Exam 1 ndash Econ 304 ndash Chuderewicz ndash Fall 2014

Name ______________KEY________________ Last 4 (PSU ID) __________

PLEASE PUT THE FIRST TWO LETTERS OF YOUR LAST NAME ON TOP RIGHT HAND CORNER OF THIS COVER SHEET ndash THANKS AND GOOD LUCK

Total Points for exam = 240

Test time = 120 minutes

Approximately one minute for every two points

To help with time management if spreading time evenly

Question 1 = 60 points 30 minutes

Question 2 = 50 points 25 minutes

Question 31 = 35 points 17 minutes

Question 32 = 45 points 22 minutes

Question 4 = 50 points 25 minutes

1

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

1 (60 points total) This question was motivated by the comic below from October 4 2014

We have two consumers Dagwood and Dagwoods barber who we will refer to from this point on as The Barber Dagwood and The Barber both prefer to perfectly smooth consumption consistent with the lifetime theory of consumption The initial conditions are the same for both consumers and are as follows

Y (current income) = 300K a (current wealth) = 0 Yf (expected future income) = 150Kaf ( expected future wealth) = 100Kr (the current real rate of interest) = -05 (negative 5)

a) (5 points) Calculate Dagwood and The Barbers optimal consumption bundle showing all work Since conditions are exactly the same for both consumers you only need to do this calculation once

CA = [(1+ (-05))(300) + 150 + 100] (2+ (-05)) = 27436

THE BARBER af up by 100K= 200K

CB = [(1+ (-05))(300) + 150 + 200] ( 2+ (-05)) = 32564

r up to 10

DAGWOOD

CB = [(1+ 10)(300) + 150 + 100] (2+ 10) = 27619

THE BARBER

CC = [(1+10)(300) + 150 + 200] (2+ 10) = 3238

2

(20 points total) Now draw two completely labeled diagrams (the two period consumption model) depicting these initial optimal consumption bundles as points CA Please put the diagrams next to each other with the left diagram representing Dagwood and the right diagram representing The Barber Note that CA is exactly the same for both consumers

10 points for each correct and completely labeled diagram

As you can tell from the comic above The Barber is very optimistic about his 401K plan which is his retirement money - representing expected wealth = af As such The Barbers expected wealth has gone up to 200K (from 100K) Dagwood on the other hand is not so excited about the future since his retirement money is in bonds not stocks so his expectation of future wealth does not change

b) (5 points) Calculate The Barbers new optimal consumption bundle showing all work and label as point CB on the diagram representing The Barber

3

Given the most recent payroll report (below) and the long and variable effectiveness lag in monetary policy Janet Yellen and the Fed decide to raise real rates of interest to 10 (10) This is the new real rate of interest faced by both consumers

c) (5 points) Calculate Dagwoodrsquos new optimal consumption bundle depicting his new optimal consumption bundle as point CB

d) (5 points) Calculate The Barbers new optimal consumption bundle depicting his new optimal consumption bundle as point CC

4

e) (10 points) Compare the reaction of Dagwood and The Barber in terms of the change in their current period consumption given the rise in the real interest rate all else constant (this is after The Barber changes his af) Be sure to refer to the substitution and income effects and how they are similardifferent for each consumer

DAGWOOD - CONSUME MORE 27619 VS 27436 - SAVER CARES ABOUT FINANCING FUTURE CONSUMPTION THE MOST AND THEREFORE CARES MOST ABOUT THE FUTURE VALUE OF PRESENT RESOURCESFV = (1 + r) (Y + a) when r rises (-05) to 10 DAGWOOD IS RICHER - INCOME EFFECT SAYS CONSUME MORE

THE BARBER THE BORROWER CONSUME LESS - 3238 VS 32564 CARES MOST ABOUT THE PV OF FUTURE RESOURCES (TO FINANCE CURRENT CONSUMPTION) PV = (yF + aF) (1 + r) WHEN r RISES THE PV OF FUTURE RESOURCES FALL - THE BARBER IS POORER SHOULD CONSUME LESS

THE SUBSTITUTION EFFECT IS THE SAME FOR BOTH HIGHER r THE HIGHER THE COST OF PRESENT CONSUMPTION IN TERMS OF FUTURE CONSUMPTION SUBSTITUTE AWAY FROM CURRENT TO FUTURE CONSUMPTION - IN SUM SUBSTITUTION EFFECT IMPLIES CONSUME LESS TODAY

FOR DAGWOOD - INCOME AND SUB EFFECTS WORK IN OPPOSITE DIRECTION - INCOME EFFECT WINS

FOR THE BARBER - INCOME AND SUB EFFECTS WORK IN SAME DIRECTION

5

In the space below draw the savings functions for both consumers side by side as you did for the two period consumption model (Dagwood on left The Barber on right) NOTE IMPORTANTLY THAT I DREW BOTH SAVING FUNCTIONS ON SAME GRAPH SO BARBER IS NECESSARILY ON LEFT (THE BORROWER) AND DAGWOOD (THE SAVER) ON RIGHT

FOR THE BARBER

POINT A S = Y - C 300 - 32564 = - 2564POINT B S = Y - C 300 - 3238 = - 238

FOR DAGWOOD

POINT A S = Y - C 300 - 27436 = 2564POINT B S = Y - C 300 - 27619 = 2381

10 points total (5 points each) for correct and completely labeled diagrams

6

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

A brand new fishing pole costs 800 fishing hours (this is your output) and the rate of depreciation is 8 (008)

The real interest rate is 2 (02)

The expected marginal product of capital is given by

MPKf = 200 ndash 2K

Initially there is no tax on capital so tao (τ) = 0 but this will change

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

UC = (02 + 08) 800 = 80 FISHING HOURS

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

80 = 200 - 2K K = 60

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

7

A correctly drawn and completely labeled diagram is worth 10 pointsc) Now conditions change The following two shocks occur simultaneously

i) the government imposes a 20 tax on capital so tao (τ) goes from zero to 20 (20)

ii) the expected marginal product of capital changes and is now MPKf = 230 ndash 2K

Resolve for K and show as point B on your ucK diagram ( 5 points)UC = (02 + 08) 800 (1 - 20) = 100

