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Exam 1 – Econ 304 – Chuderewicz – Fall 2014
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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 #3.1 = 35 points.... 17 minutes
Question #3.2 = 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 Dagwood's 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) = 150K
af ( expected future wealth) = 100K
r (the current real rate of interest) = -.05 (negative 5%)
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
2
(20 points total) Now draw two completely labeled diagrams (the two period
consumption model) depicting these initial optimal consumption bundles as points C*A.
Please put the diagrams next to each other with the left diagram representing Dagwood
and the right diagram representing The Barber. Note that C*A 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 Barber's
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 Barber's new optimal consumption bundle showing all work
and label as point C*B on the diagram representing The Barber.
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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 Dagwood’s new optimal consumption bundle depicting his new
optimal consumption bundle as point C*B.
d) (5 points) Calculate The Barber's new optimal consumption bundle depicting his new
optimal consumption bundle as point C*C.
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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 - 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 - 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
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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 - 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
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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 costs 800 fishing hours (this
is your output) and the rate of depreciation is 8%
(0.08).
The real interest rate is 2% (.02).
The expected marginal product of capital is given by
MPKf = 200 – 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 uc/K graph depicting the state of affairs and label this initial profit maximizing
condition as point A.
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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
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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 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 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 (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.
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(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 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
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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________.
Initial conditions in the goods market
Cd = 100 + .50(Y-T) – 500r
Id = 796 – 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.
S = 1792 - [100 + .50(1792 - 100) – 500r] - 100
S = 746 + 500r
746 + 500r = 796 – 500r
r = .05, S = I = 771
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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 ALONG WITH
A CHANGE IN DESIRED INVESTMENT.

The desired investment function changes and is now Id = 455 – 500r
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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!
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4. (50 points total) We assume that the world consists of two large open economies, USA
and China.
USA Initial Conditions
Cd = 280 + 0.4(Y-T) – 200rw
Id = 150 – 200rw
Y = 1000
T = 200
G =325
China Initial Conditions
CdF = 480 + .4(YF – TF) – 300rw
IdF = 225 – 300rw
YF = 1500
TF = 300
GF = 300
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
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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).
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(100 - 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)
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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 A’s, 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)
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
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WORK FOR POINTS B
USA
S = 105 + 200 (.03)......S = 111
I = 150 – 200 (.03).......I = 144
CHINA
S = 240 + 300 (.03).....S = 249
I = 225 – 300 (.03)......I = 216
NX = -33
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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