Name ___________ KEY _________________ Last 4 (PSU ID) __________

Section Please Check

Section 001 - 112 Chambers 905 - 955 am ______________

Section 002 - 022 BBH Building 1115 am - 1205 pm ______________

EXAM 1 - FALL 2018

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 = 305

Test time = 120 minutes

Approximately one minute for every two points

To help with time management if spreading time evenly

Question 1 = 60 points24 minutes

Question 2 = 75 points 30 minutes

Question 3 = 50 points 20 minutes

Question 4 = 60 points 24 minutes

Question 5 = 60 points 24 minutes

1

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

1 (60 points total) Suppose we have Dagwood who has a current income of $100K 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))(100 + 0) + 200 + 0] (2 + (05))

C = 14878

C = [(1 + (05))(300 + 0) + 200 + 0] (2 + (05))

C = 25122

C = [(1 + (-05))(300 + 0) + 200 + 0] (2 + (-05))

C = 24872

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

NLNB) Use space above

2

b)(5 points) Dagwood works in an industry that is booming and he decides to start working overtime so that his current income increases to $300K This is the only change Resolve for Dagwoods optimal consumption bundle and label as point CB

c) (5 points) Jerome Powell 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 CC

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 NO Since Dagwood is a saver he cares most about his FV of present resources since he is financing future consumption with current (present) resources When r goes down FV = (1+r)(y + a) falls and therefore Dagwood is poorer and should spread the pain and consume less in both periods - this is the income effect With numbers FV = (1 + (05)) 300 = 315 vs FV = (1 + (-05)) 300 = 285

The substitution effect works in the opposite 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 10 points for graph 5 points for showing work) In the space below draw two savings functions (on the same diagram) for Dagwood The first savings function is for the initial conditions before Dagwood starts to work overtime (when his current income = $100K) Label as point A where r = 05 and point B when r = -05

Now draw another savings function representing the conditions after Dagwood started to work overtime 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

USE THE NEXT PAGE FOR YOUR DIAGRAM

A - 4878 = 100 - 14878B - 5179 = 100 - 15179

work for point B C = [(1 + (-05))(100 + 0) + 200 + 0] (2 + (-05))C = 15179

C 4878 = 300 - 25122D 5128 = 300 - 24872

10 points for correct and completely labeled graph

f)(10 points) How would your answer change for part d) above if Dagwood never decided to work overtime and the Fed did the same as in lowering rates from 05 to a negative 05 Explain the intuition and use numbers (be specific)

The Fed policy would have worked since Dag started out as a borrower (y = 100 C = 14878)He was financing current consumption with futures resources and therefore cares most about the PV of future resources which rises with a fall in r 100(1+05) = 9224 VS 100(1 + (-05)) = 10417So Dag is richer and will spread the gain C will rise from 14878 to 15179

4

2) (75 points) The Graphic below is from the WSJ 1022018 that shows how the neutral funds rate has drifted lower through time Assume the Feds inflation target is 2 throughout this question

a)(10 points) Explain why the neutral federal funds rate has drifted lower through time (point A to point B)

r or the natural real rate of interest when the economy is at its dual mandate has fallen from 2 to 1 due to 1) an increase in Savings due to baby boomers getting close to retirement - when expected income falls savings goes up and 2) a fall in productivity growth has lowered the investment opportunities in the US recall technology gains are being used to increase the value of your leisure time via apps and not increasing output per hour In terms of the neutral funds rate

iff = r + π

4 = 2 + 2 (old point A)

3 = 1 + 2 (new point B)

5

In the space below draw a S = I graph consistent with your answer in part a) Be sure to label graph completely using actual numbers (on the vertical axis) for point A and for point B (Note you will be adding another point C to your diagram)

30 points for correct and completely labeled graph

b)(5 points) What has happened to the natural real rate of interest Be specific

it went from 2 to 1

c)(10 points) Why is this phenomenon such a big deal In your answer mention what the Fed did to fight the most previous 3 recessions and compare to what they could do if they get to the new neutral federal funds rate (point B above) and a recession begins

The Fed lowered the federal funds rate by an average of 597 to fight the most previous 3 recessions - if the neutral funds rate stays at 3 the fed will not have enough ammunition (bullets = 3) to fight the next recession this is a BIG DEAL

We now go back in time to the new economy years Below is an excerpt from The Taylor Rule A Guidepost for Monetary Policy Note you dont need to know what the Taylor Rule is we are just focusing on the implications of the new economy on the neutral federal funds rate and the neutral real rate of interest

For example the funds rate was consistently above the Taylor rule target through the latter half of the 1990s Yet the rulersquos proponents argue that productivity growth increased in 1995 and this was translating into faster economic growth Faster economic growth they argue manifests itself in higher real rates of interest and thus a higher natural real interest rate While Taylor treated this factor as a constant policy-makers who believed higher productivity was here to stay (because computers had created a ldquoNew Economyrdquo) would have adjusted the Taylor rule up accordingly

6

Faster economic growth they argue manifests itself in higher real rates of interest and thus a higher natural real interest rate

Suppose we had information on the policy makers dot plot diagram from the mid 1990s and that they estimate the neutral federal funds rate to be 55

d)(10 points) Why would we expect the neutral federal funds rate to be much higher back in the mid 1990s relative to today We are comparing 3 today to 55 back in the mid 1990s

Baby boomers were younger back then so we lose the increase in savings effect due to being closer to retirement Wealth in the stock market was large given the surge in productivity and the resulting higher profits - this increase in wealth will DECREASE savings as shown Also the surge in productivity growth due to increases in total factor productivity(A) (internet) increases investment at any given real rate of interest along with very high animal spirits (the future was so bright you have to wear shades) increases investment

Add as point C the conditions for the new economy on your diagram above consistent with your explanation from part d)

From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate

The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth

Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

e)(10 points) Explain why the Fed might increase their estimate of the neutral federal funds rate from 3 to somewhere above 3 and is this good news for policy makers and the economy

The recent corporate tax cut along with very high animal spirits might increase investment and along with it raise the natural real rate and the neutral funds rate Also record breaking stock market is increasing wealth very high CC and the cut in income taxes (T) all have a negative effect on Savings raising the natural real rate and the neutral funds rate

7

3) (50 points) The following equations characterize a countryrsquos economy

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

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

The initial labor supply curve is given as NS = 20 + 4w

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

w = 8 x 10 - (20 + 4w)

w= 12 N = 68 Y= 3128

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

8

(20 points for completely labeled and correct diagrams)

We now have numerous changes to our economic conditions (all is not constant) Think of 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 = 10 + 4w A goes up from 8 to 10

b) (10 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams

9

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 = 10 x 10 - (10 + 4w)

w= 18 N = 82 Y= 4838

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

When N = 68 MPN = 10 x 10 -68 = 32 the wage the firm needs to pay to attract 68 laborers68 = 10 + 4ww = 145 since MPN gtw32gt145 you need to hire workers to get back to profit maximization you hire 14 more workers MPN falls by 14 to 18 in order to hire 14 workers you need to raise wages by 144 = 35 145 + 35 = 18 = MPN = w back to profit maximization when N = 68 + 14 = 82

10

4)(60 points) A closed economy has full employment level of output (Y) of 2500 Government purchases G are 300 taxes (T) are 500 Desired consumption (Cd) and investment (Id) are

Cd = 600 + 05(Y ndashT) - 700r

Id = 640 - 300r

a) (5 points) Solve for the desired savings function in intercept - slope form (note the intercept is an integer)

S = 2500 - [600 + 5(2500 - 500) - 700r] - 300

S = 600 + 700r

b) (5 points) Now solve for the goods market clearing interest rate Please show all workDraw a desired savingsinvestment diagram locating this initial equilibrium and point A on the next page600 + 700r = 640 - 300r r = 04 S = I = 628

A correct and completely labeled diagram is worth 20 points

We now have two shocks that occur simultaneously

i) a change in the desired investment function ndash it is now

Id = 660 - 300r

ii) a change in the consumption function

11

Cd = 610 + 05(Y ndashT) - 700r

c) (5 points) Name three reasons why the consumption function would change the way did

There are fouronly need three 1) a (wealth) up 2) Ye up 3) ae up 4) CC up

d) (5 points) Resolve for the goods market clearing interest rate and the associated levels of desired savings and investment

New Savings function S = 2500 - [610 + 5(2500 - 500) - 700r] - 300

S = 590 + 700r

590 + 700r = 660 - 300r

r = 07 I = S = 639

Add this development to your diagram and label as point B

e) (10 points) Explain the movement to the new equilibrium from point A to point B Start with at the same r savings does not equal investment Give the actual numbers At the same interest rate which is larger Y or C + I + G Use this expression to argue why interest rates changed the way they did When rates change explain what happens to saving and investment (be specific) and why

r = 04 S = 618 and I = 648S lt I Y - C - G lt I Y lt C + I + G2500 lt 2530SINCE ABSORPTION IS GREATER THAN Y r must rise to crowd out enough C and I to get back to equilibrium when r rises by 03 C falls by -700 x 03 = 21 I falls by 9 back to equilibrium where Y = C + I + G (2500 = 2500) or S = I (639 = 639)

f)(10 points) Are your results consistent with the conditions in the US economy since President Trumps election in November of 2016 Why or why not