100 = 230 - 2K K = 65

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

AT K = 60 THE FIRM IS NO LONGER MAXIMIZING PROFIT SINCE AT K = 60 UC UP TO 100 MPK UP TO 230 - 2 (60) = 110 SO AT K = 60 UC lt MPK 100 lt 110 BUY 5 MORE FISHING POLES TO LOWER MPK TO = 100 = UC = 100 AND GET BACK TO PROFIT MAXIMIZING

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

NEED TO GET USER COST UP TO 110 (MPK = 230 - 2(60) = 110 WHEN K = 60 (THE GOAL)

((r + 18) 800) (1 - 20) = 110solve for r r = 03

8

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

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

C

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

9

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

The following equations characterize a countryrsquos closed economy

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

where the initial values of A = 6 and K = 10

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

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

w = 6 x 10 - [20 + 9w]10w = 40 w = 4 N = 56 Y = 1792

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

10

(10 points for completely labeled and correct diagrams)

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

The labor supply changes and is now NS = 28 + 9w K goes down from 10 to 8

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons

5 CHOICES 1) LOWER EXPECTED INCOME2) LOWER WEALTH3) LOOSER IMMIGRATION LAWS4) MORE PARTICIPATION5) DEMOGRAPHICS - MORE PEOPLE ENTERING THE WORKING AGE POPULATION

c) (10 points) Given the change in NS and K repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 6 x 8 - [28 + 9w]10w = 20 w = 2 N = 46 Y = 1150

11

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

Before we start this problem put the initial Y as computed in part a) here ___1792_____

And the new Y (after the change in conditions) here ___1150________

Initial conditions in the goods market

Cd = 100 + 50(Y-T) ndash 500rId = 796 ndash 500rG = 100T= 100

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

S = 1792 - [100 + 50(1792 - 100) ndash 500r] - 100

S = 746 + 500r

746 + 500r = 796 ndash 500r

r = 05 S = I = 771

12

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

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

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

The desired investment function changes and is now Id = 455 ndash 500r

13

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

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

1 (60 points total) This question was motivated by the comic below from October 4 2014

We have two consumers Dagwood and Dagwoods barber who we will refer to from this point on as The Barber Dagwood and The Barber both prefer to perfectly smooth consumption consistent with the lifetime theory of consumption The initial conditions are the same for both consumers and are as follows

Y (current income) = 300K a (current wealth) = 0 Yf (expected future income) = 150Kaf ( expected future wealth) = 100Kr (the current real rate of interest) = -05 (negative 5)

a) (5 points) Calculate Dagwood and The Barbers optimal consumption bundle showing all work Since conditions are exactly the same for both consumers you only need to do this calculation once

CA = [(1+ (-05))(300) + 150 + 100] (2+ (-05)) = 27436

THE BARBER af up by 100K= 200K

CB = [(1+ (-05))(300) + 150 + 200] ( 2+ (-05)) = 32564

r up to 10

DAGWOOD

CB = [(1+ 10)(300) + 150 + 100] (2+ 10) = 27619

THE BARBER

CC = [(1+10)(300) + 150 + 200] (2+ 10) = 3238

2

(20 points total) Now draw two completely labeled diagrams (the two period consumption model) depicting these initial optimal consumption bundles as points CA Please put the diagrams next to each other with the left diagram representing Dagwood and the right diagram representing The Barber Note that CA is exactly the same for both consumers

10 points for each correct and completely labeled diagram

As you can tell from the comic above The Barber is very optimistic about his 401K plan which is his retirement money - representing expected wealth = af As such The Barbers expected wealth has gone up to 200K (from 100K) Dagwood on the other hand is not so excited about the future since his retirement money is in bonds not stocks so his expectation of future wealth does not change

b) (5 points) Calculate The Barbers new optimal consumption bundle showing all work and label as point CB on the diagram representing The Barber

3

Given the most recent payroll report (below) and the long and variable effectiveness lag in monetary policy Janet Yellen and the Fed decide to raise real rates of interest to 10 (10) This is the new real rate of interest faced by both consumers

c) (5 points) Calculate Dagwoodrsquos new optimal consumption bundle depicting his new optimal consumption bundle as point CB

d) (5 points) Calculate The Barbers new optimal consumption bundle depicting his new optimal consumption bundle as point CC

4

e) (10 points) Compare the reaction of Dagwood and The Barber in terms of the change in their current period consumption given the rise in the real interest rate all else constant (this is after The Barber changes his af) Be sure to refer to the substitution and income effects and how they are similardifferent for each consumer

DAGWOOD - CONSUME MORE 27619 VS 27436 - SAVER CARES ABOUT FINANCING FUTURE CONSUMPTION THE MOST AND THEREFORE CARES MOST ABOUT THE FUTURE VALUE OF PRESENT RESOURCESFV = (1 + r) (Y + a) when r rises (-05) to 10 DAGWOOD IS RICHER - INCOME EFFECT SAYS CONSUME MORE

THE BARBER THE BORROWER CONSUME LESS - 3238 VS 32564 CARES MOST ABOUT THE PV OF FUTURE RESOURCES (TO FINANCE CURRENT CONSUMPTION) PV = (yF + aF) (1 + r) WHEN r RISES THE PV OF FUTURE RESOURCES FALL - THE BARBER IS POORER SHOULD CONSUME LESS

THE SUBSTITUTION EFFECT IS THE SAME FOR BOTH HIGHER r THE HIGHER THE COST OF PRESENT CONSUMPTION IN TERMS OF FUTURE CONSUMPTION SUBSTITUTE AWAY FROM CURRENT TO FUTURE CONSUMPTION - IN SUM SUBSTITUTION EFFECT IMPLIES CONSUME LESS TODAY

FOR DAGWOOD - INCOME AND SUB EFFECTS WORK IN OPPOSITE DIRECTION - INCOME EFFECT WINS

FOR THE BARBER - INCOME AND SUB EFFECTS WORK IN SAME DIRECTION

5

In the space below draw the savings functions for both consumers side by side as you did for the two period consumption model (Dagwood on left The Barber on right) NOTE IMPORTANTLY THAT I DREW BOTH SAVING FUNCTIONS ON SAME GRAPH SO BARBER IS NECESSARILY ON LEFT (THE BORROWER) AND DAGWOOD (THE SAVER) ON RIGHT

