Exam 1 – Econ 304 – Chuderewicz – Spring 2016
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Section: Please Check:
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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
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Total Points for exam = 245
Test time = 120 minutes
Approximately one minute for every two points
To help with time management if spreading time evenly
Question #1 = 65 points..... 30 minutes
Question #2 = 50 points ......25 minutes
Question #3.1 = 30 points.... 17 minutes
Question #3.2 = 45 points ....22 minutes
Question #4 = 55 points..... 27 minutes
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Please answer all questions. You must show all work or points will be taken off.
1. (65 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 (c f).
Homer’s current income = $300K and his future expected income = $300K. He has no
wealth (neither current nor expected) since he lives like today is his last! Homer faces a
real interest rate of - 0.05.(negative 5%). Please answer the following questions.
a) (5 points) State clearly what the slope of any budget line represents, in general, and then refer to this
specific case (i.e., what is the slope of Homers budget constraint and what does this mean exactly? Be
specific. (5 points)
b) (5 points) Solve for Homer’s optimal consumption basket today (C*) and his optimal consumption
basket next period (Cf*). Please provide a completely labeled graph depicting these results and label this
initial point as C*A.
(10 points for a completely labeled graph – be sure to label the no lending / no borrowing point =
NL/NB)
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c) (5 points) Janet Yellen and the Fed are finally happy with the way the
economy is headed and to be honest, is now fearful of overheating. As
such, the Fed tightens and the real rate of interest rises to 0% (0.00).
Recalculate the optimal bundle for Homer and add this point to your
graph and label as point C*B.
d) (10 points) Did the Fed policy work as in cooling the economy as measured by the change in Homer's
current consumption? That is, did Homer's consumption fall? Why or why not? Explain using the income
and substitution effects. Please use actual numbers to support your answer.
e) (5 points) Marge is worried about saving for the kids' college education and does
some research investigating whether most consumers have spending patterns like
Homer. She encounters the life cycle theory of consumption and finds that this popular economic theory
suggests that the way to maximize life time utility is to perfectly smooth consumption through time. Marge
discusses this new development with Homer and convinces him to change his preferences to that of a
perfect smoother, like our friend Dagwood. Resolve for Homers optimal basket and label as point C*C on
a NEW diagram. Note, this is after the Fed raised rates to 0%.
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DRAW A NEW DIAGRAM DEPICTING THIS NEW POINT AS C*C . (10 points for a completely
labeled graph – be sure to label the no lending / no borrowing point = NL/NB) Use the space below.
f) (5 points) Janet Yellen and the Fed still believe the current and future state of the economy is strong and
thus, to make sure the economy does not overheat, raise rates again so that the new real rate of interest is
.05 (5%). Resolve for Homer’s new optimal consumption point and label as point C*D on the ‘new’
diagram above.
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g) (5 points) Did this contractionary monetary policy work in term of lowering current consumption
(assume there are a bunch of Homers that have changed preferences like this Homer did)? Why or why
not, explain using the income and substitution effects.
h) (5 points) Without drawing any graphs, compare what Homer’s savings function looked like before
Marge talked him into being a smoother to what his savings function looked like after Marge talked him
into becoming a perfect smoother. Did the tighter monetary policy work in terms of lowering current
consumption in either case?
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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 cost 2000 fishing hours (this is your
output) and the rate of depreciation is 5% (0.05).
The real interest rate is 5% (.05).
And the expected marginal product of capital is given by MPK f
= 400 – 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)
b) (5 points) How many fishing poles should you buy to maximize profits? Show work
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 US $ depreciates and since you buy your poles from abroad, the poles become more expensive and
now cost 2400 fishing hours.
ii) the expected marginal product of capital changes and is now MPK f = 420 – 5K.
c) (5 points) Resolve for K* and show as point B on your uc/K diagram.
d) (10 points) 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).
e) (5 points) 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.
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f) Finally, draw a desired investment diagram (completely labeled with the relevant shift variables (with
the appropriate values as in τ = .20, etc.) noted next to the function in parentheses) 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, the
level of desired investment after the change in the price of capital and the change in the expected MPK.
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).
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3. PART 1 (30 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 = 8 and K = 10.
The initial labor supply curve is given as: N S = 20 + 9w.
a) (5 points) Find the equilibrium levels of the real wage, employment and output (show work).
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)
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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 = 24 + 9w .
K goes down from 10 to 8.
b) (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.
c) (10 points) Why exactly did the firm change their behavior? To answer, calculate the MPN and w at the
same N and compare. Then explain what the firm does and why and what the worker does and why.
This questions is worth 10 points so please be specific and complete!
3. PART 2 (45 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 = 1000 + .50(Y-T) – 500r
Id = 601 – 500r
G = 100
T= 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.
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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 (i.e., the change in Y) ALONG
WITH FOLLOWING TWO CHANGES!
i) The new consumption function: Cd = 450 + .5(Y - T) - 500r
ii) The new investment function: Id = 590 - 500r
e) (5 points) What could cause such a change in the consumption function? Please give two specific and
well supported reasons.
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f) (5 points) Given these changes, i.e., the change in Y from part 1 and the change in the consumption
function and investment 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.
g) (5 points) Explain exactly how the goods market clears given the shock as above. Start your answer
with: At the same r....................
h) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is
time to apply your knowledge of the 2 period consumption model to this problem. In the space below,
draw and use the two period consumption model and depict the movement from point A to point B.
Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is
to the left (west) of the consumption points. Be sure to calculate the actual level of consumption before
(point A) and after (point B) all the changes and add these actual numbers to your graph. Explain why your
graph changed the way it did. Make sure you label your graph completely. Now the discussion: Are the
results with regard to the change in income, change in consumption, and the change in investment
consistent with the economy heading into a recession or consistent with the economy in the midst of a
recovery. Please explain and be as specific as possible.
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4. (55 points total) We assume that the world consists of two large open economies, USA and China.
USA Initial Conditions
Cd = 400 + 0.4(Y-T) – 200rw
Id = 410 – 200rw
Y = 2000
T = 200
G =500
China Initial Conditions
CdF = 480 + .4(YF – TF) – 300rw
IdF = 360 – 300rw
YF = 1600
TF = 400
GF = 300
a) (10 points) What is the equilibrium interest rate that clears the international goods market? Show all
work
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b) (5 points) Now calculate the levels of desired savings and investment for each country at this equilibrium
world real interest rate .
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.
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
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We now have a change in conditions: The Government in China offers and investment tax credit (ITC) so
that Investment in China rises to:
IdF = 385 – 300rw
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)
e) (15 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. What has happened to absorption in
the US and why? How exactly was the shock of 25 to the intercept of China's investment function
financed?
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