Yes Investment has gone up given the huge corporate tax cut (t) and sky high animal spirits (AS)

Same with Consumption function - shifting up due to record breaking wealth (a) in the stock market and recording breaking consumer confidence (CC)

12

5 (60 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 = 460 ndash 200rw

Y = 2400T = 200G =500

China Initial Conditions

Cd = 500 + 5(YF ndash TF) ndash 300rw

Id = 400 ndash 200rw

Y = 2000T = 400G = 300

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

USA

S = 2400 - [400 + 5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + 5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 r = 06

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

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

1 (60 points total) Suppose we have Dagwood who has a current income of $100K 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))(100 + 0) + 200 + 0] (2 + (05))

C = 14878

C = [(1 + (05))(300 + 0) + 200 + 0] (2 + (05))

C = 25122

C = [(1 + (-05))(300 + 0) + 200 + 0] (2 + (-05))

C = 24872

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

NLNB) Use space above

2

b)(5 points) Dagwood works in an industry that is booming and he decides to start working overtime so that his current income increases to $300K This is the only change Resolve for Dagwoods optimal consumption bundle and label as point CB

c) (5 points) Jerome Powell 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 CC

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 NO Since Dagwood is a saver he cares most about his FV of present resources since he is financing future consumption with current (present) resources When r goes down FV = (1+r)(y + a) falls and therefore Dagwood is poorer and should spread the pain and consume less in both periods - this is the income effect With numbers FV = (1 + (05)) 300 = 315 vs FV = (1 + (-05)) 300 = 285

The substitution effect works in the opposite 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 10 points for graph 5 points for showing work) In the space below draw two savings functions (on the same diagram) for Dagwood The first savings function is for the initial conditions before Dagwood starts to work overtime (when his current income = $100K) Label as point A where r = 05 and point B when r = -05

Now draw another savings function representing the conditions after Dagwood started to work overtime 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

USE THE NEXT PAGE FOR YOUR DIAGRAM

A - 4878 = 100 - 14878B - 5179 = 100 - 15179

work for point B C = [(1 + (-05))(100 + 0) + 200 + 0] (2 + (-05))C = 15179

C 4878 = 300 - 25122D 5128 = 300 - 24872

10 points for correct and completely labeled graph

f)(10 points) How would your answer change for part d) above if Dagwood never decided to work overtime and the Fed did the same as in lowering rates from 05 to a negative 05 Explain the intuition and use numbers (be specific)

The Fed policy would have worked since Dag started out as a borrower (y = 100 C = 14878)He was financing current consumption with futures resources and therefore cares most about the PV of future resources which rises with a fall in r 100(1+05) = 9224 VS 100(1 + (-05)) = 10417So Dag is richer and will spread the gain C will rise from 14878 to 15179

4

2) (75 points) The Graphic below is from the WSJ 1022018 that shows how the neutral funds rate has drifted lower through time Assume the Feds inflation target is 2 throughout this question

a)(10 points) Explain why the neutral federal funds rate has drifted lower through time (point A to point B)

r or the natural real rate of interest when the economy is at its dual mandate has fallen from 2 to 1 due to 1) an increase in Savings due to baby boomers getting close to retirement - when expected income falls savings goes up and 2) a fall in productivity growth has lowered the investment opportunities in the US recall technology gains are being used to increase the value of your leisure time via apps and not increasing output per hour In terms of the neutral funds rate

iff = r + π

4 = 2 + 2 (old point A)

3 = 1 + 2 (new point B)

5

In the space below draw a S = I graph consistent with your answer in part a) Be sure to label graph completely using actual numbers (on the vertical axis) for point A and for point B (Note you will be adding another point C to your diagram)

30 points for correct and completely labeled graph

b)(5 points) What has happened to the natural real rate of interest Be specific

it went from 2 to 1

c)(10 points) Why is this phenomenon such a big deal In your answer mention what the Fed did to fight the most previous 3 recessions and compare to what they could do if they get to the new neutral federal funds rate (point B above) and a recession begins

The Fed lowered the federal funds rate by an average of 597 to fight the most previous 3 recessions - if the neutral funds rate stays at 3 the fed will not have enough ammunition (bullets = 3) to fight the next recession this is a BIG DEAL

We now go back in time to the new economy years Below is an excerpt from The Taylor Rule A Guidepost for Monetary Policy Note you dont need to know what the Taylor Rule is we are just focusing on the implications of the new economy on the neutral federal funds rate and the neutral real rate of interest

For example the funds rate was consistently above the Taylor rule target through the latter half of the 1990s Yet the rulersquos proponents argue that productivity growth increased in 1995 and this was translating into faster economic growth Faster economic growth they argue manifests itself in higher real rates of interest and thus a higher natural real interest rate While Taylor treated this factor as a constant policy-makers who believed higher productivity was here to stay (because computers had created a ldquoNew Economyrdquo) would have adjusted the Taylor rule up accordingly

6

Faster economic growth they argue manifests itself in higher real rates of interest and thus a higher natural real interest rate

Suppose we had information on the policy makers dot plot diagram from the mid 1990s and that they estimate the neutral federal funds rate to be 55

d)(10 points) Why would we expect the neutral federal funds rate to be much higher back in the mid 1990s relative to today We are comparing 3 today to 55 back in the mid 1990s

Baby boomers were younger back then so we lose the increase in savings effect due to being closer to retirement Wealth in the stock market was large given the surge in productivity and the resulting higher profits - this increase in wealth will DECREASE savings as shown Also the surge in productivity growth due to increases in total factor productivity(A) (internet) increases investment at any given real rate of interest along with very high animal spirits (the future was so bright you have to wear shades) increases investment

Add as point C the conditions for the new economy on your diagram above consistent with your explanation from part d)

From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate

The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth

Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

e)(10 points) Explain why the Fed might increase their estimate of the neutral federal funds rate from 3 to somewhere above 3 and is this good news for policy makers and the economy

The recent corporate tax cut along with very high animal spirits might increase investment and along with it raise the natural real rate and the neutral funds rate Also record breaking stock market is increasing wealth very high CC and the cut in income taxes (T) all have a negative effect on Savings raising the natural real rate and the neutral funds rate

7

3) (50 points) The following equations characterize a countryrsquos economy

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

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

The initial labor supply curve is given as NS = 20 + 4w

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

w = 8 x 10 - (20 + 4w)

w= 12 N = 68 Y= 3128

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

8

(20 points for completely labeled and correct diagrams)

We now have numerous changes to our economic conditions (all is not constant) Think of 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 = 10 + 4w A goes up from 8 to 10

b) (10 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams

9

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 = 10 x 10 - (10 + 4w)

w= 18 N = 82 Y= 4838

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

When N = 68 MPN = 10 x 10 -68 = 32 the wage the firm needs to pay to attract 68 laborers68 = 10 + 4ww = 145 since MPN gtw32gt145 you need to hire workers to get back to profit maximization you hire 14 more workers MPN falls by 14 to 18 in order to hire 14 workers you need to raise wages by 144 = 35 145 + 35 = 18 = MPN = w back to profit maximization when N = 68 + 14 = 82

10

4)(60 points) A closed economy has full employment level of output (Y) of 2500 Government purchases G are 300 taxes (T) are 500 Desired consumption (Cd) and investment (Id) are

Cd = 600 + 05(Y ndashT) - 700r

Id = 640 - 300r

a) (5 points) Solve for the desired savings function in intercept - slope form (note the intercept is an integer)

S = 2500 - [600 + 5(2500 - 500) - 700r] - 300

S = 600 + 700r

b) (5 points) Now solve for the goods market clearing interest rate Please show all workDraw a desired savingsinvestment diagram locating this initial equilibrium and point A on the next page600 + 700r = 640 - 300r r = 04 S = I = 628

A correct and completely labeled diagram is worth 20 points

We now have two shocks that occur simultaneously

i) a change in the desired investment function ndash it is now

Id = 660 - 300r

ii) a change in the consumption function

11

Cd = 610 + 05(Y ndashT) - 700r

c) (5 points) Name three reasons why the consumption function would change the way did

There are fouronly need three 1) a (wealth) up 2) Ye up 3) ae up 4) CC up

d) (5 points) Resolve for the goods market clearing interest rate and the associated levels of desired savings and investment

