Exam 1 – Econ 304 – Chuderewicz – Fall 2017
Name ______________KEY________________ Last 4 (PSU ID) __________
Section: Please Check:
Section 001 - 112 Chambers 9:05 - 9:55 am ______________
Section 002 - 112 Chambers 11:15 am - 12:05 pm ______________
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
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Please answer all questions. You must show all work or points will be taken off.
1. (50 points total) ) Homer Simpson, does not abide by the life cycle theory
of consumption. Homer has a “let’s live life like it’s our last day” mentality
and thus, he prefers to consume more today, relative to the future. In
particular, Homer prefers to consume exactly twice as much today (c),
relative to consumption next period (cf). Homer’s current income = $200K
and his future expected income = $100K. He has no wealth (neither current
nor expected) since he lives like today is his last. Given that Homer faces a
real interest rate of 5% ( 0. 05). Please answer the following questions.
a) (5 points) Calculate Homer'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] / (3 + 2r)
C* = [(1 + (.05))(200 + 0) + 100 + 0] / (3 + 2(.05))
c = 200, cf = 100
(10 points for a completely labeled graph – be sure to label the no lending / no borrowing points =
NL/NB) Use space above.
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b)(5 points) Homer works in the steel industry and given the decision to continue with the Dakota pipeline
and the fact the President Trump wants it to be made by American produced steel, Homer's conditions
change. Given that this project is expected to get finished relatively quickly, Homer plans on taking
advantage of working overtime so his current income rises to $300K. His expected income has not
changed. Resolve for Homer's optimal consumption bundle and label as point C*B..
C* = [(1 + (.05))(300 + 0) + 100 + 0] / (3 + 2(.05))
c = 267.7 cf = 133.97
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 Homer and add this point to your graph and label as
point C*C.
C* = [(1 + (-.05))(300 + 0) + 100 + 0] / (3 + 2(-.05))
c = 265.5 cf = 132.7
d) (10 points) Did the Fed policy work as in stimulating the economy as measured by the change in
Homer's current consumption? That is, did Homer's consumption rise? Why or why not? Explain using the
income and substitution effects. Please use actual numbers to support your answer.
NO..... Since Homer is a saver, he cares most about his FV of his present resources since he is
financing futures consumption with his current resources. When r goes down, FV = (1 + r) (y + a)
falls and therefore Homer is poorer and will spread the pain and consume less in both periods - this
is the income effect. With numbers: FV = (1 + .05) (300 + 0) = 315 vs FV = (1 + (- .05)) (300 + 0) =
285
The substitution effect works in the opposite direction - when r goes down so does the price of
current consumption = 1+r / 1. The price of current consumption goes from 1.05 units of future
consumption to .95 units of future consumption - since the price of current consumption has gone
down, Homer should substitute away from future consumption towards current consumption.
e) (15 points total) In the space below, draw two savings functions for Homer. The first savings function is
for the initial conditions, before Homer gets the news about extra demand in the steel industry (before his
current income rose). Label as point A where r = .05 and point B when r = -.05.
Now draw another savings function representing the conditions after Homer's current income rose. 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)
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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 6% (0.06).
The real interest rate is 4% (.04).
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And the expected marginal product of capital is given by MPK f = 250 – 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 = 250 - 5K.........K* = 45
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
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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 MPK f = 275 – 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 = 275 - 5K ..........K* = 49
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 = 45, uc = 30, MPK = 275 - 5(45) = 50, since uc= 30 is LESS than MPK=50, we need to BUY 4
golf carts to get back to profit maximization where uc = MPK = 30 when K=49 - 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 48. 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 = 48 .... MPK = 275 - 5(48) = 35 ...... so the Fed needs to get the uc = 35......
35 = [(r + .06) 240] /(1 - .20)......[35 x (1 - .20)] / 240 - .06....... r = .0566
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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 I D 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 I dC.
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).
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3. PART 1 (55 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 = 10 and K = 10.
The initial labor supply curve is given as: N S = 20 + 9w.
a) (10 points) Find the equilibrium levels of the real wage, employment and output (show work).
w = 10 * 10 - [20 + 9w]
10 w = 80..... w = 8, N = 92, Y = 9200 - 4232 = 4968
w = 10 * 9 - [30 + 9w]
10 w = 60, w = 6, N = 84, Y = 7560 - 3258 = 4032
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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.
(20 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: N S = 30 + 9w .
K goes down from 10 to 9.
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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) LOWER EXPECTED INCOME
2) LOWER WEALTH
3) LOOSER IMMIGRATION LAWS
4) MORE LABOR FORCE PARTICIPATION
5) DEMOGRAPHICS - YOUNGER POPULATION - MORE PEOPLE
ENTERING LABOR FORCE
c) (10 points) Given the change in N S 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.
d) (10 points) Explain exactly why the profit maximizing level of labor has changed given the change in N S
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 = 92..... MPN = -2 (MPN = 10 * 9 - 92 = -2), for wage: 92 = 30 + 9w.... w = 6.88 w>MPN, fire
people - if you fire 8 people, the MPN will rise to = 6......as you fire people you can pay a lower wage if you layoff 8 people, you can lower wage .88888 from 6.8888 to 6 BACK TO PROFIT MAX
WHERE mpn = w = 6.
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3. PART 2 (60 points total for PART 2)
Before we start this problem, put the initial Y as computed in part a) here _____4968_______.