FOR THE BARBER

POINT A S = Y - C 300 - 32564 = - 2564POINT B S = Y - C 300 - 3238 = - 238

FOR DAGWOOD

POINT A S = Y - C 300 - 27436 = 2564POINT B S = Y - C 300 - 27619 = 2381

10 points total (5 points each) for correct and completely labeled diagrams

6

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

A brand new fishing pole costs 800 fishing hours (this is your output) and the rate of depreciation is 8 (008)

The real interest rate is 2 (02)

The expected marginal product of capital is given by

MPKf = 200 ndash 2K

Initially there is no tax on capital so tao (τ) = 0 but this will change

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

UC = (02 + 08) 800 = 80 FISHING HOURS

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

80 = 200 - 2K K = 60

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

7

A correctly drawn and completely labeled diagram is worth 10 pointsc) Now conditions change The following two shocks occur simultaneously

i) the government imposes a 20 tax on capital so tao (τ) goes from zero to 20 (20)

ii) the expected marginal product of capital changes and is now MPKf = 230 ndash 2K

Resolve for K and show as point B on your ucK diagram ( 5 points)UC = (02 + 08) 800 (1 - 20) = 100

100 = 230 - 2K K = 65

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

AT K = 60 THE FIRM IS NO LONGER MAXIMIZING PROFIT SINCE AT K = 60 UC UP TO 100 MPK UP TO 230 - 2 (60) = 110 SO AT K = 60 UC lt MPK 100 lt 110 BUY 5 MORE FISHING POLES TO LOWER MPK TO = 100 = UC = 100 AND GET BACK TO PROFIT MAXIMIZING

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

NEED TO GET USER COST UP TO 110 (MPK = 230 - 2(60) = 110 WHEN K = 60 (THE GOAL)

((r + 18) 800) (1 - 20) = 110solve for r r = 03

8

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

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

C

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

9

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

The following equations characterize a countryrsquos closed economy

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

where the initial values of A = 6 and K = 10

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

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

w = 6 x 10 - [20 + 9w]10w = 40 w = 4 N = 56 Y = 1792

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

10

(10 points for completely labeled and correct diagrams)

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

The labor supply changes and is now NS = 28 + 9w K goes down from 10 to 8

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons

5 CHOICES 1) LOWER EXPECTED INCOME2) LOWER WEALTH3) LOOSER IMMIGRATION LAWS4) MORE PARTICIPATION5) DEMOGRAPHICS - MORE PEOPLE ENTERING THE WORKING AGE POPULATION

c) (10 points) Given the change in NS and K repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 6 x 8 - [28 + 9w]10w = 20 w = 2 N = 46 Y = 1150

11

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

Before we start this problem put the initial Y as computed in part a) here ___1792_____

And the new Y (after the change in conditions) here ___1150________

Initial conditions in the goods market

Cd = 100 + 50(Y-T) ndash 500rId = 796 ndash 500rG = 100T= 100

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

S = 1792 - [100 + 50(1792 - 100) ndash 500r] - 100

S = 746 + 500r

746 + 500r = 796 ndash 500r

r = 05 S = I = 771

12

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

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

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

The desired investment function changes and is now Id = 455 ndash 500r

13

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

(20 points total) Now draw two completely labeled diagrams (the two period consumption model) depicting these initial optimal consumption bundles as points CA Please put the diagrams next to each other with the left diagram representing Dagwood and the right diagram representing The Barber Note that CA is exactly the same for both consumers

10 points for each correct and completely labeled diagram

As you can tell from the comic above The Barber is very optimistic about his 401K plan which is his retirement money - representing expected wealth = af As such The Barbers expected wealth has gone up to 200K (from 100K) Dagwood on the other hand is not so excited about the future since his retirement money is in bonds not stocks so his expectation of future wealth does not change

b) (5 points) Calculate The Barbers new optimal consumption bundle showing all work and label as point CB on the diagram representing The Barber

3

Given the most recent payroll report (below) and the long and variable effectiveness lag in monetary policy Janet Yellen and the Fed decide to raise real rates of interest to 10 (10) This is the new real rate of interest faced by both consumers

c) (5 points) Calculate Dagwoodrsquos new optimal consumption bundle depicting his new optimal consumption bundle as point CB

d) (5 points) Calculate The Barbers new optimal consumption bundle depicting his new optimal consumption bundle as point CC

4

e) (10 points) Compare the reaction of Dagwood and The Barber in terms of the change in their current period consumption given the rise in the real interest rate all else constant (this is after The Barber changes his af) Be sure to refer to the substitution and income effects and how they are similardifferent for each consumer

DAGWOOD - CONSUME MORE 27619 VS 27436 - SAVER CARES ABOUT FINANCING FUTURE CONSUMPTION THE MOST AND THEREFORE CARES MOST ABOUT THE FUTURE VALUE OF PRESENT RESOURCESFV = (1 + r) (Y + a) when r rises (-05) to 10 DAGWOOD IS RICHER - INCOME EFFECT SAYS CONSUME MORE

THE BARBER THE BORROWER CONSUME LESS - 3238 VS 32564 CARES MOST ABOUT THE PV OF FUTURE RESOURCES (TO FINANCE CURRENT CONSUMPTION) PV = (yF + aF) (1 + r) WHEN r RISES THE PV OF FUTURE RESOURCES FALL - THE BARBER IS POORER SHOULD CONSUME LESS

THE SUBSTITUTION EFFECT IS THE SAME FOR BOTH HIGHER r THE HIGHER THE COST OF PRESENT CONSUMPTION IN TERMS OF FUTURE CONSUMPTION SUBSTITUTE AWAY FROM CURRENT TO FUTURE CONSUMPTION - IN SUM SUBSTITUTION EFFECT IMPLIES CONSUME LESS TODAY

FOR DAGWOOD - INCOME AND SUB EFFECTS WORK IN OPPOSITE DIRECTION - INCOME EFFECT WINS

FOR THE BARBER - INCOME AND SUB EFFECTS WORK IN SAME DIRECTION

5

In the space below draw the savings functions for both consumers side by side as you did for the two period consumption model (Dagwood on left The Barber on right) NOTE IMPORTANTLY THAT I DREW BOTH SAVING FUNCTIONS ON SAME GRAPH SO BARBER IS NECESSARILY ON LEFT (THE BORROWER) AND DAGWOOD (THE SAVER) ON RIGHT