New Savings function S = 2500 - [610 + 5(2500 - 500) - 700r] - 300

S = 590 + 700r

590 + 700r = 660 - 300r

r = 07 I = S = 639

Add this development to your diagram and label as point B

e) (10 points) Explain the movement to the new equilibrium from point A to point B Start with at the same r savings does not equal investment Give the actual numbers At the same interest rate which is larger Y or C + I + G Use this expression to argue why interest rates changed the way they did When rates change explain what happens to saving and investment (be specific) and why

r = 04 S = 618 and I = 648S lt I Y - C - G lt I Y lt C + I + G2500 lt 2530SINCE ABSORPTION IS GREATER THAN Y r must rise to crowd out enough C and I to get back to equilibrium when r rises by 03 C falls by -700 x 03 = 21 I falls by 9 back to equilibrium where Y = C + I + G (2500 = 2500) or S = I (639 = 639)

f)(10 points) Are your results consistent with the conditions in the US economy since President Trumps election in November of 2016 Why or why not

Yes Investment has gone up given the huge corporate tax cut (t) and sky high animal spirits (AS)

Same with Consumption function - shifting up due to record breaking wealth (a) in the stock market and recording breaking consumer confidence (CC)

12

5 (60 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 = 460 ndash 200rw

Y = 2400T = 200G =500

China Initial Conditions

Cd = 500 + 5(YF ndash TF) ndash 300rw

Id = 400 ndash 200rw

Y = 2000T = 400G = 300

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

USA

S = 2400 - [400 + 5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + 5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 r = 06

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

b)(5 points) Dagwood works in an industry that is booming and he decides to start working overtime so that his current income increases to $300K This is the only change Resolve for Dagwoods optimal consumption bundle and label as point CB

c) (5 points) Jerome Powell 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 CC

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 NO Since Dagwood is a saver he cares most about his FV of present resources since he is financing future consumption with current (present) resources When r goes down FV = (1+r)(y + a) falls and therefore Dagwood is poorer and should spread the pain and consume less in both periods - this is the income effect With numbers FV = (1 + (05)) 300 = 315 vs FV = (1 + (-05)) 300 = 285

The substitution effect works in the opposite 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 10 points for graph 5 points for showing work) In the space below draw two savings functions (on the same diagram) for Dagwood The first savings function is for the initial conditions before Dagwood starts to work overtime (when his current income = $100K) Label as point A where r = 05 and point B when r = -05

Now draw another savings function representing the conditions after Dagwood started to work overtime 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

USE THE NEXT PAGE FOR YOUR DIAGRAM

A - 4878 = 100 - 14878B - 5179 = 100 - 15179

work for point B C = [(1 + (-05))(100 + 0) + 200 + 0] (2 + (-05))C = 15179

C 4878 = 300 - 25122D 5128 = 300 - 24872

10 points for correct and completely labeled graph

f)(10 points) How would your answer change for part d) above if Dagwood never decided to work overtime and the Fed did the same as in lowering rates from 05 to a negative 05 Explain the intuition and use numbers (be specific)

The Fed policy would have worked since Dag started out as a borrower (y = 100 C = 14878)He was financing current consumption with futures resources and therefore cares most about the PV of future resources which rises with a fall in r 100(1+05) = 9224 VS 100(1 + (-05)) = 10417So Dag is richer and will spread the gain C will rise from 14878 to 15179

4

2) (75 points) The Graphic below is from the WSJ 1022018 that shows how the neutral funds rate has drifted lower through time Assume the Feds inflation target is 2 throughout this question

a)(10 points) Explain why the neutral federal funds rate has drifted lower through time (point A to point B)

r or the natural real rate of interest when the economy is at its dual mandate has fallen from 2 to 1 due to 1) an increase in Savings due to baby boomers getting close to retirement - when expected income falls savings goes up and 2) a fall in productivity growth has lowered the investment opportunities in the US recall technology gains are being used to increase the value of your leisure time via apps and not increasing output per hour In terms of the neutral funds rate

iff = r + π

4 = 2 + 2 (old point A)

3 = 1 + 2 (new point B)

5

In the space below draw a S = I graph consistent with your answer in part a) Be sure to label graph completely using actual numbers (on the vertical axis) for point A and for point B (Note you will be adding another point C to your diagram)

30 points for correct and completely labeled graph

b)(5 points) What has happened to the natural real rate of interest Be specific

it went from 2 to 1

c)(10 points) Why is this phenomenon such a big deal In your answer mention what the Fed did to fight the most previous 3 recessions and compare to what they could do if they get to the new neutral federal funds rate (point B above) and a recession begins

The Fed lowered the federal funds rate by an average of 597 to fight the most previous 3 recessions - if the neutral funds rate stays at 3 the fed will not have enough ammunition (bullets = 3) to fight the next recession this is a BIG DEAL

We now go back in time to the new economy years Below is an excerpt from The Taylor Rule A Guidepost for Monetary Policy Note you dont need to know what the Taylor Rule is we are just focusing on the implications of the new economy on the neutral federal funds rate and the neutral real rate of interest

For example the funds rate was consistently above the Taylor rule target through the latter half of the 1990s Yet the rulersquos proponents argue that productivity growth increased in 1995 and this was translating into faster economic growth Faster economic growth they argue manifests itself in higher real rates of interest and thus a higher natural real interest rate While Taylor treated this factor as a constant policy-makers who believed higher productivity was here to stay (because computers had created a ldquoNew Economyrdquo) would have adjusted the Taylor rule up accordingly

6

Faster economic growth they argue manifests itself in higher real rates of interest and thus a higher natural real interest rate

Suppose we had information on the policy makers dot plot diagram from the mid 1990s and that they estimate the neutral federal funds rate to be 55

d)(10 points) Why would we expect the neutral federal funds rate to be much higher back in the mid 1990s relative to today We are comparing 3 today to 55 back in the mid 1990s

Baby boomers were younger back then so we lose the increase in savings effect due to being closer to retirement Wealth in the stock market was large given the surge in productivity and the resulting higher profits - this increase in wealth will DECREASE savings as shown Also the surge in productivity growth due to increases in total factor productivity(A) (internet) increases investment at any given real rate of interest along with very high animal spirits (the future was so bright you have to wear shades) increases investment

Add as point C the conditions for the new economy on your diagram above consistent with your explanation from part d)

From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate

The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth

Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

e)(10 points) Explain why the Fed might increase their estimate of the neutral federal funds rate from 3 to somewhere above 3 and is this good news for policy makers and the economy

The recent corporate tax cut along with very high animal spirits might increase investment and along with it raise the natural real rate and the neutral funds rate Also record breaking stock market is increasing wealth very high CC and the cut in income taxes (T) all have a negative effect on Savings raising the natural real rate and the neutral funds rate

7

3) (50 points) The following equations characterize a countryrsquos economy

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

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

The initial labor supply curve is given as NS = 20 + 4w

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

w = 8 x 10 - (20 + 4w)

w= 12 N = 68 Y= 3128

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

8

(20 points for completely labeled and correct diagrams)

We now have numerous changes to our economic conditions (all is not constant) Think of 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 = 10 + 4w A goes up from 8 to 10

b) (10 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams

9

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 = 10 x 10 - (10 + 4w)

w= 18 N = 82 Y= 4838

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

When N = 68 MPN = 10 x 10 -68 = 32 the wage the firm needs to pay to attract 68 laborers68 = 10 + 4ww = 145 since MPN gtw32gt145 you need to hire workers to get back to profit maximization you hire 14 more workers MPN falls by 14 to 18 in order to hire 14 workers you need to raise wages by 144 = 35 145 + 35 = 18 = MPN = w back to profit maximization when N = 68 + 14 = 82

10

4)(60 points) A closed economy has full employment level of output (Y) of 2500 Government purchases G are 300 taxes (T) are 500 Desired consumption (Cd) and investment (Id) are

Cd = 600 + 05(Y ndashT) - 700r

Id = 640 - 300r

a) (5 points) Solve for the desired savings function in intercept - slope form (note the intercept is an integer)

S = 2500 - [600 + 5(2500 - 500) - 700r] - 300

S = 600 + 700r

b) (5 points) Now solve for the goods market clearing interest rate Please show all workDraw a desired savingsinvestment diagram locating this initial equilibrium and point A on the next page600 + 700r = 640 - 300r r = 04 S = I = 628

A correct and completely labeled diagram is worth 20 points

We now have two shocks that occur simultaneously

i) a change in the desired investment function ndash it is now

Id = 660 - 300r

ii) a change in the consumption function

11

Cd = 610 + 05(Y ndashT) - 700r

c) (5 points) Name three reasons why the consumption function would change the way did

There are fouronly need three 1) a (wealth) up 2) Ye up 3) ae up 4) CC up

d) (5 points) Resolve for the goods market clearing interest rate and the associated levels of desired savings and investment

