart we buy MPK falls by 5 when we buy 4 MPK falls by 4 x 5 = 20from 50 to 30 = uc

e) (5 points) Suppose that the Federal Reserve had a goal to get the capital stock the number of golf carts purchased to equal 52 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

What is MPK when K = 52 MPK = 300 - 5(52) = 40 so the Fed needs to get the uc = 40 40 = [(r + 07) 240] (1 - 20)[40 x (1 - 20)] 240 - 07 r = 0633

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables) 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 after the two shocks 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)

6

3 PART 1 (40 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 SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

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

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

The initial labor supply curve is given as NS = 14 + 4w

a) (5 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 8 - [14 + 4w]

5w = 50 w = 10 N = 54 Y = 1998

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

(15 points for completely labeled and correct diagrams)

7

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 = 6 + 4w K goes down from 8 to 7

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons Be sure to explain your answer

5 CHOICES 1) HIGHER EXPECTED INCOME2) HIGHER WEALTH3) TIGHTER IMMIGRATION LAWS4) LESS PARTICIPATION5) DEMOGRAPHICS - AGING POPULATION - LESS PEOPLE ENTERING LABOR FORCE

c) (5 points) Given the change in NS and K 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 = 8 x 7 - [6 + 4w]

5w = 50 w = 10 N = 46 Y = 1518

d) (10 points) Explain exactly why the profit maximizing level of labor has changed given the change in NS

and K Be very specific with your answer as in using numbers Begin your answer with At the same level of labor input N = (what it was at point A) the firm is no longer

N = 54w = 12 and MPN = 2 (MPN = 8 x 7 - 54) SO wgtMPN fire people - if you fire 8 people the MPN will rise to = 10as you fire people you can pay a lower wage - if you layoff 4 people wage falls by one layoff 8 people wage falls by 2 from 12 to 10back at profit max where w = 10 = MPN when N = 46

8

3 PART 2 (40 points total for PART 2)

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

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

Initial conditions in the goods market

Cd = 299 + 50(Y-T) ndash 500rId = 330 ndash 500rG = 500T= 200

e) (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 = 1998 - [299 + 50(1998 - 200) ndash 500r] - 500

S = 300 + 500r

300 + 500r = 330 ndash 500r

r = 03 S = I = 315 Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

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

9

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN THE CONSUMPTION FUNCTION

The new consumption function is Cd = 49 + 50(Y-T) ndash 500r

f) (5 points) What could cause such a change in the consumption function Please give two specific and well supported reasons Be sure to explain your answer

4 POSSIBILITIES

LOWER WEALTH (a)LOWER EXPECTED INCOME (yf)LOWER EXPECTED WEALTH (af)LOWER CONSUMER CONFIDENCE (CC)

g) (10 points) Given these changes ie changes in Y from part 1 and the change in the consumption function 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 = 1518 - [49 + 50(1518 - 200) ndash 500r] - 500

S = 310 + 500r

310 + 500r = 330 ndash 500r

r = 02 S = I = 320

h) (5 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be a specific as possible with regard to the changes in the consumption function and the change in labor supply (please refer to each for full credit)

YES FOR THE MOST PART - THE CONSUMPTION FUNCTION SHIFTED DOWN CONSISTENT WITH LOSSES IN WEALTH ($14 TRILLION WORTH WAS LOST IN THE GREAT RECESSION) - LOWER CC EXPECTED WEALTH EXPECTED INCOME - ALL PERFECTLY CONSISTENT WITH GREAT RECESSION

LABOR SUPPLY - YES IF YOU THINK ABOUT LESS PARTICIPATION SINCE JOB MARKET CONDITIONS WERE SO BAD BUT NO IF YOU THINK OF THE LOSS OF WEALTH THIS WOULD RESULT IN HIGHER LABOR SUPPLY NOT LOWER LABOR SUPPLY AS IN PROBLEM

10

4 (50 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 05(Y-T) ndash 300rw

Id = 430 ndash 200rw

Y = 2300T = 300G =500

China Initial Conditions

CdF = 600 + 5(YF ndash TF) ndash 300rw

IdF = 310 ndash 200rw

YF = 2000TF = 400GF = 300

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

S = 2300 - [400 + 5(2300 - 300) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [600 + 5(2000 - 400) - 300 r ] - 300