FOR THE BARBER

POINT A S = Y - C 300 - 32564 = - 2564POINT B S = Y - C 300 - 3238 = - 238

FOR DAGWOOD

POINT A S = Y - C 300 - 27436 = 2564POINT B S = Y - C 300 - 27619 = 2381

10 points total (5 points each) for correct and completely labeled diagrams

6

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

A brand new fishing pole costs 800 fishing hours (this is your output) and the rate of depreciation is 8 (008)

The real interest rate is 2 (02)

The expected marginal product of capital is given by

MPKf = 200 ndash 2K

Initially there is no tax on capital so tao (τ) = 0 but this will change

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

UC = (02 + 08) 800 = 80 FISHING HOURS

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

80 = 200 - 2K K = 60

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

7

A correctly drawn and completely labeled diagram is worth 10 pointsc) Now conditions change The following two shocks occur simultaneously

i) the government imposes a 20 tax on capital so tao (τ) goes from zero to 20 (20)

ii) the expected marginal product of capital changes and is now MPKf = 230 ndash 2K

Resolve for K and show as point B on your ucK diagram ( 5 points)UC = (02 + 08) 800 (1 - 20) = 100

100 = 230 - 2K K = 65

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

AT K = 60 THE FIRM IS NO LONGER MAXIMIZING PROFIT SINCE AT K = 60 UC UP TO 100 MPK UP TO 230 - 2 (60) = 110 SO AT K = 60 UC lt MPK 100 lt 110 BUY 5 MORE FISHING POLES TO LOWER MPK TO = 100 = UC = 100 AND GET BACK TO PROFIT MAXIMIZING

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

NEED TO GET USER COST UP TO 110 (MPK = 230 - 2(60) = 110 WHEN K = 60 (THE GOAL)

((r + 18) 800) (1 - 20) = 110solve for r r = 03

8

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

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

C

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

9

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

The following equations characterize a countryrsquos closed economy

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

where the initial values of A = 6 and K = 10

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

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

w = 6 x 10 - [20 + 9w]10w = 40 w = 4 N = 56 Y = 1792

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

10

(10 points for completely labeled and correct diagrams)

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

The labor supply changes and is now NS = 28 + 9w K goes down from 10 to 8

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons

5 CHOICES 1) LOWER EXPECTED INCOME2) LOWER WEALTH3) LOOSER IMMIGRATION LAWS4) MORE PARTICIPATION5) DEMOGRAPHICS - MORE PEOPLE ENTERING THE WORKING AGE POPULATION

c) (10 points) Given the change in NS and K repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 6 x 8 - [28 + 9w]10w = 20 w = 2 N = 46 Y = 1150

11

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

Before we start this problem put the initial Y as computed in part a) here ___1792_____

And the new Y (after the change in conditions) here ___1150________

Initial conditions in the goods market

Cd = 100 + 50(Y-T) ndash 500rId = 796 ndash 500rG = 100T= 100

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

S = 1792 - [100 + 50(1792 - 100) ndash 500r] - 100

S = 746 + 500r

746 + 500r = 796 ndash 500r

r = 05 S = I = 771

12

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

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

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

The desired investment function changes and is now Id = 455 ndash 500r

13

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

Given the most recent payroll report (below) and the long and variable effectiveness lag in monetary policy Janet Yellen and the Fed decide to raise real rates of interest to 10 (10) This is the new real rate of interest faced by both consumers

c) (5 points) Calculate Dagwoodrsquos new optimal consumption bundle depicting his new optimal consumption bundle as point CB

d) (5 points) Calculate The Barbers new optimal consumption bundle depicting his new optimal consumption bundle as point CC

4

e) (10 points) Compare the reaction of Dagwood and The Barber in terms of the change in their current period consumption given the rise in the real interest rate all else constant (this is after The Barber changes his af) Be sure to refer to the substitution and income effects and how they are similardifferent for each consumer

DAGWOOD - CONSUME MORE 27619 VS 27436 - SAVER CARES ABOUT FINANCING FUTURE CONSUMPTION THE MOST AND THEREFORE CARES MOST ABOUT THE FUTURE VALUE OF PRESENT RESOURCESFV = (1 + r) (Y + a) when r rises (-05) to 10 DAGWOOD IS RICHER - INCOME EFFECT SAYS CONSUME MORE

THE BARBER THE BORROWER CONSUME LESS - 3238 VS 32564 CARES MOST ABOUT THE PV OF FUTURE RESOURCES (TO FINANCE CURRENT CONSUMPTION) PV = (yF + aF) (1 + r) WHEN r RISES THE PV OF FUTURE RESOURCES FALL - THE BARBER IS POORER SHOULD CONSUME LESS

THE SUBSTITUTION EFFECT IS THE SAME FOR BOTH HIGHER r THE HIGHER THE COST OF PRESENT CONSUMPTION IN TERMS OF FUTURE CONSUMPTION SUBSTITUTE AWAY FROM CURRENT TO FUTURE CONSUMPTION - IN SUM SUBSTITUTION EFFECT IMPLIES CONSUME LESS TODAY

FOR DAGWOOD - INCOME AND SUB EFFECTS WORK IN OPPOSITE DIRECTION - INCOME EFFECT WINS

FOR THE BARBER - INCOME AND SUB EFFECTS WORK IN SAME DIRECTION

5

In the space below draw the savings functions for both consumers side by side as you did for the two period consumption model (Dagwood on left The Barber on right) NOTE IMPORTANTLY THAT I DREW BOTH SAVING FUNCTIONS ON SAME GRAPH SO BARBER IS NECESSARILY ON LEFT (THE BORROWER) AND DAGWOOD (THE SAVER) ON RIGHT

FOR THE BARBER

POINT A S = Y - C 300 - 32564 = - 2564POINT B S = Y - C 300 - 3238 = - 238

FOR DAGWOOD

POINT A S = Y - C 300 - 27436 = 2564POINT B S = Y - C 300 - 27619 = 2381

10 points total (5 points each) for correct and completely labeled diagrams

6

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

A brand new fishing pole costs 800 fishing hours (this is your output) and the rate of depreciation is 8 (008)

The real interest rate is 2 (02)