New Savings function S = 2500 - [610 + 5(2500 - 500) - 700r] - 300

S = 590 + 700r

590 + 700r = 660 - 300r

r = 07 I = S = 639

Add this development to your diagram and label as point B

e) (10 points) Explain the movement to the new equilibrium from point A to point B Start with at the same r savings does not equal investment Give the actual numbers At the same interest rate which is larger Y or C + I + G Use this expression to argue why interest rates changed the way they did When rates change explain what happens to saving and investment (be specific) and why

r = 04 S = 618 and I = 648S lt I Y - C - G lt I Y lt C + I + G2500 lt 2530SINCE ABSORPTION IS GREATER THAN Y r must rise to crowd out enough C and I to get back to equilibrium when r rises by 03 C falls by -700 x 03 = 21 I falls by 9 back to equilibrium where Y = C + I + G (2500 = 2500) or S = I (639 = 639)

f)(10 points) Are your results consistent with the conditions in the US economy since President Trumps election in November of 2016 Why or why not

Yes Investment has gone up given the huge corporate tax cut (t) and sky high animal spirits (AS)

Same with Consumption function - shifting up due to record breaking wealth (a) in the stock market and recording breaking consumer confidence (CC)

12

5 (60 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 = 460 ndash 200rw

Y = 2400T = 200G =500

China Initial Conditions

Cd = 500 + 5(YF ndash TF) ndash 300rw

Id = 400 ndash 200rw

Y = 2000T = 400G = 300

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

USA

S = 2400 - [400 + 5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + 5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 r = 06

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

USE THE NEXT PAGE FOR YOUR DIAGRAM

A - 4878 = 100 - 14878B - 5179 = 100 - 15179

work for point B C = [(1 + (-05))(100 + 0) + 200 + 0] (2 + (-05))C = 15179

C 4878 = 300 - 25122D 5128 = 300 - 24872

10 points for correct and completely labeled graph

f)(10 points) How would your answer change for part d) above if Dagwood never decided to work overtime and the Fed did the same as in lowering rates from 05 to a negative 05 Explain the intuition and use numbers (be specific)

The Fed policy would have worked since Dag started out as a borrower (y = 100 C = 14878)He was financing current consumption with futures resources and therefore cares most about the PV of future resources which rises with a fall in r 100(1+05) = 9224 VS 100(1 + (-05)) = 10417So Dag is richer and will spread the gain C will rise from 14878 to 15179

4

2) (75 points) The Graphic below is from the WSJ 1022018 that shows how the neutral funds rate has drifted lower through time Assume the Feds inflation target is 2 throughout this question

a)(10 points) Explain why the neutral federal funds rate has drifted lower through time (point A to point B)

r or the natural real rate of interest when the economy is at its dual mandate has fallen from 2 to 1 due to 1) an increase in Savings due to baby boomers getting close to retirement - when expected income falls savings goes up and 2) a fall in productivity growth has lowered the investment opportunities in the US recall technology gains are being used to increase the value of your leisure time via apps and not increasing output per hour In terms of the neutral funds rate

iff = r + π

4 = 2 + 2 (old point A)

3 = 1 + 2 (new point B)

5

In the space below draw a S = I graph consistent with your answer in part a) Be sure to label graph completely using actual numbers (on the vertical axis) for point A and for point B (Note you will be adding another point C to your diagram)

30 points for correct and completely labeled graph

b)(5 points) What has happened to the natural real rate of interest Be specific

it went from 2 to 1

c)(10 points) Why is this phenomenon such a big deal In your answer mention what the Fed did to fight the most previous 3 recessions and compare to what they could do if they get to the new neutral federal funds rate (point B above) and a recession begins

The Fed lowered the federal funds rate by an average of 597 to fight the most previous 3 recessions - if the neutral funds rate stays at 3 the fed will not have enough ammunition (bullets = 3) to fight the next recession this is a BIG DEAL

We now go back in time to the new economy years Below is an excerpt from The Taylor Rule A Guidepost for Monetary Policy Note you dont need to know what the Taylor Rule is we are just focusing on the implications of the new economy on the neutral federal funds rate and the neutral real rate of interest

For example the funds rate was consistently above the Taylor rule target through the latter half of the 1990s Yet the rulersquos proponents argue that productivity growth increased in 1995 and this was translating into faster economic growth Faster economic growth they argue manifests itself in higher real rates of interest and thus a higher natural real interest rate While Taylor treated this factor as a constant policy-makers who believed higher productivity was here to stay (because computers had created a ldquoNew Economyrdquo) would have adjusted the Taylor rule up accordingly

6

Faster economic growth they argue manifests itself in higher real rates of interest and thus a higher natural real interest rate

Suppose we had information on the policy makers dot plot diagram from the mid 1990s and that they estimate the neutral federal funds rate to be 55

d)(10 points) Why would we expect the neutral federal funds rate to be much higher back in the mid 1990s relative to today We are comparing 3 today to 55 back in the mid 1990s

Baby boomers were younger back then so we lose the increase in savings effect due to being closer to retirement Wealth in the stock market was large given the surge in productivity and the resulting higher profits - this increase in wealth will DECREASE savings as shown Also the surge in productivity growth due to increases in total factor productivity(A) (internet) increases investment at any given real rate of interest along with very high animal spirits (the future was so bright you have to wear shades) increases investment

Add as point C the conditions for the new economy on your diagram above consistent with your explanation from part d)

From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate

The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth

Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

e)(10 points) Explain why the Fed might increase their estimate of the neutral federal funds rate from 3 to somewhere above 3 and is this good news for policy makers and the economy

The recent corporate tax cut along with very high animal spirits might increase investment and along with it raise the natural real rate and the neutral funds rate Also record breaking stock market is increasing wealth very high CC and the cut in income taxes (T) all have a negative effect on Savings raising the natural real rate and the neutral funds rate

7

3) (50 points) The following equations characterize a countryrsquos economy

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

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

The initial labor supply curve is given as NS = 20 + 4w

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

w = 8 x 10 - (20 + 4w)

w= 12 N = 68 Y= 3128

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

8

(20 points for completely labeled and correct diagrams)

We now have numerous changes to our economic conditions (all is not constant) Think of 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 = 10 + 4w A goes up from 8 to 10

b) (10 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams

9

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 = 10 x 10 - (10 + 4w)

w= 18 N = 82 Y= 4838

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

When N = 68 MPN = 10 x 10 -68 = 32 the wage the firm needs to pay to attract 68 laborers68 = 10 + 4ww = 145 since MPN gtw32gt145 you need to hire workers to get back to profit maximization you hire 14 more workers MPN falls by 14 to 18 in order to hire 14 workers you need to raise wages by 144 = 35 145 + 35 = 18 = MPN = w back to profit maximization when N = 68 + 14 = 82

10

4)(60 points) A closed economy has full employment level of output (Y) of 2500 Government purchases G are 300 taxes (T) are 500 Desired consumption (Cd) and investment (Id) are

Cd = 600 + 05(Y ndashT) - 700r

Id = 640 - 300r

a) (5 points) Solve for the desired savings function in intercept - slope form (note the intercept is an integer)

S = 2500 - [600 + 5(2500 - 500) - 700r] - 300

S = 600 + 700r

b) (5 points) Now solve for the goods market clearing interest rate Please show all workDraw a desired savingsinvestment diagram locating this initial equilibrium and point A on the next page600 + 700r = 640 - 300r r = 04 S = I = 628

A correct and completely labeled diagram is worth 20 points

We now have two shocks that occur simultaneously

i) a change in the desired investment function ndash it is now

Id = 660 - 300r

ii) a change in the consumption function

11

Cd = 610 + 05(Y ndashT) - 700r

c) (5 points) Name three reasons why the consumption function would change the way did

There are fouronly need three 1) a (wealth) up 2) Ye up 3) ae up 4) CC up

d) (5 points) Resolve for the goods market clearing interest rate and the associated levels of desired savings and investment

New Savings function S = 2500 - [610 + 5(2500 - 500) - 700r] - 300

S = 590 + 700r

590 + 700r = 660 - 300r

r = 07 I = S = 639

Add this development to your diagram and label as point B

e) (10 points) Explain the movement to the new equilibrium from point A to point B Start with at the same r savings does not equal investment Give the actual numbers At the same interest rate which is larger Y or C + I + G Use this expression to argue why interest rates changed the way they did When rates change explain what happens to saving and investment (be specific) and why

r = 04 S = 618 and I = 648S lt I Y - C - G lt I Y lt C + I + G2500 lt 2530SINCE ABSORPTION IS GREATER THAN Y r must rise to crowd out enough C and I to get back to equilibrium when r rises by 03 C falls by -700 x 03 = 21 I falls by 9 back to equilibrium where Y = C + I + G (2500 = 2500) or S = I (639 = 639)

f)(10 points) Are your results consistent with the conditions in the US economy since President Trumps election in November of 2016 Why or why not

Yes Investment has gone up given the huge corporate tax cut (t) and sky high animal spirits (AS)

Same with Consumption function - shifting up due to record breaking wealth (a) in the stock market and recording breaking consumer confidence (CC)

12

5 (60 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 = 460 ndash 200rw

Y = 2400T = 200G =500

China Initial Conditions

Cd = 500 + 5(YF ndash TF) ndash 300rw

Id = 400 ndash 200rw

Y = 2000T = 400G = 300

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

USA

S = 2400 - [400 + 5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + 5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 r = 06