S = 300 + 300r

[400 + 300r] - [430 - 200r] + [300 + 300r] - [310 - 200r] = 0

-40 + 1000r = 0 r = 04

11

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

USA

S = 400 + 300(04) = 412I = 430 - 200(04) = 422

NX = -10

CHINA

S = 300 + 300(04) = 312I = 310 - 200(04) = 302

NX = + 10

c) (5 points) 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 in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater than the income we generate Y Absorption in the US is 2310 Y = 2300 Absorption in China is 1990 Y =2000 China is the saver - USA is spending beyond its means

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

15 points for correct and completely labeled diagrams

We now have a change in conditions The Investment function changes for the US and is now

Id = 450 ndash 200rw

12

d) (5 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)

[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0

-60 + 1000r = 0 r = 06

USA

S = 400 + 300(06) = 418I = 450 - 200(06) = 438

NX = -20

CHINA

S = 300 + 300(06) = 318I = 310 - 200(06) = 298

NX = +20

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 Also what happened to investment in both countries and why Again be specific

NO the US has not gone to AA their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10

Investment in the US rose by 16 given the positive shock to the investment function At same r investment would have risen by 20 but r has to go up to finance this investment - when r goes up by 02 4 units of investment are crowded out in the US20 minus 4 = 16

Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US at the same K uc gt MPK China needs to sell machines to get back to profit maximization Since I = K - Kt + dKtwhen K falls so does I

13

What is MPK when K = 52 MPK = 300 - 5(52) = 40 so the Fed needs to get the uc = 40 40 = [(r + 07) 240] (1 - 20)[40 x (1 - 20)] 240 - 07 r = 0633

f) Finally draw a desired investment diagram (completely labeled with the relevant shift variables) 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 after the two shocks 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)

6

3 PART 1 (40 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 SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

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

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

The initial labor supply curve is given as NS = 14 + 4w

a) (5 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 8 - [14 + 4w]

5w = 50 w = 10 N = 54 Y = 1998

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

(15 points for completely labeled and correct diagrams)

7

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 = 6 + 4w K goes down from 8 to 7

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons Be sure to explain your answer

5 CHOICES 1) HIGHER EXPECTED INCOME2) HIGHER WEALTH3) TIGHTER IMMIGRATION LAWS4) LESS PARTICIPATION5) DEMOGRAPHICS - AGING POPULATION - LESS PEOPLE ENTERING LABOR FORCE

c) (5 points) Given the change in NS and K 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 = 8 x 7 - [6 + 4w]

5w = 50 w = 10 N = 46 Y = 1518

d) (10 points) Explain exactly why the profit maximizing level of labor has changed given the change in NS

and K Be very specific with your answer as in using numbers Begin your answer with At the same level of labor input N = (what it was at point A) the firm is no longer

N = 54w = 12 and MPN = 2 (MPN = 8 x 7 - 54) SO wgtMPN fire people - if you fire 8 people the MPN will rise to = 10as you fire people you can pay a lower wage - if you layoff 4 people wage falls by one layoff 8 people wage falls by 2 from 12 to 10back at profit max where w = 10 = MPN when N = 46

8

3 PART 2 (40 points total for PART 2)

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

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

Initial conditions in the goods market

Cd = 299 + 50(Y-T) ndash 500rId = 330 ndash 500rG = 500T= 200

e) (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 = 1998 - [299 + 50(1998 - 200) ndash 500r] - 500

S = 300 + 500r

300 + 500r = 330 ndash 500r

r = 03 S = I = 315 Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

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

9

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN THE CONSUMPTION FUNCTION

The new consumption function is Cd = 49 + 50(Y-T) ndash 500r

f) (5 points) What could cause such a change in the consumption function Please give two specific and well supported reasons Be sure to explain your answer