And the new Y (after the change in conditions) here _____4032______.
Initial conditions in the goods market
Cd = 1500 + .50(Y-T) – 500r
Id = 604 – 500r
G = 500
T= 100
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 = 4968 - [1500 + .5 (4968 - 100) - 500r] - 500
S = 534 + 500 r
534 + 500 r = 604 - 500r
r = .07, S = I = 569
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 (the change in Y) ALONG WITH
A CHANGE IN THE CONSUMPTION FUNCTION.
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The new consumption function is Cd = 1012 + .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.
LOSS OF WEALTH, EXPECTED INCOME, EXPECTED WEALTH OR LOWER CONSUMER
CONFIDENCE - CONSUME LESS AT ANY GIVEN INCOME AND REAL INTEREST RATES
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 = 4032 - [1012 + .5 (4032 - 100) - 500r] - 500
S = 554 + 500 r
554 + 500 r = 604 - 500r
r = .05, S = I = 579
h) (10 points) Explain the movement to the new equilibrium from point A to point B. Start with at the same
r, savings does not equal investment. Give the actual numbers. At the same interest rate, which is larger, Y
or C + I + G? Use this expression to argue why interest rates changed the way they did.
at r = .07, S= 554 + 500 (.07) = 589..... I = 604 - 500 (.07) = 569
S > I.....589 > 569 .............Y > C + I + G .....in order to increase absorption (C + I + G), r has to fall
(stimulates C and I).
i) (15 points) Considering this entire problem, are your results consistent with the Great Recession why or why not? Please focus your discussion exclusively to the change in labor supply, the change in Y,
and the change in the consumption function. Use real world developments / statistics that we mentioned in
class to support your explanations (5 points for each explanation).
YES - LABOR SUPPLY INCREASED CONSISTENT WITH GR - $14 TRILLION IN WEALTH
LOST (STOCKS AND REAL ESTATE) - WORKERS WILLING TO WORK MORE AT ANY
GIVEN WAGE
YES! OUTPUT FELL LIKE A ROCK DURING THE GREAT RECESSION
YES! CONSUMPTION FUNCTION FELL REFLECTING THE LOSS OF WEALTH, PEOPLE
WERE CONSUMING LESS AT ANY GIVEN INCOME AND REAL INTEREST RATE
4. (55 points total) Open Economy – Two Large country problem
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USA Initial Conditions
Cd = 320 + 0.4(Y-T) – 200rw
Id = 120 – 200 rw
Y = 1000 S = 1000 - [ 320 - .4(1000 - 200) - 200 r ] - 275
T = 200 S = 85 + 200 r
G =275
China Initial Conditions
CdF = 480 + .4(YF – TF) – 300rw
IdF = 255 – 300 rw
YF = 1500 S = 1500 - [ 480 - .4(1500 - 300) - 300 r ] - 300
TF = 300 S = 240 + 300 r
GF = 300
a) (5 points) What is the equilibrium real interest rate that clears the international goods
market? Show all work.
[85 + 200 rw ] - [120 – 200 rw ] + [ 240 + 300 rw] - [255 – 300 rw] = 0
1000 rw - 50 = 0 ........ rw = .05
b) (10 points) Compare the level of absorption in each country to the income generated in
each country. Is the US spending beyond its means? Is China the lender? Explain using
real numbers!
USA
Cd = 320 + 0.4(1000 - 200) – 200 (.05)
Id = 120 – 200 (.05)
C = 630
I = 110
G = 275
ABSORPTION = 630 + 110 + 275 = 1015 INCOME = 1000.....NX = -15
USA IS SPENDING BEYOND ITS MEANS BY 15
S = 95, I = 110
CHINA
CdF = 480 + .4(1500 – 300) – 300 (.05)
IdF = 255 – 300 (.05)
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C = 945
I = 240
G = 300
ABSORPTION = 945 + 240 + 300 = 1485 INCOME = 1500.....NX = +15
CHINA IS LIVING WITHIN ITS MEANS BY 15
S = 255, I = 240
In the space below, draw two diagrams side by side, with the USA on the left and China
country 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 diagrams completely labeling the
trade deficit/surplus on each graph, etc.
(15 points for correct and completely labeled diagram)
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c) (10 points) Now let the US suffer an adverse shock to the investment function so that
the new investment function for the US is:
Id = 95 – 200 rw
[85 + 200 rw ] - [95 – 200 rw ] + [240 + 300 rw] - [255 – 300 rw] = 0
1000 rw - 25 = 0 ........ rw = .025
USA S = 90, I = 90, NX = 0
CHINA S = 247.5, I = 247.5, NX = 0
d) (10 points) What has happened to the USA’s trade balance and why? Make sure you
define absorption and comment on the influence that the adverse investment shock has on
absorption in the US. What happened to absorption in China and why?
Trade Deficit has vanished - the decrease in investment the US has caused
absorption (C + I + G) in the US to fall by 15. Absorption in China rose by 15 since
interest rates had to fall to get us back to equilibrium - Consumption and
Investment in China rose be 7.5 total equals 15 - so absorption in China rose by
15....- bye bye trade surplus!
e) (5 points) Are these results (in part d)) consistent with the US going to AA, the
proposition put forth by Fareed-Zakaria in the Colbert clip? Put differently, are your
results consistent with the US "living within it's means?" Why or why not?
Yes of course it is - we are now living within our means!!!! Y = C + I + G!
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