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

2) (75 points) The Graphic below is from the WSJ 1022018 that shows how the neutral funds rate has drifted lower through time Assume the Feds inflation target is 2 throughout this question

a)(10 points) Explain why the neutral federal funds rate has drifted lower through time (point A to point B)

r or the natural real rate of interest when the economy is at its dual mandate has fallen from 2 to 1 due to 1) an increase in Savings due to baby boomers getting close to retirement - when expected income falls savings goes up and 2) a fall in productivity growth has lowered the investment opportunities in the US recall technology gains are being used to increase the value of your leisure time via apps and not increasing output per hour In terms of the neutral funds rate

iff = r + π

4 = 2 + 2 (old point A)

3 = 1 + 2 (new point B)

5

In the space below draw a S = I graph consistent with your answer in part a) Be sure to label graph completely using actual numbers (on the vertical axis) for point A and for point B (Note you will be adding another point C to your diagram)

30 points for correct and completely labeled graph

b)(5 points) What has happened to the natural real rate of interest Be specific

it went from 2 to 1

c)(10 points) Why is this phenomenon such a big deal In your answer mention what the Fed did to fight the most previous 3 recessions and compare to what they could do if they get to the new neutral federal funds rate (point B above) and a recession begins

The Fed lowered the federal funds rate by an average of 597 to fight the most previous 3 recessions - if the neutral funds rate stays at 3 the fed will not have enough ammunition (bullets = 3) to fight the next recession this is a BIG DEAL

We now go back in time to the new economy years Below is an excerpt from The Taylor Rule A Guidepost for Monetary Policy Note you dont need to know what the Taylor Rule is we are just focusing on the implications of the new economy on the neutral federal funds rate and the neutral real rate of interest

For example the funds rate was consistently above the Taylor rule target through the latter half of the 1990s Yet the rulersquos proponents argue that productivity growth increased in 1995 and this was translating into faster economic growth Faster economic growth they argue manifests itself in higher real rates of interest and thus a higher natural real interest rate While Taylor treated this factor as a constant policy-makers who believed higher productivity was here to stay (because computers had created a ldquoNew Economyrdquo) would have adjusted the Taylor rule up accordingly

6

Faster economic growth they argue manifests itself in higher real rates of interest and thus a higher natural real interest rate

Suppose we had information on the policy makers dot plot diagram from the mid 1990s and that they estimate the neutral federal funds rate to be 55

d)(10 points) Why would we expect the neutral federal funds rate to be much higher back in the mid 1990s relative to today We are comparing 3 today to 55 back in the mid 1990s

Baby boomers were younger back then so we lose the increase in savings effect due to being closer to retirement Wealth in the stock market was large given the surge in productivity and the resulting higher profits - this increase in wealth will DECREASE savings as shown Also the surge in productivity growth due to increases in total factor productivity(A) (internet) increases investment at any given real rate of interest along with very high animal spirits (the future was so bright you have to wear shades) increases investment

Add as point C the conditions for the new economy on your diagram above consistent with your explanation from part d)

From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate

The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth

Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

e)(10 points) Explain why the Fed might increase their estimate of the neutral federal funds rate from 3 to somewhere above 3 and is this good news for policy makers and the economy

The recent corporate tax cut along with very high animal spirits might increase investment and along with it raise the natural real rate and the neutral funds rate Also record breaking stock market is increasing wealth very high CC and the cut in income taxes (T) all have a negative effect on Savings raising the natural real rate and the neutral funds rate

7

3) (50 points) The following equations characterize a countryrsquos economy

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

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

The initial labor supply curve is given as NS = 20 + 4w

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

w = 8 x 10 - (20 + 4w)

w= 12 N = 68 Y= 3128

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

8

(20 points for completely labeled and correct diagrams)

We now have numerous changes to our economic conditions (all is not constant) Think of 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 = 10 + 4w A goes up from 8 to 10

b) (10 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams

9

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 = 10 x 10 - (10 + 4w)

w= 18 N = 82 Y= 4838

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

When N = 68 MPN = 10 x 10 -68 = 32 the wage the firm needs to pay to attract 68 laborers68 = 10 + 4ww = 145 since MPN gtw32gt145 you need to hire workers to get back to profit maximization you hire 14 more workers MPN falls by 14 to 18 in order to hire 14 workers you need to raise wages by 144 = 35 145 + 35 = 18 = MPN = w back to profit maximization when N = 68 + 14 = 82

10

4)(60 points) A closed economy has full employment level of output (Y) of 2500 Government purchases G are 300 taxes (T) are 500 Desired consumption (Cd) and investment (Id) are

Cd = 600 + 05(Y ndashT) - 700r

Id = 640 - 300r

a) (5 points) Solve for the desired savings function in intercept - slope form (note the intercept is an integer)

S = 2500 - [600 + 5(2500 - 500) - 700r] - 300

S = 600 + 700r

b) (5 points) Now solve for the goods market clearing interest rate Please show all workDraw a desired savingsinvestment diagram locating this initial equilibrium and point A on the next page600 + 700r = 640 - 300r r = 04 S = I = 628

A correct and completely labeled diagram is worth 20 points

We now have two shocks that occur simultaneously

i) a change in the desired investment function ndash it is now

Id = 660 - 300r

ii) a change in the consumption function

11

Cd = 610 + 05(Y ndashT) - 700r

c) (5 points) Name three reasons why the consumption function would change the way did

There are fouronly need three 1) a (wealth) up 2) Ye up 3) ae up 4) CC up

d) (5 points) Resolve for the goods market clearing interest rate and the associated levels of desired savings and investment

New Savings function S = 2500 - [610 + 5(2500 - 500) - 700r] - 300

S = 590 + 700r

590 + 700r = 660 - 300r

r = 07 I = S = 639

Add this development to your diagram and label as point B

e) (10 points) Explain the movement to the new equilibrium from point A to point B Start with at the same r savings does not equal investment Give the actual numbers At the same interest rate which is larger Y or C + I + G Use this expression to argue why interest rates changed the way they did When rates change explain what happens to saving and investment (be specific) and why

r = 04 S = 618 and I = 648S lt I Y - C - G lt I Y lt C + I + G2500 lt 2530SINCE ABSORPTION IS GREATER THAN Y r must rise to crowd out enough C and I to get back to equilibrium when r rises by 03 C falls by -700 x 03 = 21 I falls by 9 back to equilibrium where Y = C + I + G (2500 = 2500) or S = I (639 = 639)

f)(10 points) Are your results consistent with the conditions in the US economy since President Trumps election in November of 2016 Why or why not

Yes Investment has gone up given the huge corporate tax cut (t) and sky high animal spirits (AS)

Same with Consumption function - shifting up due to record breaking wealth (a) in the stock market and recording breaking consumer confidence (CC)

12

5 (60 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 = 460 ndash 200rw

Y = 2400T = 200G =500

China Initial Conditions

Cd = 500 + 5(YF ndash TF) ndash 300rw

Id = 400 ndash 200rw

Y = 2000T = 400G = 300

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

USA

S = 2400 - [400 + 5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + 5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 r = 06

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

In the space below draw a S = I graph consistent with your answer in part a) Be sure to label graph completely using actual numbers (on the vertical axis) for point A and for point B (Note you will be adding another point C to your diagram)

30 points for correct and completely labeled graph

b)(5 points) What has happened to the natural real rate of interest Be specific

it went from 2 to 1

c)(10 points) Why is this phenomenon such a big deal In your answer mention what the Fed did to fight the most previous 3 recessions and compare to what they could do if they get to the new neutral federal funds rate (point B above) and a recession begins

The Fed lowered the federal funds rate by an average of 597 to fight the most previous 3 recessions - if the neutral funds rate stays at 3 the fed will not have enough ammunition (bullets = 3) to fight the next recession this is a BIG DEAL

We now go back in time to the new economy years Below is an excerpt from The Taylor Rule A Guidepost for Monetary Policy Note you dont need to know what the Taylor Rule is we are just focusing on the implications of the new economy on the neutral federal funds rate and the neutral real rate of interest

For example the funds rate was consistently above the Taylor rule target through the latter half of the 1990s Yet the rulersquos proponents argue that productivity growth increased in 1995 and this was translating into faster economic growth Faster economic growth they argue manifests itself in higher real rates of interest and thus a higher natural real interest rate While Taylor treated this factor as a constant policy-makers who believed higher productivity was here to stay (because computers had created a ldquoNew Economyrdquo) would have adjusted the Taylor rule up accordingly

6

Faster economic growth they argue manifests itself in higher real rates of interest and thus a higher natural real interest rate

Suppose we had information on the policy makers dot plot diagram from the mid 1990s and that they estimate the neutral federal funds rate to be 55

d)(10 points) Why would we expect the neutral federal funds rate to be much higher back in the mid 1990s relative to today We are comparing 3 today to 55 back in the mid 1990s