4 POSSIBILITIES

LOWER WEALTH (a)LOWER EXPECTED INCOME (yf)LOWER EXPECTED WEALTH (af)LOWER CONSUMER CONFIDENCE (CC)

g) (10 points) Given these changes ie changes in Y from part 1 and the change in the consumption function 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 = 1518 - [49 + 50(1518 - 200) ndash 500r] - 500

S = 310 + 500r

310 + 500r = 330 ndash 500r

r = 02 S = I = 320

h) (5 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be a specific as possible with regard to the changes in the consumption function and the change in labor supply (please refer to each for full credit)

YES FOR THE MOST PART - THE CONSUMPTION FUNCTION SHIFTED DOWN CONSISTENT WITH LOSSES IN WEALTH ($14 TRILLION WORTH WAS LOST IN THE GREAT RECESSION) - LOWER CC EXPECTED WEALTH EXPECTED INCOME - ALL PERFECTLY CONSISTENT WITH GREAT RECESSION

LABOR SUPPLY - YES IF YOU THINK ABOUT LESS PARTICIPATION SINCE JOB MARKET CONDITIONS WERE SO BAD BUT NO IF YOU THINK OF THE LOSS OF WEALTH THIS WOULD RESULT IN HIGHER LABOR SUPPLY NOT LOWER LABOR SUPPLY AS IN PROBLEM

10

4 (50 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 05(Y-T) ndash 300rw

Id = 430 ndash 200rw

Y = 2300T = 300G =500

China Initial Conditions

CdF = 600 + 5(YF ndash TF) ndash 300rw

IdF = 310 ndash 200rw

YF = 2000TF = 400GF = 300

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

S = 2300 - [400 + 5(2300 - 300) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [600 + 5(2000 - 400) - 300 r ] - 300

S = 300 + 300r

[400 + 300r] - [430 - 200r] + [300 + 300r] - [310 - 200r] = 0

-40 + 1000r = 0 r = 04

11

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

USA

S = 400 + 300(04) = 412I = 430 - 200(04) = 422

NX = -10

CHINA

S = 300 + 300(04) = 312I = 310 - 200(04) = 302

NX = + 10

c) (5 points) 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 in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater than the income we generate Y Absorption in the US is 2310 Y = 2300 Absorption in China is 1990 Y =2000 China is the saver - USA is spending beyond its means

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

15 points for correct and completely labeled diagrams

We now have a change in conditions The Investment function changes for the US and is now

Id = 450 ndash 200rw

12

d) (5 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)

[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0

-60 + 1000r = 0 r = 06

USA

S = 400 + 300(06) = 418I = 450 - 200(06) = 438

NX = -20

CHINA

S = 300 + 300(06) = 318I = 310 - 200(06) = 298

NX = +20

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 Also what happened to investment in both countries and why Again be specific

NO the US has not gone to AA their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10

Investment in the US rose by 16 given the positive shock to the investment function At same r investment would have risen by 20 but r has to go up to finance this investment - when r goes up by 02 4 units of investment are crowded out in the US20 minus 4 = 16

Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US at the same K uc gt MPK China needs to sell machines to get back to profit maximization Since I = K - Kt + dKtwhen K falls so does I

13

3 PART 1 (40 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 SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS

The following equations characterize a countryrsquos closed economy

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

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

The initial labor supply curve is given as NS = 14 + 4w

a) (5 points) Find the equilibrium levels of the real wage employment and output (show work)

w = 8 x 8 - [14 + 4w]

5w = 50 w = 10 N = 54 Y = 1998

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

(15 points for completely labeled and correct diagrams)

7

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 = 6 + 4w K goes down from 8 to 7

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons Be sure to explain your answer

5 CHOICES 1) HIGHER EXPECTED INCOME2) HIGHER WEALTH3) TIGHTER IMMIGRATION LAWS4) LESS PARTICIPATION5) DEMOGRAPHICS - AGING POPULATION - LESS PEOPLE ENTERING LABOR FORCE

c) (5 points) Given the change in NS and K 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 = 8 x 7 - [6 + 4w]

