Exam 1 –Econ 304 – Chuderewicz –Spring 2017
Name ______KEY______Last 4 (PSU ID) ______
Section: Please Check:
Section 001 - 010Sparks10:10 am ______
Section 002 - 121Sparks 11:15 am ______
PLEASE PUT THE FIRST TWO LETTERS OF YOUR LAST NAME ON TOP RIGHT HAND CORNER OF THIS COVER SHEET – ONLY NON-PROGRAMMABLE CALCULATORS ALLOWED. THANKS AND GOOD LUCK!!!
Total Points for exam = 230
Test time = 120 minutes
Approximately one minute for every two points
To help with time management if spreading time evenly
Question #1 = 50 points..... 25 minutes
Question #2 = 50 points ...... 25 minutes
Question #3.1 = 40 points.... 20 minutes
Question #3.2 = 40 points ....20 minutes
Question #5 = 50 points..... 25 minutes
Please answer all questions. You must show all work or points will be taken off.
1. (50 points total) Suppose we have Dagwood, who has a current income of $200K and expected future income of $200K. He has zero in current wealth and zero in expected wealth.
Dagwood’s behavior is consistent with the life-cycle theory of consumption as his preferences are to perfectly smooth consumption. Given that Dagwood faces a real interest rate of 5% ( 0. 05). Please answer the following questions.
a) (5 points) Calculate Dagwood’s optimal consumption bundle showing all work. Then draw a completely labeled graph (the two period consumption model) depicting this initial optimal consumption bundle as point C*A.
C* = [(1 + r)(y + a) + yf + af] / (2 + r)
C* = [(1 + (.05))(200 + 0) + 200 + 0] / (2 + (.05))
C* = 200
(10 points for a completely labeled graph – be sure to label the no lending / no borrowing points =
NL/NB) Use space above.
b)(5 points) Dagwood works in an industry that is becoming obsolete and thus, quits his job and goes back to school (college). As a result, he has to take a part time job so his current income is now $100K. The good news that is expected future income has risen to $350K, given his new degree! Resolve for Dagwood's optimal consumption bundle and label as point C*B..
C* = [(1 + (.05))(100 + 0) + 350 + 0] / (2 + (.05))
C* = 222
c) (5 points) Janet Yellen and the Fed are not happy with the state of the economy and worry about an impending recession. As a result, the Fed lowers rates so that the new real rate is negative 5%. Recalculate the optimal bundle for Dagwood and add this point to your graph and label as point C*B.
C* = [(1 + (-.05))(100 + 0) + 350 + 0] / (2 + (-.05))
C* = 228
d) (10 points) Did the Fed policy work as in stimulating the economy as measured by the change in Dagwood's current consumption? That is, did Dagwood's consumption rise? Why or why not? Explain using the income and substitution effects. Please use actual numbers to support your answer.
YES.....Since Dagwood is a borrower, he cares most about his PV of futures resources since he is financing consumption today by borrowing from the future. When r goes down, PV = (yf + af) / (1 + r) rises and therefore Dagwood is richer and should spread the gain and consume more in both periods - this is the income effect. With numbers: PV = 350 / (1 + (.05)) = 333.33 vs PV = 350 / (1 + (-.05)) = 368.42.
The substitution effect works in the same direction - when r goes down so does the price of current consumption = 1+r / 1. The price of current consumption goes from 1.05 units of future consumption to .95 units of future consumption - since the price of current consumption has gone down, Dagwood should substitute away from future consumption towards current consumption.
e) (15 points total)In the space below, draw two savings functions for Dagwood. The first savings function is for the initial conditions, before Dagwood quits his job (when his current income equals future income = $200K). Label as point A where r = .05 and point B when r = -.05.
Now draw another savings function representing the conditions after Dagwood quit his job where his current income is $100K and his expected future income is $350K. Label as point C where r = .05 and then point D, where r = -.05. Please put only the relevant shift variables in parentheses next to each savings function. Please show work for each of the four points (A, B, C, D)
10 points for correct and completely labeled graph
2. (50 points total) You own a golf resort and you need to determine how many golf carts you need to buy to maximize profits. Please answer the following questions given the information below. Please be sure to SHOW all work!
A brand new golf cart costs 200 rounds of golf (this is your output) and the rate of depreciation is 7% (0.07).
The real interest rate is 3% (.03).
And the expected marginal product of capital is given by MPKf = 275 – 5K.