Baby boomers were younger back then so we lose the increase in savings effect due to being closer to retirement Wealth in the stock market was large given the surge in productivity and the resulting higher profits - this increase in wealth will DECREASE savings as shown Also the surge in productivity growth due to increases in total factor productivity(A) (internet) increases investment at any given real rate of interest along with very high animal spirits (the future was so bright you have to wear shades) increases investment

Add as point C the conditions for the new economy on your diagram above consistent with your explanation from part d)

From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate

The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth

Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

e)(10 points) Explain why the Fed might increase their estimate of the neutral federal funds rate from 3 to somewhere above 3 and is this good news for policy makers and the economy

The recent corporate tax cut along with very high animal spirits might increase investment and along with it raise the natural real rate and the neutral funds rate Also record breaking stock market is increasing wealth very high CC and the cut in income taxes (T) all have a negative effect on Savings raising the natural real rate and the neutral funds rate

7

3) (50 points) The following equations characterize a countryrsquos economy

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

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

The initial labor supply curve is given as NS = 20 + 4w

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

w = 8 x 10 - (20 + 4w)

w= 12 N = 68 Y= 3128

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

8

(20 points for completely labeled and correct diagrams)

We now have numerous changes to our economic conditions (all is not constant) Think of 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 = 10 + 4w A goes up from 8 to 10

b) (10 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams

9

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 = 10 x 10 - (10 + 4w)

w= 18 N = 82 Y= 4838

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

When N = 68 MPN = 10 x 10 -68 = 32 the wage the firm needs to pay to attract 68 laborers68 = 10 + 4ww = 145 since MPN gtw32gt145 you need to hire workers to get back to profit maximization you hire 14 more workers MPN falls by 14 to 18 in order to hire 14 workers you need to raise wages by 144 = 35 145 + 35 = 18 = MPN = w back to profit maximization when N = 68 + 14 = 82

10

4)(60 points) A closed economy has full employment level of output (Y) of 2500 Government purchases G are 300 taxes (T) are 500 Desired consumption (Cd) and investment (Id) are

Cd = 600 + 05(Y ndashT) - 700r

Id = 640 - 300r

a) (5 points) Solve for the desired savings function in intercept - slope form (note the intercept is an integer)

S = 2500 - [600 + 5(2500 - 500) - 700r] - 300

S = 600 + 700r

b) (5 points) Now solve for the goods market clearing interest rate Please show all workDraw a desired savingsinvestment diagram locating this initial equilibrium and point A on the next page600 + 700r = 640 - 300r r = 04 S = I = 628

A correct and completely labeled diagram is worth 20 points

We now have two shocks that occur simultaneously

i) a change in the desired investment function ndash it is now

Id = 660 - 300r

ii) a change in the consumption function

11

Cd = 610 + 05(Y ndashT) - 700r

c) (5 points) Name three reasons why the consumption function would change the way did

There are fouronly need three 1) a (wealth) up 2) Ye up 3) ae up 4) CC up

d) (5 points) Resolve for the goods market clearing interest rate and the associated levels of desired savings and investment

New Savings function S = 2500 - [610 + 5(2500 - 500) - 700r] - 300

S = 590 + 700r

590 + 700r = 660 - 300r

r = 07 I = S = 639

Add this development to your diagram and label as point B

e) (10 points) Explain the movement to the new equilibrium from point A to point B Start with at the same r savings does not equal investment Give the actual numbers At the same interest rate which is larger Y or C + I + G Use this expression to argue why interest rates changed the way they did When rates change explain what happens to saving and investment (be specific) and why

r = 04 S = 618 and I = 648S lt I Y - C - G lt I Y lt C + I + G2500 lt 2530SINCE ABSORPTION IS GREATER THAN Y r must rise to crowd out enough C and I to get back to equilibrium when r rises by 03 C falls by -700 x 03 = 21 I falls by 9 back to equilibrium where Y = C + I + G (2500 = 2500) or S = I (639 = 639)

f)(10 points) Are your results consistent with the conditions in the US economy since President Trumps election in November of 2016 Why or why not

Yes Investment has gone up given the huge corporate tax cut (t) and sky high animal spirits (AS)

Same with Consumption function - shifting up due to record breaking wealth (a) in the stock market and recording breaking consumer confidence (CC)

12

5 (60 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 = 460 ndash 200rw

Y = 2400T = 200G =500

China Initial Conditions

Cd = 500 + 5(YF ndash TF) ndash 300rw

Id = 400 ndash 200rw

Y = 2000T = 400G = 300

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

USA

S = 2400 - [400 + 5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + 5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 r = 06

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

Faster economic growth they argue manifests itself in higher real rates of interest and thus a higher natural real interest rate

Suppose we had information on the policy makers dot plot diagram from the mid 1990s and that they estimate the neutral federal funds rate to be 55

d)(10 points) Why would we expect the neutral federal funds rate to be much higher back in the mid 1990s relative to today We are comparing 3 today to 55 back in the mid 1990s

Baby boomers were younger back then so we lose the increase in savings effect due to being closer to retirement Wealth in the stock market was large given the surge in productivity and the resulting higher profits - this increase in wealth will DECREASE savings as shown Also the surge in productivity growth due to increases in total factor productivity(A) (internet) increases investment at any given real rate of interest along with very high animal spirits (the future was so bright you have to wear shades) increases investment

Add as point C the conditions for the new economy on your diagram above consistent with your explanation from part d)

From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate

The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth

Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

e)(10 points) Explain why the Fed might increase their estimate of the neutral federal funds rate from 3 to somewhere above 3 and is this good news for policy makers and the economy

The recent corporate tax cut along with very high animal spirits might increase investment and along with it raise the natural real rate and the neutral funds rate Also record breaking stock market is increasing wealth very high CC and the cut in income taxes (T) all have a negative effect on Savings raising the natural real rate and the neutral funds rate

7

3) (50 points) The following equations characterize a countryrsquos economy

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

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

The initial labor supply curve is given as NS = 20 + 4w

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

w = 8 x 10 - (20 + 4w)

w= 12 N = 68 Y= 3128

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

8

(20 points for completely labeled and correct diagrams)

We now have numerous changes to our economic conditions (all is not constant) Think of 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 = 10 + 4w A goes up from 8 to 10

b) (10 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams

9

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 = 10 x 10 - (10 + 4w)

w= 18 N = 82 Y= 4838

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

When N = 68 MPN = 10 x 10 -68 = 32 the wage the firm needs to pay to attract 68 laborers68 = 10 + 4ww = 145 since MPN gtw32gt145 you need to hire workers to get back to profit maximization you hire 14 more workers MPN falls by 14 to 18 in order to hire 14 workers you need to raise wages by 144 = 35 145 + 35 = 18 = MPN = w back to profit maximization when N = 68 + 14 = 82

10

4)(60 points) A closed economy has full employment level of output (Y) of 2500 Government purchases G are 300 taxes (T) are 500 Desired consumption (Cd) and investment (Id) are

Cd = 600 + 05(Y ndashT) - 700r

Id = 640 - 300r

a) (5 points) Solve for the desired savings function in intercept - slope form (note the intercept is an integer)

S = 2500 - [600 + 5(2500 - 500) - 700r] - 300

S = 600 + 700r

b) (5 points) Now solve for the goods market clearing interest rate Please show all workDraw a desired savingsinvestment diagram locating this initial equilibrium and point A on the next page600 + 700r = 640 - 300r r = 04 S = I = 628

A correct and completely labeled diagram is worth 20 points

We now have two shocks that occur simultaneously

i) a change in the desired investment function ndash it is now

Id = 660 - 300r

ii) a change in the consumption function

11

Cd = 610 + 05(Y ndashT) - 700r

c) (5 points) Name three reasons why the consumption function would change the way did

There are fouronly need three 1) a (wealth) up 2) Ye up 3) ae up 4) CC up

d) (5 points) Resolve for the goods market clearing interest rate and the associated levels of desired savings and investment

New Savings function S = 2500 - [610 + 5(2500 - 500) - 700r] - 300

S = 590 + 700r

590 + 700r = 660 - 300r

r = 07 I = S = 639

Add this development to your diagram and label as point B

e) (10 points) Explain the movement to the new equilibrium from point A to point B Start with at the same r savings does not equal investment Give the actual numbers At the same interest rate which is larger Y or C + I + G Use this expression to argue why interest rates changed the way they did When rates change explain what happens to saving and investment (be specific) and why

r = 04 S = 618 and I = 648S lt I Y - C - G lt I Y lt C + I + G2500 lt 2530SINCE ABSORPTION IS GREATER THAN Y r must rise to crowd out enough C and I to get back to equilibrium when r rises by 03 C falls by -700 x 03 = 21 I falls by 9 back to equilibrium where Y = C + I + G (2500 = 2500) or S = I (639 = 639)

f)(10 points) Are your results consistent with the conditions in the US economy since President Trumps election in November of 2016 Why or why not

Yes Investment has gone up given the huge corporate tax cut (t) and sky high animal spirits (AS)