5w = 50 w = 10 N = 46 Y = 1518

d) (10 points) Explain exactly why the profit maximizing level of labor has changed given the change in NS

and K Be very specific with your answer as in using numbers Begin your answer with At the same level of labor input N = (what it was at point A) the firm is no longer

N = 54w = 12 and MPN = 2 (MPN = 8 x 7 - 54) SO wgtMPN fire people - if you fire 8 people the MPN will rise to = 10as you fire people you can pay a lower wage - if you layoff 4 people wage falls by one layoff 8 people wage falls by 2 from 12 to 10back at profit max where w = 10 = MPN when N = 46

8

3 PART 2 (40 points total for PART 2)

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

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

Initial conditions in the goods market

Cd = 299 + 50(Y-T) ndash 500rId = 330 ndash 500rG = 500T= 200

e) (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 = 1998 - [299 + 50(1998 - 200) ndash 500r] - 500

S = 300 + 500r

300 + 500r = 330 ndash 500r

r = 03 S = I = 315 Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

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

9

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN THE CONSUMPTION FUNCTION

The new consumption function is Cd = 49 + 50(Y-T) ndash 500r

f) (5 points) What could cause such a change in the consumption function Please give two specific and well supported reasons Be sure to explain your answer

4 POSSIBILITIES

LOWER WEALTH (a)LOWER EXPECTED INCOME (yf)LOWER EXPECTED WEALTH (af)LOWER CONSUMER CONFIDENCE (CC)

g) (10 points) Given these changes ie changes in Y from part 1 and the change in the consumption function 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 = 1518 - [49 + 50(1518 - 200) ndash 500r] - 500

S = 310 + 500r

310 + 500r = 330 ndash 500r

r = 02 S = I = 320

h) (5 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be a specific as possible with regard to the changes in the consumption function and the change in labor supply (please refer to each for full credit)

YES FOR THE MOST PART - THE CONSUMPTION FUNCTION SHIFTED DOWN CONSISTENT WITH LOSSES IN WEALTH ($14 TRILLION WORTH WAS LOST IN THE GREAT RECESSION) - LOWER CC EXPECTED WEALTH EXPECTED INCOME - ALL PERFECTLY CONSISTENT WITH GREAT RECESSION

LABOR SUPPLY - YES IF YOU THINK ABOUT LESS PARTICIPATION SINCE JOB MARKET CONDITIONS WERE SO BAD BUT NO IF YOU THINK OF THE LOSS OF WEALTH THIS WOULD RESULT IN HIGHER LABOR SUPPLY NOT LOWER LABOR SUPPLY AS IN PROBLEM

10

4 (50 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 05(Y-T) ndash 300rw

Id = 430 ndash 200rw

Y = 2300T = 300G =500

China Initial Conditions

CdF = 600 + 5(YF ndash TF) ndash 300rw

IdF = 310 ndash 200rw

YF = 2000TF = 400GF = 300

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

S = 2300 - [400 + 5(2300 - 300) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [600 + 5(2000 - 400) - 300 r ] - 300

S = 300 + 300r

[400 + 300r] - [430 - 200r] + [300 + 300r] - [310 - 200r] = 0

-40 + 1000r = 0 r = 04

11

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

USA

S = 400 + 300(04) = 412I = 430 - 200(04) = 422

NX = -10

CHINA

S = 300 + 300(04) = 312I = 310 - 200(04) = 302

NX = + 10

c) (5 points) 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 in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater than the income we generate Y Absorption in the US is 2310 Y = 2300 Absorption in China is 1990 Y =2000 China is the saver - USA is spending beyond its means

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

15 points for correct and completely labeled diagrams

We now have a change in conditions The Investment function changes for the US and is now

Id = 450 ndash 200rw

12

d) (5 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)

[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0

-60 + 1000r = 0 r = 06

USA

S = 400 + 300(06) = 418I = 450 - 200(06) = 438

NX = -20

CHINA

S = 300 + 300(06) = 318I = 310 - 200(06) = 298

NX = +20

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 Also what happened to investment in both countries and why Again be specific

NO the US has not gone to AA their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10

