a) (5 points) Calculate Dagwood and The Barber's optimal consumption bundle showing all work. Since conditions are exactly the same for both consumers, you only need to do this calculation once.
C*A = [(1+ (-.05))(300) + 150 + 100] / (2+ (-.05)) = 274.36
THE BARBER af up by 100K.....= 200K
C*B = [(1+ (-.05))(300) + 150 + 200] /( 2+ (-.05)) = 325.64
r up to 10%
DAGWOOD
C*B = [(1+ .10)(300) + 150 + 100] / (2+ .10) = 276.19
THE BARBER
C*C = [(1+.10)(300) + 150 + 200] / (2+ .10) = 323.8
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 similar/different for each consumer.
DAGWOOD - CONSUME MORE 276.19 VS 274.36 - SAVER CARES ABOUT FINANCING FUTURE CONSUMPTION THE MOST AND THEREFORE CARES MOST ABOUT THE FUTURE VALUE OF PRESENT RESOURCES:
FV = (1 + r) (Y + a), when r rises (-.05) to .10, DAGWOOD IS RICHER -
FV went from (1 + (-.05))(300) = 285 to (1 + .10)(300) = 330! INCOME EFFECT 'SAYS' CONSUME MORE
THE BARBER, THE BORROWER, CONSUME LESS - 323.8 VS 325.64, 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 -PV = (150 + 200)/ (1 + (-.05)) = 368.4 to (150 + 200)/ (1 + .10) = 318.18 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
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 RIGHT, The Barber on LEFT
.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 - 325.64 = - 25.64
POINT B:S = Y - C ...... 300 - 323.8 = - 23.8
FOR DAGWOOD
POINT A: S = Y - C ...... 300 - 274.36 = 25.64
POINT B: S = Y - C ...... 300 - 276.19 = 23.81
10 points total (5 points each) for correct and completely labeled diagrams
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) 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 uc/K graph depicting the state of affairs and label this initial profit maximizing condition as point A.
A correctly drawn and completely labeled diagram is worth 10 points
c) 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 – 2K.
Resolve for K* and show as point B on your uc/K 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 (i.e., why does the firm change its behavior?), making sure you refer to the firm’s 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 < MPK, 100 < 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 (i.e., 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) = 110...... solve for r, r = .03
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 IdA. Note importantly that we do not have numbers for desired investment, but that’s ok, we are focusing on the change in desired investment. Then show, as point B, the level of desired investment after the change intao (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 IdC.
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).
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 country’s closed economy.
Production function: Y = A·K·N – N2/2
Marginal product of labor: MPN = A·K – 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 points for completely labeled and correct diagrams)
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 INCOME
2) LOWER WEALTH
3) LOOSER IMMIGRATION LAWS
4) MORE PARTICIPATION
5) DEMOGRAPHICS - MORE PEOPLE ENTERING THE WORKING AGE POPULATION
c) (10 points) Given the change in NS and K*, repeat part a)(i.e., 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
WHY DOES FIRM CHANGE BEHAVIOR? @N=56, W NOT EQUAL TO MPN
56 = 28 + 9w ...... w = 3.1111.....MPN... 6 x 8 - 56 = -8 - need FIRE workers!
3. PART 2 (NEW GRADER – 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______.
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) – 500r] - 100
S = 746 + 500r
746 + 500r = 796 – 500r
r = .05, S = I = 771
Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A.
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 (i.e., changes in K*, Y, and Id, note, the new Id = 455 – 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) – 500r] - 100
S = 425 + 500r
425 + 500r = 455 – 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!
4. (50 points total) We assume that the world consists of two large open economies, USA and China.
a) What is the equilibrium interest rate that clears the international goods market? Show all work (10 points).
USA
S = 1000 - [ 280 - .4(1000 - 200) - 200 r ] - 325
S = 75 + 200 r
CHINA
S = 1500 - [ 480 - .4(1500 - 300) - 300 r ] - 300
S = 240 + 300 r
[75 + 200 rw ] - [150 – 200 rw ]+[ 240 + 300 rw] - [225 – 300 rw]= 0
1000 rw - 60 = 0 ...... rw = .06
b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points).
USA
S = 75 + 200 (.06)...... S = 87
I = 150 – 200 (.06).....I = 138 NX = -51
CHINA
S = 240 + 300 (.06).....S = 258
I = 225 – 300 (.06)...... I = 207 NX = 51
c) Which country is ‘spending beyond its means’ and which country is the saver? What exactly do we mean by the phrase ‘spending beyond its means’ 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 + 0.4(1000 - 200) – 200 (.06) = 588
Id = 150 – 200 (.06) = 138
G = 325
C + I + G = 588 + 138 + 325 = 1051 (51 HIGHER THAN INCOME)
ABSORPTION IN CHINA
CdF = 480 + .4(1500 - 300) – 300 (.06) = 942
IdF = 225 – 300 (.06) = 207
G = 300
C + I + G = 942 + 207 + 300 = 1149 (51 LOWER THAN INCOME)
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 A’s, two on each diagram). Be sure to label diagram completely.
10 points for correct and completely labeled diagrams
Now the USexperiences apositive 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)
USA
S = 1050 - [ 280 - .4(1050 - 200) - 200 r ] - 325
S = 105 + 200 r
[105 + 200 rw ] - [150 – 200 rw ]+[ 240 + 300 rw] - [225 – 300 rw]= 0
1000 rw - 30 = 0 ...... rw = .03
WORK FOR POINTS B
USA
S = 105 + 200 (.03)...... S = 111
I = 150 – 200 (.03)...... I = 144 NX = -33
CHINA
S = 240 + 300 (.03).....S = 249
I = 225 – 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 > 1000).
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