Same with Consumption function - shifting up due to record breaking wealth (a) in the stock market and recording breaking consumer confidence (CC)

12

5 (60 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 = 460 ndash 200rw

Y = 2400T = 200G =500

China Initial Conditions

Cd = 500 + 5(YF ndash TF) ndash 300rw

Id = 400 ndash 200rw

Y = 2000T = 400G = 300

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

USA

S = 2400 - [400 + 5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + 5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 r = 06

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

3) (50 points) The following equations characterize a countryrsquos economy

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

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

The initial labor supply curve is given as NS = 20 + 4w

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

w = 8 x 10 - (20 + 4w)

w= 12 N = 68 Y= 3128

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

8

(20 points for completely labeled and correct diagrams)

We now have numerous changes to our economic conditions (all is not constant) Think of 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 = 10 + 4w A goes up from 8 to 10

b) (10 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams

9

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 = 10 x 10 - (10 + 4w)

w= 18 N = 82 Y= 4838

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

When N = 68 MPN = 10 x 10 -68 = 32 the wage the firm needs to pay to attract 68 laborers68 = 10 + 4ww = 145 since MPN gtw32gt145 you need to hire workers to get back to profit maximization you hire 14 more workers MPN falls by 14 to 18 in order to hire 14 workers you need to raise wages by 144 = 35 145 + 35 = 18 = MPN = w back to profit maximization when N = 68 + 14 = 82

10

4)(60 points) A closed economy has full employment level of output (Y) of 2500 Government purchases G are 300 taxes (T) are 500 Desired consumption (Cd) and investment (Id) are

Cd = 600 + 05(Y ndashT) - 700r

Id = 640 - 300r

a) (5 points) Solve for the desired savings function in intercept - slope form (note the intercept is an integer)

S = 2500 - [600 + 5(2500 - 500) - 700r] - 300

S = 600 + 700r

b) (5 points) Now solve for the goods market clearing interest rate Please show all workDraw a desired savingsinvestment diagram locating this initial equilibrium and point A on the next page600 + 700r = 640 - 300r r = 04 S = I = 628

A correct and completely labeled diagram is worth 20 points

We now have two shocks that occur simultaneously

i) a change in the desired investment function ndash it is now

Id = 660 - 300r

ii) a change in the consumption function

11

Cd = 610 + 05(Y ndashT) - 700r

c) (5 points) Name three reasons why the consumption function would change the way did

There are fouronly need three 1) a (wealth) up 2) Ye up 3) ae up 4) CC up

d) (5 points) Resolve for the goods market clearing interest rate and the associated levels of desired savings and investment

New Savings function S = 2500 - [610 + 5(2500 - 500) - 700r] - 300

S = 590 + 700r

590 + 700r = 660 - 300r

r = 07 I = S = 639

Add this development to your diagram and label as point B

e) (10 points) Explain the movement to the new equilibrium from point A to point B Start with at the same r savings does not equal investment Give the actual numbers At the same interest rate which is larger Y or C + I + G Use this expression to argue why interest rates changed the way they did When rates change explain what happens to saving and investment (be specific) and why

r = 04 S = 618 and I = 648S lt I Y - C - G lt I Y lt C + I + G2500 lt 2530SINCE ABSORPTION IS GREATER THAN Y r must rise to crowd out enough C and I to get back to equilibrium when r rises by 03 C falls by -700 x 03 = 21 I falls by 9 back to equilibrium where Y = C + I + G (2500 = 2500) or S = I (639 = 639)

f)(10 points) Are your results consistent with the conditions in the US economy since President Trumps election in November of 2016 Why or why not

Yes Investment has gone up given the huge corporate tax cut (t) and sky high animal spirits (AS)

Same with Consumption function - shifting up due to record breaking wealth (a) in the stock market and recording breaking consumer confidence (CC)

12

5 (60 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 = 460 ndash 200rw

Y = 2400T = 200G =500

China Initial Conditions

Cd = 500 + 5(YF ndash TF) ndash 300rw

Id = 400 ndash 200rw

Y = 2000T = 400G = 300

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

USA

S = 2400 - [400 + 5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + 5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 r = 06

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

(20 points for completely labeled and correct diagrams)

We now have numerous changes to our economic conditions (all is not constant) Think of 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 = 10 + 4w A goes up from 8 to 10

b) (10 points) Given the change in NS and A repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams

9

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 = 10 x 10 - (10 + 4w)

w= 18 N = 82 Y= 4838

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

When N = 68 MPN = 10 x 10 -68 = 32 the wage the firm needs to pay to attract 68 laborers68 = 10 + 4ww = 145 since MPN gtw32gt145 you need to hire workers to get back to profit maximization you hire 14 more workers MPN falls by 14 to 18 in order to hire 14 workers you need to raise wages by 144 = 35 145 + 35 = 18 = MPN = w back to profit maximization when N = 68 + 14 = 82

10

4)(60 points) A closed economy has full employment level of output (Y) of 2500 Government purchases G are 300 taxes (T) are 500 Desired consumption (Cd) and investment (Id) are

Cd = 600 + 05(Y ndashT) - 700r

Id = 640 - 300r

a) (5 points) Solve for the desired savings function in intercept - slope form (note the intercept is an integer)

S = 2500 - [600 + 5(2500 - 500) - 700r] - 300

S = 600 + 700r

b) (5 points) Now solve for the goods market clearing interest rate Please show all workDraw a desired savingsinvestment diagram locating this initial equilibrium and point A on the next page600 + 700r = 640 - 300r r = 04 S = I = 628

A correct and completely labeled diagram is worth 20 points

We now have two shocks that occur simultaneously

i) a change in the desired investment function ndash it is now

Id = 660 - 300r

ii) a change in the consumption function

11

Cd = 610 + 05(Y ndashT) - 700r

c) (5 points) Name three reasons why the consumption function would change the way did

There are fouronly need three 1) a (wealth) up 2) Ye up 3) ae up 4) CC up

d) (5 points) Resolve for the goods market clearing interest rate and the associated levels of desired savings and investment

New Savings function S = 2500 - [610 + 5(2500 - 500) - 700r] - 300

S = 590 + 700r

590 + 700r = 660 - 300r

r = 07 I = S = 639

Add this development to your diagram and label as point B

e) (10 points) Explain the movement to the new equilibrium from point A to point B Start with at the same r savings does not equal investment Give the actual numbers At the same interest rate which is larger Y or C + I + G Use this expression to argue why interest rates changed the way they did When rates change explain what happens to saving and investment (be specific) and why

r = 04 S = 618 and I = 648S lt I Y - C - G lt I Y lt C + I + G2500 lt 2530SINCE ABSORPTION IS GREATER THAN Y r must rise to crowd out enough C and I to get back to equilibrium when r rises by 03 C falls by -700 x 03 = 21 I falls by 9 back to equilibrium where Y = C + I + G (2500 = 2500) or S = I (639 = 639)

f)(10 points) Are your results consistent with the conditions in the US economy since President Trumps election in November of 2016 Why or why not

Yes Investment has gone up given the huge corporate tax cut (t) and sky high animal spirits (AS)

Same with Consumption function - shifting up due to record breaking wealth (a) in the stock market and recording breaking consumer confidence (CC)

12

5 (60 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 = 460 ndash 200rw

Y = 2400T = 200G =500

China Initial Conditions

Cd = 500 + 5(YF ndash TF) ndash 300rw

Id = 400 ndash 200rw

Y = 2000T = 400G = 300

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

USA

S = 2400 - [400 + 5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + 5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 r = 06

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

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 = 10 x 10 - (10 + 4w)

w= 18 N = 82 Y= 4838

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

When N = 68 MPN = 10 x 10 -68 = 32 the wage the firm needs to pay to attract 68 laborers68 = 10 + 4ww = 145 since MPN gtw32gt145 you need to hire workers to get back to profit maximization you hire 14 more workers MPN falls by 14 to 18 in order to hire 14 workers you need to raise wages by 144 = 35 145 + 35 = 18 = MPN = w back to profit maximization when N = 68 + 14 = 82

10

4)(60 points) A closed economy has full employment level of output (Y) of 2500 Government purchases G are 300 taxes (T) are 500 Desired consumption (Cd) and investment (Id) are

Cd = 600 + 05(Y ndashT) - 700r

Id = 640 - 300r

a) (5 points) Solve for the desired savings function in intercept - slope form (note the intercept is an integer)

S = 2500 - [600 + 5(2500 - 500) - 700r] - 300

S = 600 + 700r

b) (5 points) Now solve for the goods market clearing interest rate Please show all workDraw a desired savingsinvestment diagram locating this initial equilibrium and point A on the next page600 + 700r = 640 - 300r r = 04 S = I = 628

A correct and completely labeled diagram is worth 20 points

We now have two shocks that occur simultaneously

i) a change in the desired investment function ndash it is now

Id = 660 - 300r

ii) a change in the consumption function

11

Cd = 610 + 05(Y ndashT) - 700r

c) (5 points) Name three reasons why the consumption function would change the way did