Investment in the US rose by 16 given the positive shock to the investment function At same r investment would have risen by 20 but r has to go up to finance this investment - when r goes up by 02 4 units of investment are crowded out in the US20 minus 4 = 16

Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US at the same K uc gt MPK China needs to sell machines to get back to profit maximization Since I = K - Kt + dKtwhen K falls so does I

13

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 = 6 + 4w K goes down from 8 to 7

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons Be sure to explain your answer

5 CHOICES 1) HIGHER EXPECTED INCOME2) HIGHER WEALTH3) TIGHTER IMMIGRATION LAWS4) LESS PARTICIPATION5) DEMOGRAPHICS - AGING POPULATION - LESS PEOPLE ENTERING LABOR FORCE

c) (5 points) Given the change in NS and K 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 = 8 x 7 - [6 + 4w]

5w = 50 w = 10 N = 46 Y = 1518

d) (10 points) Explain exactly why the profit maximizing level of labor has changed given the change in NS

and K Be very specific with your answer as in using numbers Begin your answer with At the same level of labor input N = (what it was at point A) the firm is no longer

N = 54w = 12 and MPN = 2 (MPN = 8 x 7 - 54) SO wgtMPN fire people - if you fire 8 people the MPN will rise to = 10as you fire people you can pay a lower wage - if you layoff 4 people wage falls by one layoff 8 people wage falls by 2 from 12 to 10back at profit max where w = 10 = MPN when N = 46

8

3 PART 2 (40 points total for PART 2)

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

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

Initial conditions in the goods market

Cd = 299 + 50(Y-T) ndash 500rId = 330 ndash 500rG = 500T= 200

e) (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 = 1998 - [299 + 50(1998 - 200) ndash 500r] - 500

S = 300 + 500r

300 + 500r = 330 ndash 500r

r = 03 S = I = 315 Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

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

9

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN THE CONSUMPTION FUNCTION

The new consumption function is Cd = 49 + 50(Y-T) ndash 500r

f) (5 points) What could cause such a change in the consumption function Please give two specific and well supported reasons Be sure to explain your answer

4 POSSIBILITIES

LOWER WEALTH (a)LOWER EXPECTED INCOME (yf)LOWER EXPECTED WEALTH (af)LOWER CONSUMER CONFIDENCE (CC)

g) (10 points) Given these changes ie changes in Y from part 1 and the change in the consumption function 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 = 1518 - [49 + 50(1518 - 200) ndash 500r] - 500

S = 310 + 500r

310 + 500r = 330 ndash 500r

r = 02 S = I = 320

h) (5 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be a specific as possible with regard to the changes in the consumption function and the change in labor supply (please refer to each for full credit)

YES FOR THE MOST PART - THE CONSUMPTION FUNCTION SHIFTED DOWN CONSISTENT WITH LOSSES IN WEALTH ($14 TRILLION WORTH WAS LOST IN THE GREAT RECESSION) - LOWER CC EXPECTED WEALTH EXPECTED INCOME - ALL PERFECTLY CONSISTENT WITH GREAT RECESSION

LABOR SUPPLY - YES IF YOU THINK ABOUT LESS PARTICIPATION SINCE JOB MARKET CONDITIONS WERE SO BAD BUT NO IF YOU THINK OF THE LOSS OF WEALTH THIS WOULD RESULT IN HIGHER LABOR SUPPLY NOT LOWER LABOR SUPPLY AS IN PROBLEM

10

4 (50 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 05(Y-T) ndash 300rw

Id = 430 ndash 200rw

Y = 2300T = 300G =500

China Initial Conditions

CdF = 600 + 5(YF ndash TF) ndash 300rw

IdF = 310 ndash 200rw

YF = 2000TF = 400GF = 300

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

S = 2300 - [400 + 5(2300 - 300) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [600 + 5(2000 - 400) - 300 r ] - 300

S = 300 + 300r

[400 + 300r] - [430 - 200r] + [300 + 300r] - [310 - 200r] = 0

-40 + 1000r = 0 r = 04

11

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

USA

S = 400 + 300(04) = 412I = 430 - 200(04) = 422

NX = -10

CHINA

S = 300 + 300(04) = 312I = 310 - 200(04) = 302

NX = + 10

c) (5 points) 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 in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater than the income we generate Y Absorption in the US is 2310 Y = 2300 Absorption in China is 1990 Y =2000 China is the saver - USA is spending beyond its means