The expected marginal product of capital is given by

MPKf = 200 ndash 2K

Initially there is no tax on capital so tao (τ) = 0 but this will change

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

UC = (02 + 08) 800 = 80 FISHING HOURS

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

80 = 200 - 2K K = 60

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

7

A correctly drawn and completely labeled diagram is worth 10 pointsc) Now conditions change The following two shocks occur simultaneously

i) the government imposes a 20 tax on capital so tao (τ) goes from zero to 20 (20)

ii) the expected marginal product of capital changes and is now MPKf = 230 ndash 2K

Resolve for K and show as point B on your ucK diagram ( 5 points)UC = (02 + 08) 800 (1 - 20) = 100

100 = 230 - 2K K = 65

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

AT K = 60 THE FIRM IS NO LONGER MAXIMIZING PROFIT SINCE AT K = 60 UC UP TO 100 MPK UP TO 230 - 2 (60) = 110 SO AT K = 60 UC lt MPK 100 lt 110 BUY 5 MORE FISHING POLES TO LOWER MPK TO = 100 = UC = 100 AND GET BACK TO PROFIT MAXIMIZING

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

NEED TO GET USER COST UP TO 110 (MPK = 230 - 2(60) = 110 WHEN K = 60 (THE GOAL)

((r + 18) 800) (1 - 20) = 110solve for r r = 03

8

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

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

C

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

9

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

The following equations characterize a countryrsquos closed economy

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

where the initial values of A = 6 and K = 10

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

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

w = 6 x 10 - [20 + 9w]10w = 40 w = 4 N = 56 Y = 1792

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

10

(10 points for completely labeled and correct diagrams)

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

The labor supply changes and is now NS = 28 + 9w K goes down from 10 to 8

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons

5 CHOICES 1) LOWER EXPECTED INCOME2) LOWER WEALTH3) LOOSER IMMIGRATION LAWS4) MORE PARTICIPATION5) DEMOGRAPHICS - MORE PEOPLE ENTERING THE WORKING AGE POPULATION

c) (10 points) Given the change in NS and K repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 6 x 8 - [28 + 9w]10w = 20 w = 2 N = 46 Y = 1150

11

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

Before we start this problem put the initial Y as computed in part a) here ___1792_____

And the new Y (after the change in conditions) here ___1150________

Initial conditions in the goods market

Cd = 100 + 50(Y-T) ndash 500rId = 796 ndash 500rG = 100T= 100

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

S = 1792 - [100 + 50(1792 - 100) ndash 500r] - 100

S = 746 + 500r

746 + 500r = 796 ndash 500r

r = 05 S = I = 771

12

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

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

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

The desired investment function changes and is now Id = 455 ndash 500r

13

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

e) (10 points) Compare the reaction of Dagwood and The Barber in terms of the change in their current period consumption given the rise in the real interest rate all else constant (this is after The Barber changes his af) Be sure to refer to the substitution and income effects and how they are similardifferent for each consumer

DAGWOOD - CONSUME MORE 27619 VS 27436 - SAVER CARES ABOUT FINANCING FUTURE CONSUMPTION THE MOST AND THEREFORE CARES MOST ABOUT THE FUTURE VALUE OF PRESENT RESOURCESFV = (1 + r) (Y + a) when r rises (-05) to 10 DAGWOOD IS RICHER - INCOME EFFECT SAYS CONSUME MORE

THE BARBER THE BORROWER CONSUME LESS - 3238 VS 32564 CARES MOST ABOUT THE PV OF FUTURE RESOURCES (TO FINANCE CURRENT CONSUMPTION) PV = (yF + aF) (1 + r) WHEN r RISES THE PV OF FUTURE RESOURCES FALL - THE BARBER IS POORER SHOULD CONSUME LESS

THE SUBSTITUTION EFFECT IS THE SAME FOR BOTH HIGHER r THE HIGHER THE COST OF PRESENT CONSUMPTION IN TERMS OF FUTURE CONSUMPTION SUBSTITUTE AWAY FROM CURRENT TO FUTURE CONSUMPTION - IN SUM SUBSTITUTION EFFECT IMPLIES CONSUME LESS TODAY

FOR DAGWOOD - INCOME AND SUB EFFECTS WORK IN OPPOSITE DIRECTION - INCOME EFFECT WINS

FOR THE BARBER - INCOME AND SUB EFFECTS WORK IN SAME DIRECTION

5

In the space below draw the savings functions for both consumers side by side as you did for the two period consumption model (Dagwood on left The Barber on right) NOTE IMPORTANTLY THAT I DREW BOTH SAVING FUNCTIONS ON SAME GRAPH SO BARBER IS NECESSARILY ON LEFT (THE BORROWER) AND DAGWOOD (THE SAVER) ON RIGHT

FOR THE BARBER

POINT A S = Y - C 300 - 32564 = - 2564POINT B S = Y - C 300 - 3238 = - 238

FOR DAGWOOD

POINT A S = Y - C 300 - 27436 = 2564POINT B S = Y - C 300 - 27619 = 2381

10 points total (5 points each) for correct and completely labeled diagrams

6

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

A brand new fishing pole costs 800 fishing hours (this is your output) and the rate of depreciation is 8 (008)

The real interest rate is 2 (02)

The expected marginal product of capital is given by

MPKf = 200 ndash 2K

Initially there is no tax on capital so tao (τ) = 0 but this will change

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

UC = (02 + 08) 800 = 80 FISHING HOURS

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

80 = 200 - 2K K = 60

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

7

A correctly drawn and completely labeled diagram is worth 10 pointsc) Now conditions change The following two shocks occur simultaneously

i) the government imposes a 20 tax on capital so tao (τ) goes from zero to 20 (20)

ii) the expected marginal product of capital changes and is now MPKf = 230 ndash 2K

Resolve for K and show as point B on your ucK diagram ( 5 points)UC = (02 + 08) 800 (1 - 20) = 100

100 = 230 - 2K K = 65

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

AT K = 60 THE FIRM IS NO LONGER MAXIMIZING PROFIT SINCE AT K = 60 UC UP TO 100 MPK UP TO 230 - 2 (60) = 110 SO AT K = 60 UC lt MPK 100 lt 110 BUY 5 MORE FISHING POLES TO LOWER MPK TO = 100 = UC = 100 AND GET BACK TO PROFIT MAXIMIZING

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

NEED TO GET USER COST UP TO 110 (MPK = 230 - 2(60) = 110 WHEN K = 60 (THE GOAL)