There are fouronly need three 1) a (wealth) up 2) Ye up 3) ae up 4) CC up

d) (5 points) Resolve for the goods market clearing interest rate and the associated levels of desired savings and investment

New Savings function S = 2500 - [610 + 5(2500 - 500) - 700r] - 300

S = 590 + 700r

590 + 700r = 660 - 300r

r = 07 I = S = 639

Add this development to your diagram and label as point B

e) (10 points) Explain the movement to the new equilibrium from point A to point B Start with at the same r savings does not equal investment Give the actual numbers At the same interest rate which is larger Y or C + I + G Use this expression to argue why interest rates changed the way they did When rates change explain what happens to saving and investment (be specific) and why

r = 04 S = 618 and I = 648S lt I Y - C - G lt I Y lt C + I + G2500 lt 2530SINCE ABSORPTION IS GREATER THAN Y r must rise to crowd out enough C and I to get back to equilibrium when r rises by 03 C falls by -700 x 03 = 21 I falls by 9 back to equilibrium where Y = C + I + G (2500 = 2500) or S = I (639 = 639)

f)(10 points) Are your results consistent with the conditions in the US economy since President Trumps election in November of 2016 Why or why not

Yes Investment has gone up given the huge corporate tax cut (t) and sky high animal spirits (AS)

Same with Consumption function - shifting up due to record breaking wealth (a) in the stock market and recording breaking consumer confidence (CC)

12

5 (60 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 = 460 ndash 200rw

Y = 2400T = 200G =500

China Initial Conditions

Cd = 500 + 5(YF ndash TF) ndash 300rw

Id = 400 ndash 200rw

Y = 2000T = 400G = 300

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

USA

S = 2400 - [400 + 5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + 5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 r = 06

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

4)(60 points) A closed economy has full employment level of output (Y) of 2500 Government purchases G are 300 taxes (T) are 500 Desired consumption (Cd) and investment (Id) are

Cd = 600 + 05(Y ndashT) - 700r

Id = 640 - 300r

a) (5 points) Solve for the desired savings function in intercept - slope form (note the intercept is an integer)

S = 2500 - [600 + 5(2500 - 500) - 700r] - 300

S = 600 + 700r

b) (5 points) Now solve for the goods market clearing interest rate Please show all workDraw a desired savingsinvestment diagram locating this initial equilibrium and point A on the next page600 + 700r = 640 - 300r r = 04 S = I = 628

A correct and completely labeled diagram is worth 20 points

We now have two shocks that occur simultaneously

i) a change in the desired investment function ndash it is now

Id = 660 - 300r

ii) a change in the consumption function

11

Cd = 610 + 05(Y ndashT) - 700r

c) (5 points) Name three reasons why the consumption function would change the way did

There are fouronly need three 1) a (wealth) up 2) Ye up 3) ae up 4) CC up

d) (5 points) Resolve for the goods market clearing interest rate and the associated levels of desired savings and investment

New Savings function S = 2500 - [610 + 5(2500 - 500) - 700r] - 300

S = 590 + 700r

590 + 700r = 660 - 300r

r = 07 I = S = 639

Add this development to your diagram and label as point B

e) (10 points) Explain the movement to the new equilibrium from point A to point B Start with at the same r savings does not equal investment Give the actual numbers At the same interest rate which is larger Y or C + I + G Use this expression to argue why interest rates changed the way they did When rates change explain what happens to saving and investment (be specific) and why

r = 04 S = 618 and I = 648S lt I Y - C - G lt I Y lt C + I + G2500 lt 2530SINCE ABSORPTION IS GREATER THAN Y r must rise to crowd out enough C and I to get back to equilibrium when r rises by 03 C falls by -700 x 03 = 21 I falls by 9 back to equilibrium where Y = C + I + G (2500 = 2500) or S = I (639 = 639)

f)(10 points) Are your results consistent with the conditions in the US economy since President Trumps election in November of 2016 Why or why not

Yes Investment has gone up given the huge corporate tax cut (t) and sky high animal spirits (AS)

Same with Consumption function - shifting up due to record breaking wealth (a) in the stock market and recording breaking consumer confidence (CC)

12

5 (60 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 = 460 ndash 200rw

Y = 2400T = 200G =500

China Initial Conditions

Cd = 500 + 5(YF ndash TF) ndash 300rw

Id = 400 ndash 200rw

Y = 2000T = 400G = 300

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

USA

S = 2400 - [400 + 5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + 5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 r = 06

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

Cd = 610 + 05(Y ndashT) - 700r

c) (5 points) Name three reasons why the consumption function would change the way did

There are fouronly need three 1) a (wealth) up 2) Ye up 3) ae up 4) CC up

d) (5 points) Resolve for the goods market clearing interest rate and the associated levels of desired savings and investment

New Savings function S = 2500 - [610 + 5(2500 - 500) - 700r] - 300

S = 590 + 700r

590 + 700r = 660 - 300r

r = 07 I = S = 639

Add this development to your diagram and label as point B

e) (10 points) Explain the movement to the new equilibrium from point A to point B Start with at the same r savings does not equal investment Give the actual numbers At the same interest rate which is larger Y or C + I + G Use this expression to argue why interest rates changed the way they did When rates change explain what happens to saving and investment (be specific) and why

r = 04 S = 618 and I = 648S lt I Y - C - G lt I Y lt C + I + G2500 lt 2530SINCE ABSORPTION IS GREATER THAN Y r must rise to crowd out enough C and I to get back to equilibrium when r rises by 03 C falls by -700 x 03 = 21 I falls by 9 back to equilibrium where Y = C + I + G (2500 = 2500) or S = I (639 = 639)

f)(10 points) Are your results consistent with the conditions in the US economy since President Trumps election in November of 2016 Why or why not

Yes Investment has gone up given the huge corporate tax cut (t) and sky high animal spirits (AS)

Same with Consumption function - shifting up due to record breaking wealth (a) in the stock market and recording breaking consumer confidence (CC)

12

5 (60 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 = 460 ndash 200rw

Y = 2400T = 200G =500

China Initial Conditions

Cd = 500 + 5(YF ndash TF) ndash 300rw

Id = 400 ndash 200rw

Y = 2000T = 400G = 300

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

USA

S = 2400 - [400 + 5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + 5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 r = 06

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

5 (60 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 = 460 ndash 200rw

Y = 2400T = 200G =500

China Initial Conditions

Cd = 500 + 5(YF ndash TF) ndash 300rw

Id = 400 ndash 200rw

Y = 2000T = 400G = 300

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

USA

S = 2400 - [400 + 5(2400 - 200) - 300 r ] - 500

S = 400 + 300r

CHINA

S = 2000 - [500 + 5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[400 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-60 + 1000r = 0 r = 06

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

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(06) = 418I = 460 - 200(06) = 448

NX = -30

CHINA

S = 400 + 300(06) = 418I = 400 - 200(06) = 388

NX = + 30

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 absorption in each country to its income Explain USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y Absorption in the US is 2430 Y = 2400 Absorption in China is 1970 Y =2000

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

20 points for correct and completely labeled diagrams

14

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

We now have a change in conditions China experiences some economic growth and their output rises to 2100 All else remains the same

d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR CHINA

S = 2100 - [500 + 5(2100 - 400) - 300 r ] - 300

S = 450 + 300r

[400 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0

-10 + 1000r = 0 r = 01

USA

S = 400 + 300(01) = 403I = 460 - 200(01) = 458

NX = -55

CHINA

S = 450 + 300(01) = 453I = 400 - 200(01) = 398

NX = +55

e) (5 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

NO things are getting worse - we are spending even more beyond our means - trade deficit has risen from 30 to 55 US has NOT gone to AA

f)(10 points) We know that world output has gone up by 100 and we also know via the equation below that the worlds absorption has to rise by 100 (right hand side of the equation below) Explain where this 100 in additional output was absorbed in each country Use specific numbers

Yus + YChina = [C + I + G] US + [C + I + G] China

15

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)

Real interest rates have fallen by 05 from 06 to 01 As a result Consumption and Investment in both the US and China will rise for the US C rises by -300 x -05 = 15 I in US rises by 10 Same for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China due to higher output since mpc = 50 in China an increase of 100 in Y results in an increase in C by 50 Total increase = 100

16

• From the article The Fed Gets Optimistic (92618) that we discussed in class the Fed gave us some forward guidance as to the future path of the federal funds rate
• The Federal Open Market Committee raised short-term interest rates for the third time this year while signaling one more to come in December and perhaps three or four more next year That was no surprise More interesting is that the Fed is getting a little more optimistic about economic growth
• Some numbers The current target range for the Federal Funds rate is 2 - 225 One more quarter point rise in December will put the target range to 225 - 25 Four more in 2019 will put the range at 325 - 35 clearly higher than the current estimate of the neutral federal funds rate in the graphic from the WSJ above (Point B above = 3)