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

15 points for correct and completely labeled diagrams

We now have a change in conditions The Investment function changes for the US and is now

Id = 450 ndash 200rw

12

d) (5 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)

[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0

-60 + 1000r = 0 r = 06

USA

S = 400 + 300(06) = 418I = 450 - 200(06) = 438

NX = -20

CHINA

S = 300 + 300(06) = 318I = 310 - 200(06) = 298

NX = +20

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 Also what happened to investment in both countries and why Again be specific

NO the US has not gone to AA their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10

Investment in the US rose by 16 given the positive shock to the investment function At same r investment would have risen by 20 but r has to go up to finance this investment - when r goes up by 02 4 units of investment are crowded out in the US20 minus 4 = 16

Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US at the same K uc gt MPK China needs to sell machines to get back to profit maximization Since I = K - Kt + dKtwhen K falls so does I

13

3 PART 2 (40 points total for PART 2)

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

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

Initial conditions in the goods market

Cd = 299 + 50(Y-T) ndash 500rId = 330 ndash 500rG = 500T= 200

e) (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 = 1998 - [299 + 50(1998 - 200) ndash 500r] - 500

S = 300 + 500r

300 + 500r = 330 ndash 500r

r = 03 S = I = 315 Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A

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

9

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN THE CONSUMPTION FUNCTION

The new consumption function is Cd = 49 + 50(Y-T) ndash 500r

f) (5 points) What could cause such a change in the consumption function Please give two specific and well supported reasons Be sure to explain your answer

4 POSSIBILITIES

LOWER WEALTH (a)LOWER EXPECTED INCOME (yf)LOWER EXPECTED WEALTH (af)LOWER CONSUMER CONFIDENCE (CC)

g) (10 points) Given these changes ie changes in Y from part 1 and the change in the consumption function 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 = 1518 - [49 + 50(1518 - 200) ndash 500r] - 500

S = 310 + 500r

310 + 500r = 330 ndash 500r

r = 02 S = I = 320

h) (5 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be a specific as possible with regard to the changes in the consumption function and the change in labor supply (please refer to each for full credit)

YES FOR THE MOST PART - THE CONSUMPTION FUNCTION SHIFTED DOWN CONSISTENT WITH LOSSES IN WEALTH ($14 TRILLION WORTH WAS LOST IN THE GREAT RECESSION) - LOWER CC EXPECTED WEALTH EXPECTED INCOME - ALL PERFECTLY CONSISTENT WITH GREAT RECESSION

LABOR SUPPLY - YES IF YOU THINK ABOUT LESS PARTICIPATION SINCE JOB MARKET CONDITIONS WERE SO BAD BUT NO IF YOU THINK OF THE LOSS OF WEALTH THIS WOULD RESULT IN HIGHER LABOR SUPPLY NOT LOWER LABOR SUPPLY AS IN PROBLEM

10

4 (50 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 05(Y-T) ndash 300rw

Id = 430 ndash 200rw

Y = 2300T = 300G =500

China Initial Conditions

CdF = 600 + 5(YF ndash TF) ndash 300rw

IdF = 310 ndash 200rw

YF = 2000TF = 400GF = 300

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

S = 2300 - [400 + 5(2300 - 300) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [600 + 5(2000 - 400) - 300 r ] - 300

S = 300 + 300r

[400 + 300r] - [430 - 200r] + [300 + 300r] - [310 - 200r] = 0

-40 + 1000r = 0 r = 04

11

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

USA

S = 400 + 300(04) = 412I = 430 - 200(04) = 422

NX = -10

CHINA

S = 300 + 300(04) = 312I = 310 - 200(04) = 302

NX = + 10

c) (5 points) 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 in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater than the income we generate Y Absorption in the US is 2310 Y = 2300 Absorption in China is 1990 Y =2000 China is the saver - USA is spending beyond its means