((r + 18) 800) (1 - 20) = 110solve for r r = 03

8

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

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

C

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

9

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

The following equations characterize a countryrsquos closed economy

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

where the initial values of A = 6 and K = 10

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

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

w = 6 x 10 - [20 + 9w]10w = 40 w = 4 N = 56 Y = 1792

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

10

(10 points for completely labeled and correct diagrams)

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

The labor supply changes and is now NS = 28 + 9w K goes down from 10 to 8

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons

5 CHOICES 1) LOWER EXPECTED INCOME2) LOWER WEALTH3) LOOSER IMMIGRATION LAWS4) MORE PARTICIPATION5) DEMOGRAPHICS - MORE PEOPLE ENTERING THE WORKING AGE POPULATION

c) (10 points) Given the change in NS and K repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 6 x 8 - [28 + 9w]10w = 20 w = 2 N = 46 Y = 1150

11

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

Before we start this problem put the initial Y as computed in part a) here ___1792_____

And the new Y (after the change in conditions) here ___1150________

Initial conditions in the goods market

Cd = 100 + 50(Y-T) ndash 500rId = 796 ndash 500rG = 100T= 100

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

S = 1792 - [100 + 50(1792 - 100) ndash 500r] - 100

S = 746 + 500r

746 + 500r = 796 ndash 500r

r = 05 S = I = 771

12

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

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

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

The desired investment function changes and is now Id = 455 ndash 500r

13

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

In the space below draw the savings functions for both consumers side by side as you did for the two period consumption model (Dagwood on left The Barber on right) NOTE IMPORTANTLY THAT I DREW BOTH SAVING FUNCTIONS ON SAME GRAPH SO BARBER IS NECESSARILY ON LEFT (THE BORROWER) AND DAGWOOD (THE SAVER) ON RIGHT

FOR THE BARBER

POINT A S = Y - C 300 - 32564 = - 2564POINT B S = Y - C 300 - 3238 = - 238

FOR DAGWOOD

POINT A S = Y - C 300 - 27436 = 2564POINT B S = Y - C 300 - 27619 = 2381

10 points total (5 points each) for correct and completely labeled diagrams

6

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

A brand new fishing pole costs 800 fishing hours (this is your output) and the rate of depreciation is 8 (008)

The real interest rate is 2 (02)

The expected marginal product of capital is given by

MPKf = 200 ndash 2K

Initially there is no tax on capital so tao (τ) = 0 but this will change

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

UC = (02 + 08) 800 = 80 FISHING HOURS

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

80 = 200 - 2K K = 60

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

7

A correctly drawn and completely labeled diagram is worth 10 pointsc) Now conditions change The following two shocks occur simultaneously

i) the government imposes a 20 tax on capital so tao (τ) goes from zero to 20 (20)

ii) the expected marginal product of capital changes and is now MPKf = 230 ndash 2K

Resolve for K and show as point B on your ucK diagram ( 5 points)UC = (02 + 08) 800 (1 - 20) = 100

100 = 230 - 2K K = 65

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

AT K = 60 THE FIRM IS NO LONGER MAXIMIZING PROFIT SINCE AT K = 60 UC UP TO 100 MPK UP TO 230 - 2 (60) = 110 SO AT K = 60 UC lt MPK 100 lt 110 BUY 5 MORE FISHING POLES TO LOWER MPK TO = 100 = UC = 100 AND GET BACK TO PROFIT MAXIMIZING

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

NEED TO GET USER COST UP TO 110 (MPK = 230 - 2(60) = 110 WHEN K = 60 (THE GOAL)

((r + 18) 800) (1 - 20) = 110solve for r r = 03

8

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

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

C

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

9

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

The following equations characterize a countryrsquos closed economy

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

where the initial values of A = 6 and K = 10

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

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

w = 6 x 10 - [20 + 9w]10w = 40 w = 4 N = 56 Y = 1792

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

10

(10 points for completely labeled and correct diagrams)

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

The labor supply changes and is now NS = 28 + 9w K goes down from 10 to 8

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons

5 CHOICES 1) LOWER EXPECTED INCOME2) LOWER WEALTH3) LOOSER IMMIGRATION LAWS4) MORE PARTICIPATION5) DEMOGRAPHICS - MORE PEOPLE ENTERING THE WORKING AGE POPULATION

c) (10 points) Given the change in NS and K repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 6 x 8 - [28 + 9w]10w = 20 w = 2 N = 46 Y = 1150

11

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

Before we start this problem put the initial Y as computed in part a) here ___1792_____

And the new Y (after the change in conditions) here ___1150________

Initial conditions in the goods market

Cd = 100 + 50(Y-T) ndash 500rId = 796 ndash 500rG = 100T= 100

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

S = 1792 - [100 + 50(1792 - 100) ndash 500r] - 100

S = 746 + 500r

746 + 500r = 796 ndash 500r

r = 05 S = I = 771

12

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

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

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

The desired investment function changes and is now Id = 455 ndash 500r

13

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

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

A brand new fishing pole costs 800 fishing hours (this is your output) and the rate of depreciation is 8 (008)

The real interest rate is 2 (02)

The expected marginal product of capital is given by

MPKf = 200 ndash 2K

Initially there is no tax on capital so tao (τ) = 0 but this will change

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

UC = (02 + 08) 800 = 80 FISHING HOURS

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

80 = 200 - 2K K = 60

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

7

A correctly drawn and completely labeled diagram is worth 10 pointsc) Now conditions change The following two shocks occur simultaneously

i) the government imposes a 20 tax on capital so tao (τ) goes from zero to 20 (20)

ii) the expected marginal product of capital changes and is now MPKf = 230 ndash 2K

Resolve for K and show as point B on your ucK diagram ( 5 points)UC = (02 + 08) 800 (1 - 20) = 100

100 = 230 - 2K K = 65

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

AT K = 60 THE FIRM IS NO LONGER MAXIMIZING PROFIT SINCE AT K = 60 UC UP TO 100 MPK UP TO 230 - 2 (60) = 110 SO AT K = 60 UC lt MPK 100 lt 110 BUY 5 MORE FISHING POLES TO LOWER MPK TO = 100 = UC = 100 AND GET BACK TO PROFIT MAXIMIZING

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

NEED TO GET USER COST UP TO 110 (MPK = 230 - 2(60) = 110 WHEN K = 60 (THE GOAL)