There is a tax on capital so tao (τ) = 20% (.20)
a) (5 points) What is the (tax adjusted) user cost of capital and what is this user cost expressed in? (Show work)
uc = [(.03 + .07) 200] / (1 - .20) = 25 rounds of golf
b) (5 points) How many golf carts should you buy to maximize profits? Show work
25 = 275 - 5K...... K* = 50
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
Now conditions change. The following two shocks occur simultaneously:
i) the price of golf carts rises to 240 rounds of golf.
ii) the expected marginal product of capital changes and is now MPKf = 300 – 5K.
c) (5 points) Resolve for K* and show as point B on your uc/K diagram.
uc = [(.03 + .07) 240] /(1 - .20) = 30
30 = 300 - 5K ...... K* = 54
d) (10 points) Given the two shocks as above, explain the intuition underlying the change in the profit maximizing level of carts (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).
@ K = 50, uc = 30, MPK = 300 - 5(50) = 50, since uc= 30 is LESS than MPK=50, we need to BUY4golf carts to get back to profit maximization where uc = MPK = 30 when K=54 - for every cart we buy. MPK falls by 5, when we buy 4, MPK falls by 4 x 5 = 20....from 50 to 30 = uc!
e) (5 points) Suppose that the Federal Reserve had a goal to get the capital stock, the number of golf carts purchased to equal 52. Given the two shocks as above, what would they have to do to the real rate of interest to achieve their objective? Please show all work and I am looking for a specific number (i.e., r = ?). Please add this development to your diagram as point C.
What is MPK when K = 52 .... MPK = 300 - 5(52) = 40 ...... so the Fed needs to get the uc = 40......
40 = [(r + .07)240] /(1 - .20)...... [40 x (1 - .20)] / 240 - .07...... r = .0633
f) Finally, draw a desired investment diagram (completely labeled with the relevant shift variables) depicting the initial equilibrium as point A (simply draw a negatively sloped ID curve going through point A). Label the initial level of desired investment as 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, after the two shocks. Finally, show how the Fed policy maps to your investment diagram and label as point C with the corresponding level of investment labeled as 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(40 points total for this part) This problem is broken into two parts that are totally connected to each other. In this first part of the question, you apply Chapter 3 (labor mkt., etc) material and in PART 2, you get to use Chapter 4 (goods market equilibrium) material. PLEASE SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS.
The following equations characterize a 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 = 8 and K = 8.
The initial labor supply curve is given as: NS = 14 + 4w.
a) (5 points) Find the equilibrium levels of the real wage, employment and output (show work).
w = 8 x 8 - [14 + 4w]
5w = 50, w = 10, N* = 54, Y = 1998
In the space below, draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph. Be sure to label everything including these initial equilibrium points as point A.
(15 points for completely labeled and correct diagrams)
We now have numerous changes to our economic conditions (all is not constant). Think of all these changes happening together, that is, we go from one state of economic affairs to a different state of economic affairs. Below are the changes.
- The labor supply changes and is now: NS = 6 + 4w .
- K goes down from 8 to 7.
b) (5 points) What could cause such a change in labor supply? Please give two specific and well supported reasons. Be sure to explain your answer.
5 CHOICES
1) HIGHER EXPECTED INCOME
2) HIGHER WEALTH
3) TIGHTER IMMIGRATION LAWS
4) LESS PARTICIPATION
5) DEMOGRAPHICS - AGING POPULATION - LESS PEOPLE ENTERING LABOR FORCE
c) (5 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 = 8 x 7 - [6 + 4w]
5w = 50, w = 10, N* = 46, Y = 1518
d) (10 points) Explain exactly why the profit maximizing level of labor has changed given the change in NS and K. Be very specific with your answer as in using numbers. Begin your answer with: At the same level of labor input N = (what it was at point A), the firm is no longer ......
@ N = 54.....w = 12 and MPN = 2 (MPN = 8 x 7 - 54) SO w>MPN, fire people - if you fire 8 people, the MPN will rise to = 10...... as you fire people you can pay a lower wage - if you layoff 4 people, wage falls by one, layoff 8 people, wage falls by 2 from 12 to 10....back at profit max where w = 10 = MPN when N = 46.
3. PART 2 (40 points total for PART 2)
Before we start this problem, put the initial Y as computed in part a) here ______.
And the new Y (after the change in conditions) here ______.
Initial conditions in the goods market
Cd = 299 + .50(Y-T) – 500r
Id = 330 – 500r
G = 500
T= 200
e) (10 points) Given the initial conditions, solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment.
S = 1998 - [299 + .50(1998 - 200) – 500r] - 500
S = 300 + 500r
300 + 500r = 330 – 500r
r = .03, S = I = 315
Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A.
10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function).
NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 ALONG WITH A CHANGE IN THE CONSUMPTION FUNCTION.
The new consumption function is Cd = 49 + .50(Y-T) – 500r
f) (5 points) What could cause such a change in the consumption function? Please give two specific and well supported reasons. Be sure to explain your answer.
4 POSSIBILITIES
LOWER WEALTH (a)
LOWER EXPECTED INCOME (yf)
LOWER EXPECTED WEALTH (af)
LOWER CONSUMER CONFIDENCE (CC)
g) (10 points) Given these changes, i.e., changes in Y from part 1 and the change in the consumption function, calculate the new equilibrium levels of the real interest rate, desired savings and investment. Please add this new equilibrium point to your diagram and label as point B.
S = 1518 - [49 + .50(1518 - 200) – 500r] - 500
S = 310 + 500r
310 + 500r = 330 – 500r
r = .02, S = I = 320
h) (5 points) Considering this entire problem, are your results consistent with the Great Recession - why or why not? Please be a specific as possible with regard to the changes in the consumption function and the change in labor supply (please refer to each for full credit!)
YES, FOR THE MOST PART - THE CONSUMPTION FUNCTION SHIFTED DOWN CONSISTENT WITH LOSSES IN WEALTH ($14 TRILLION WORTH WAS LOST IN THE GREAT RECESSION) - LOWER CC, EXPECTED WEALTH, EXPECTED INCOME - ALL PERFECTLY CONSISTENT WITH GREAT RECESSION
LABOR SUPPLY - YES IF YOU THINK ABOUT LESS PARTICIPATION SINCE JOB MARKET CONDITIONS WERE SO BAD ....BUT NO IF YOU THINK OF THE LOSS OF WEALTH, THIS WOULD RESULT IN HIGHER LABOR SUPPLY, NOT LOWER LABOR SUPPLY AS IN PROBLEM
4. (50 points total) We assume that the world consists of two large open economies, USA and China.
USA Initial Conditions
Cd = 400 + 0.5(Y-T) – 300rw
Id = 430 – 200rw
Y = 2300
T = 300
G =500
China Initial Conditions
CdF = 600 + .5(YF – TF) – 300rw
IdF = 310 – 200rw
YF = 2000
TF = 400
GF = 300
a) (10 points) What is the equilibrium interest rate that clears the international goods market? Show all work
USA
S = 2300 - [400 + .5(2300 - 300) - 300 r ] - 500
S = 400 + 300r
CHINA
S = 2000 - [600 + .5(2000 - 400) - 300 r ] - 300
S = 300 + 300r
[400 + 300r] - [430 - 200r] + [300 + 300r] - [310 - 200r] = 0
-40 + 1000r = 0 ...... r* = .04
b) (5 points) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate .
USA
S = 400 + 300(.04) = 412
I = 430 - 200(.04) = 422
NX = -10
CHINA
S = 300 + 300(.04) = 312
I =310 - 200(.04) = 302
NX = + 10
c) (5 points) 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 in each country to its income. Explain.
USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater than the income we generate Y. Absorption in the US is 2310, Y = 2300, Absorption in China is 1990, Y =2000. China is the saver - USA is spending beyond its means.
Draw two diagrams side by side, with the US on the left and the China on right. Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses.
15 points for correct and completely labeled diagrams
We now have a change in conditions: The Investment function changes for the US and is now:
Id = 450 – 200rw
d) (5 points) Resolve for the world real interest rate that clears the international goods markets along with the ‘new’ Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams. (10 points)
[400 + 300r] - [450 - 200r] + [300 + 300r] - [310 - 200r] = 0
-60 + 1000r = 0 ...... r* = .06
USA
S = 400 + 300(.06) = 418
I = 450 - 200(.06) = 438
NX = -20
CHINA
S = 300 + 300(.06) = 318
I =310 - 200(.06) = 298
NX = +20
e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means. Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA). Are your results consistent with the US going to AA? Why or why not? Explain and please be specific. Also, what happened to investment in both countries and why. Again, be specific.
NO, the US has not gone to AA ... their trade deficit is getting larger - absorption exceeds income by 20 - started out with a trade deficit of 10.
Investment in the US rose by 16 given the positive shock to the investment function. At same r, investment would have risen by 20 but r has to go up to finance this investment - when r goes up by .02, 4 units of investment are 'crowded' out in the US....20 minus 4 = 16!
Investment in China fell (from 302 to 298) because r had to rise to finance the increase in investment in the US... at the same K, uc > MPK, China needs to sell machines to get back to profit maximization. Since I = K* - Kt + dKt.....when K* falls, so does I.
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