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

15 points for correct and completely labeled diagrams

We now have a change in conditions The Investment function changes for the US and is now

Id = 450 ndash 200rw

12

d) (5 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)

[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0

-60 + 1000r = 0 r = 06

USA

S = 400 + 300(06) = 418I = 450 - 200(06) = 438

NX = -20

CHINA

S = 300 + 300(06) = 318I = 310 - 200(06) = 298

NX = +20

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 Also what happened to investment in both countries and why Again be specific

NO the US has not gone to AA their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10

Investment in the US rose by 16 given the positive shock to the investment function At same r investment would have risen by 20 but r has to go up to finance this investment - when r goes up by 02 4 units of investment are crowded out in the US20 minus 4 = 16

Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US at the same K uc gt MPK China needs to sell machines to get back to profit maximization Since I = K - Kt + dKtwhen K falls so does I

13

NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN THE CONSUMPTION FUNCTION

The new consumption function is Cd = 49 + 50(Y-T) ndash 500r

f) (5 points) What could cause such a change in the consumption function Please give two specific and well supported reasons Be sure to explain your answer

4 POSSIBILITIES

LOWER WEALTH (a)LOWER EXPECTED INCOME (yf)LOWER EXPECTED WEALTH (af)LOWER CONSUMER CONFIDENCE (CC)

g) (10 points) Given these changes ie changes in Y from part 1 and the change in the consumption function 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 = 1518 - [49 + 50(1518 - 200) ndash 500r] - 500

S = 310 + 500r

310 + 500r = 330 ndash 500r

r = 02 S = I = 320

h) (5 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be a specific as possible with regard to the changes in the consumption function and the change in labor supply (please refer to each for full credit)

YES FOR THE MOST PART - THE CONSUMPTION FUNCTION SHIFTED DOWN CONSISTENT WITH LOSSES IN WEALTH ($14 TRILLION WORTH WAS LOST IN THE GREAT RECESSION) - LOWER CC EXPECTED WEALTH EXPECTED INCOME - ALL PERFECTLY CONSISTENT WITH GREAT RECESSION

LABOR SUPPLY - YES IF YOU THINK ABOUT LESS PARTICIPATION SINCE JOB MARKET CONDITIONS WERE SO BAD BUT NO IF YOU THINK OF THE LOSS OF WEALTH THIS WOULD RESULT IN HIGHER LABOR SUPPLY NOT LOWER LABOR SUPPLY AS IN PROBLEM

10

4 (50 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 05(Y-T) ndash 300rw

Id = 430 ndash 200rw

Y = 2300T = 300G =500

China Initial Conditions

CdF = 600 + 5(YF ndash TF) ndash 300rw

IdF = 310 ndash 200rw

YF = 2000TF = 400GF = 300

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

S = 2300 - [400 + 5(2300 - 300) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [600 + 5(2000 - 400) - 300 r ] - 300

S = 300 + 300r

[400 + 300r] - [430 - 200r] + [300 + 300r] - [310 - 200r] = 0

-40 + 1000r = 0 r = 04

11

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

USA

S = 400 + 300(04) = 412I = 430 - 200(04) = 422

NX = -10

CHINA

S = 300 + 300(04) = 312I = 310 - 200(04) = 302

NX = + 10

c) (5 points) 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 in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater than the income we generate Y Absorption in the US is 2310 Y = 2300 Absorption in China is 1990 Y =2000 China is the saver - USA is spending beyond its means

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

15 points for correct and completely labeled diagrams

We now have a change in conditions The Investment function changes for the US and is now

Id = 450 ndash 200rw

12

d) (5 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)

[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0

-60 + 1000r = 0 r = 06

USA

S = 400 + 300(06) = 418I = 450 - 200(06) = 438

NX = -20

CHINA

S = 300 + 300(06) = 318I = 310 - 200(06) = 298

NX = +20

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 Also what happened to investment in both countries and why Again be specific

NO the US has not gone to AA their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10

Investment in the US rose by 16 given the positive shock to the investment function At same r investment would have risen by 20 but r has to go up to finance this investment - when r goes up by 02 4 units of investment are crowded out in the US20 minus 4 = 16

Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US at the same K uc gt MPK China needs to sell machines to get back to profit maximization Since I = K - Kt + dKtwhen K falls so does I

13

4 (50 points total) We assume that the world consists of two large open economies USA and China

USA Initial Conditions

Cd = 400 + 05(Y-T) ndash 300rw

Id = 430 ndash 200rw

Y = 2300T = 300G =500

China Initial Conditions

CdF = 600 + 5(YF ndash TF) ndash 300rw

IdF = 310 ndash 200rw

YF = 2000TF = 400GF = 300

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

S = 2300 - [400 + 5(2300 - 300) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [600 + 5(2000 - 400) - 300 r ] - 300

S = 300 + 300r

[400 + 300r] - [430 - 200r] + [300 + 300r] - [310 - 200r] = 0

-40 + 1000r = 0 r = 04

11

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

USA

S = 400 + 300(04) = 412I = 430 - 200(04) = 422

NX = -10

CHINA

S = 300 + 300(04) = 312I = 310 - 200(04) = 302

NX = + 10

c) (5 points) 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 in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater than the income we generate Y Absorption in the US is 2310 Y = 2300 Absorption in China is 1990 Y =2000 China is the saver - USA is spending beyond its means

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

15 points for correct and completely labeled diagrams

We now have a change in conditions The Investment function changes for the US and is now

Id = 450 ndash 200rw

12

d) (5 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)

[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0

-60 + 1000r = 0 r = 06

USA

S = 400 + 300(06) = 418I = 450 - 200(06) = 438

NX = -20

CHINA

S = 300 + 300(06) = 318I = 310 - 200(06) = 298

NX = +20

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 Also what happened to investment in both countries and why Again be specific

NO the US has not gone to AA their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10

Investment in the US rose by 16 given the positive shock to the investment function At same r investment would have risen by 20 but r has to go up to finance this investment - when r goes up by 02 4 units of investment are crowded out in the US20 minus 4 = 16

Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US at the same K uc gt MPK China needs to sell machines to get back to profit maximization Since I = K - Kt + dKtwhen K falls so does I

13

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

USA

S = 400 + 300(04) = 412I = 430 - 200(04) = 422

NX = -10

CHINA

S = 300 + 300(04) = 312I = 310 - 200(04) = 302

NX = + 10

c) (5 points) 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 in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater than the income we generate Y Absorption in the US is 2310 Y = 2300 Absorption in China is 1990 Y =2000 China is the saver - USA is spending beyond its means

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

15 points for correct and completely labeled diagrams

We now have a change in conditions The Investment function changes for the US and is now

Id = 450 ndash 200rw

12

d) (5 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)

[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0

-60 + 1000r = 0 r = 06

USA

S = 400 + 300(06) = 418I = 450 - 200(06) = 438

NX = -20

CHINA

S = 300 + 300(06) = 318I = 310 - 200(06) = 298

NX = +20

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 Also what happened to investment in both countries and why Again be specific

NO the US has not gone to AA their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10

Investment in the US rose by 16 given the positive shock to the investment function At same r investment would have risen by 20 but r has to go up to finance this investment - when r goes up by 02 4 units of investment are crowded out in the US20 minus 4 = 16

Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US at the same K uc gt MPK China needs to sell machines to get back to profit maximization Since I = K - Kt + dKtwhen K falls so does I

13

d) (5 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)

[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0

-60 + 1000r = 0 r = 06

USA

S = 400 + 300(06) = 418I = 450 - 200(06) = 438

NX = -20

CHINA

S = 300 + 300(06) = 318I = 310 - 200(06) = 298

NX = +20

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 Also what happened to investment in both countries and why Again be specific

NO the US has not gone to AA their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10

Investment in the US rose by 16 given the positive shock to the investment function At same r investment would have risen by 20 but r has to go up to finance this investment - when r goes up by 02 4 units of investment are crowded out in the US20 minus 4 = 16

Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US at the same K uc gt MPK China needs to sell machines to get back to profit maximization Since I = K - Kt + dKtwhen K falls so does I

13