((r + 18) 800) (1 - 20) = 110solve for r r = 03

8

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

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

C

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

9

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

The following equations characterize a countryrsquos closed economy

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

where the initial values of A = 6 and K = 10

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

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

w = 6 x 10 - [20 + 9w]10w = 40 w = 4 N = 56 Y = 1792

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

10

(10 points for completely labeled and correct diagrams)

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

The labor supply changes and is now NS = 28 + 9w K goes down from 10 to 8

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons

5 CHOICES 1) LOWER EXPECTED INCOME2) LOWER WEALTH3) LOOSER IMMIGRATION LAWS4) MORE PARTICIPATION5) DEMOGRAPHICS - MORE PEOPLE ENTERING THE WORKING AGE POPULATION

c) (10 points) Given the change in NS and K repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 6 x 8 - [28 + 9w]10w = 20 w = 2 N = 46 Y = 1150

11

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

Before we start this problem put the initial Y as computed in part a) here ___1792_____

And the new Y (after the change in conditions) here ___1150________

Initial conditions in the goods market

Cd = 100 + 50(Y-T) ndash 500rId = 796 ndash 500rG = 100T= 100

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

S = 1792 - [100 + 50(1792 - 100) ndash 500r] - 100

S = 746 + 500r

746 + 500r = 796 ndash 500r

r = 05 S = I = 771

12

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

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

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

The desired investment function changes and is now Id = 455 ndash 500r

13

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

A correctly drawn and completely labeled diagram is worth 10 pointsc) Now conditions change The following two shocks occur simultaneously

i) the government imposes a 20 tax on capital so tao (τ) goes from zero to 20 (20)

ii) the expected marginal product of capital changes and is now MPKf = 230 ndash 2K

Resolve for K and show as point B on your ucK diagram ( 5 points)UC = (02 + 08) 800 (1 - 20) = 100

100 = 230 - 2K K = 65

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

AT K = 60 THE FIRM IS NO LONGER MAXIMIZING PROFIT SINCE AT K = 60 UC UP TO 100 MPK UP TO 230 - 2 (60) = 110 SO AT K = 60 UC lt MPK 100 lt 110 BUY 5 MORE FISHING POLES TO LOWER MPK TO = 100 = UC = 100 AND GET BACK TO PROFIT MAXIMIZING

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

NEED TO GET USER COST UP TO 110 (MPK = 230 - 2(60) = 110 WHEN K = 60 (THE GOAL)

((r + 18) 800) (1 - 20) = 110solve for r r = 03

8

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

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

C

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

9

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

The following equations characterize a countryrsquos closed economy

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

where the initial values of A = 6 and K = 10

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

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

w = 6 x 10 - [20 + 9w]10w = 40 w = 4 N = 56 Y = 1792

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

10

(10 points for completely labeled and correct diagrams)

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

The labor supply changes and is now NS = 28 + 9w K goes down from 10 to 8

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons

5 CHOICES 1) LOWER EXPECTED INCOME2) LOWER WEALTH3) LOOSER IMMIGRATION LAWS4) MORE PARTICIPATION5) DEMOGRAPHICS - MORE PEOPLE ENTERING THE WORKING AGE POPULATION

c) (10 points) Given the change in NS and K repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 6 x 8 - [28 + 9w]10w = 20 w = 2 N = 46 Y = 1150

11

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

Before we start this problem put the initial Y as computed in part a) here ___1792_____

And the new Y (after the change in conditions) here ___1150________

Initial conditions in the goods market

Cd = 100 + 50(Y-T) ndash 500rId = 796 ndash 500rG = 100T= 100

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

S = 1792 - [100 + 50(1792 - 100) ndash 500r] - 100

S = 746 + 500r

746 + 500r = 796 ndash 500r

r = 05 S = I = 771

12

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

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

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

The desired investment function changes and is now Id = 455 ndash 500r

13

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

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

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

C

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

9

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

The following equations characterize a countryrsquos closed economy

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

where the initial values of A = 6 and K = 10

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

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

w = 6 x 10 - [20 + 9w]10w = 40 w = 4 N = 56 Y = 1792

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

10

(10 points for completely labeled and correct diagrams)

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

The labor supply changes and is now NS = 28 + 9w K goes down from 10 to 8

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons

5 CHOICES 1) LOWER EXPECTED INCOME2) LOWER WEALTH3) LOOSER IMMIGRATION LAWS4) MORE PARTICIPATION5) DEMOGRAPHICS - MORE PEOPLE ENTERING THE WORKING AGE POPULATION

c) (10 points) Given the change in NS and K repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 6 x 8 - [28 + 9w]10w = 20 w = 2 N = 46 Y = 1150

11

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

Before we start this problem put the initial Y as computed in part a) here ___1792_____

And the new Y (after the change in conditions) here ___1150________

Initial conditions in the goods market

Cd = 100 + 50(Y-T) ndash 500rId = 796 ndash 500rG = 100T= 100

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

S = 1792 - [100 + 50(1792 - 100) ndash 500r] - 100

S = 746 + 500r

746 + 500r = 796 ndash 500r

r = 05 S = I = 771

12

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

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

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

The desired investment function changes and is now Id = 455 ndash 500r

13

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

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

The following equations characterize a countryrsquos closed economy

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

where the initial values of A = 6 and K = 10

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

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

w = 6 x 10 - [20 + 9w]10w = 40 w = 4 N = 56 Y = 1792

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

10

(10 points for completely labeled and correct diagrams)

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

The labor supply changes and is now NS = 28 + 9w K goes down from 10 to 8

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons

5 CHOICES 1) LOWER EXPECTED INCOME2) LOWER WEALTH3) LOOSER IMMIGRATION LAWS4) MORE PARTICIPATION5) DEMOGRAPHICS - MORE PEOPLE ENTERING THE WORKING AGE POPULATION

c) (10 points) Given the change in NS and K repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 6 x 8 - [28 + 9w]10w = 20 w = 2 N = 46 Y = 1150

11

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

Before we start this problem put the initial Y as computed in part a) here ___1792_____

And the new Y (after the change in conditions) here ___1150________

Initial conditions in the goods market

Cd = 100 + 50(Y-T) ndash 500rId = 796 ndash 500rG = 100T= 100

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

S = 1792 - [100 + 50(1792 - 100) ndash 500r] - 100

S = 746 + 500r

746 + 500r = 796 ndash 500r

r = 05 S = I = 771

12

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

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

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

The desired investment function changes and is now Id = 455 ndash 500r

13

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

(10 points for completely labeled and correct diagrams)

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

The labor supply changes and is now NS = 28 + 9w K goes down from 10 to 8

b) (5 points) What could cause such a change in labor supply Please give two specific and well supported reasons

5 CHOICES 1) LOWER EXPECTED INCOME2) LOWER WEALTH3) LOOSER IMMIGRATION LAWS4) MORE PARTICIPATION5) DEMOGRAPHICS - MORE PEOPLE ENTERING THE WORKING AGE POPULATION

c) (10 points) Given the change in NS and K repeat part a) (ie find the equilibrium levels of the real wage employment and output) Add these results to your labor market and production function diagrams respectively and label as point(s) B Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function

w = 6 x 8 - [28 + 9w]10w = 20 w = 2 N = 46 Y = 1150

11

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

Before we start this problem put the initial Y as computed in part a) here ___1792_____

And the new Y (after the change in conditions) here ___1150________

Initial conditions in the goods market

Cd = 100 + 50(Y-T) ndash 500rId = 796 ndash 500rG = 100T= 100

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

S = 1792 - [100 + 50(1792 - 100) ndash 500r] - 100

S = 746 + 500r

746 + 500r = 796 ndash 500r

r = 05 S = I = 771

12

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

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

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

The desired investment function changes and is now Id = 455 ndash 500r

13

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

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

Before we start this problem put the initial Y as computed in part a) here ___1792_____

And the new Y (after the change in conditions) here ___1150________

Initial conditions in the goods market

Cd = 100 + 50(Y-T) ndash 500rId = 796 ndash 500rG = 100T= 100

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

S = 1792 - [100 + 50(1792 - 100) ndash 500r] - 100

S = 746 + 500r

746 + 500r = 796 ndash 500r

r = 05 S = I = 771

12

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

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

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

The desired investment function changes and is now Id = 455 ndash 500r

13

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

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

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

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

The desired investment function changes and is now Id = 455 ndash 500r

13

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

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

5 CHOICES

1) HIGHER τ

2) HIGHER PK

3) LOWER ITC

4) LOWER A

5) LOWER AS

f) (10 points) Given these changes (ie changes in K Y and Id note the new Id = 455 ndash 500r) calculate the new equilibrium levels of the real interest rate desired savings and investment Please add this new equilibrium point to your diagram and label as point B

S = 1150 - [100 + 50(1150 - 100) ndash 500r] - 100

S = 425 + 500r

425 + 500r = 455 ndash 500r

r = 03 S = I = 440

g) (10 points) Considering this entire problem are your results consistent with the Great Recession - why or why not Please be as specific as possible with regard to the changes in your savings function investment function and the change in labor supply Be sure to connect what happened to these 3 functions in this problem to the real world

SAVINGS FUNCTION - YES OUTPUT FELL DURING GREAT RECESSION CONSISTENT WITH THIS EXAMPLE

INVESTMENT FUNCTION SHIFTING LEFT BIG TIME YES BIG DECREASE IN ANIMAL SPIRITS DURING GR

LABOR SUPPLY YES PEOPLE LOST LOTS OF WEALTH IN STOCKS AND REAL ESTATE - WORK MORE AT ANY GIVEN REAL WAGE

14

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

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

USA Initial Conditions

Cd = 280 + 04(Y-T) ndash 200rw

Id = 150 ndash 200rw

Y = 1000T = 200G =325

China Initial Conditions

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

IdF = 225 ndash 300rw

YF = 1500TF = 300GF = 300

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

USAS = 1000 - [ 280 - 4(1000 - 200) - 200 r ] - 325S = 75 + 200 r

CHINAS = 1500 - [ 480 - 4(1500 - 300) - 300 r ] - 300S = 240 + 300 r

[75 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 60 = 0 rw = 06

15

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

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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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

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WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

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

USAS = 75 + 200 (06)S = 87 I = 150 ndash 200 (06)I = 138 NX = -51

CHINAS = 240 + 300 (06)S = 258I = 225 ndash 300 (06)I = 207 NX = 51

c) Which country is lsquospending beyond its meansrsquo and which country is the saver What exactly do we mean by the phrase lsquospending beyond its meansrsquo in this context Be sure to define and use the word absorption in your answer and compare the level of absorption in each country to its income Explain (10 points) USA IS SPENDING BEYOND ITS MEANS WHICH MEANS ABSORPTION (C + I + G) IS GREATER THAN INCOME (Y)

ABSORPTION IN USA

Cd = 280 + 04(100 - 200) ndash 200 (06) = 588Id = 150 ndash 200 (06) = 138G = 325

C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)

ABSORPTION IN CHINA

CdF = 480 + 4(1500 - 300) ndash 300 (06) = 942

IdF = 225 ndash 300 (06) = 207

G = 300

C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)

16

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

18

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 (there are four point Arsquos two on each diagram) Be sure to label diagram completely

10 points for correct and completely labeled diagrams

Now the US experiences a positive productivity shock As a result output in the US goes up to 1050

d) (10 points) Resolve for the world real interest rate that clears the international goods markets and add these results to your diagram labeling this new equilibrium as points B (there are four of them) (10 points)

USAS = 1050 - [ 280 - 4(1050 - 200) - 200 r ] - 325S = 105 + 200 r

[105 + 200 rw ] - [150 ndash 200 rw ] + [ 240 + 300 rw] - [225 ndash 300 rw] = 0

1000 rw - 30 = 0 rw = 03

17

WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

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WORK FOR POINTS B

USAS = 105 + 200 (03)S = 111 I = 150 ndash 200 (03)I = 144 NX = -33

CHINAS = 240 + 300 (03)S = 249I = 225 ndash 300 (03)I = 216 NX = 33

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

YES AND NO - WE ARE MOVING IN THE RIGHT DIRECTION AS IN GOING TO AA - GETTING CLOSER TO SPENDING WITHIN OUR MEANS TRADE BALANCE WENT FROM - 51 TO - 33 BUT WE ARE STILL SPENDING BEYOND OUR MEANS SINCE ABSORPTION STILL EXCEEDS INCOME (1033 gt 1000)

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