Name ______________________________________________ __________
Section: Please Check:
Please check section that you are registered in:
Section 001 - MWF: 9:05 - 9:55 AM : 104 Keller Building _________
Section 004 - MWF: 11:15 AM - 12:05 PM : 101 Chambers Building________
EXAM #1 – Spring 2022
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 = 345
Test time = 120 minutes
Approximately one minute for every two points
To help with time management if spreading time evenly
Question #1 = 85 points.....30 minutes
Question #2 = 70 points ......25 minutes
Question #3 = 60 points.... 20 minutes
Question #4 = 60 points ....20 minutes
Question #5 = 70 points..... 25minutes
1
Please answer all questions. You must show all work or points will be taken off.
Instructions: Please show all work or points will be taken off. Good luck!
1. (85 points total) Dagwood’s neighbor, 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 equals $250K and his
future expected income = $250K. He has no wealth (neither
current nor expected) since he lives like today is his last! Homer faces an initial real interest rate
of -0.05. Please answer the following questions.
a) (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 point as C*A.
CA* = [(1 + (-0.05))(250 ) + 250 ] / (3 + 2 x (-0.05))
CA* =336.2, 168.1
CB* = [(1 + (0.01))(250) + 250 ] / (3 + 2 x (0.01))
CB* = 332.78, 166.39
2
(10 points for a completely labeled graph – be sure to label the no lending / no borrowing
points = NL/NB and the slope of each budget constraint)
3
b) (5 points) In steps Jerome Powell and the Fed. Given that the economy appears to be on sound
footing, the Fed raises interest rates so that the real rate of
interest rises to 0.01. Recalculate the optimal bundle for
Homer and add this point to your graph and label as point
C*B.
c) (10 points) Is Homer better or worse off due to the RISE in the real rate of interest? Explain
being sure to discuss exactly how the substitution and income effects play a role in Homer's
consumption decisions. Also, comment on whether these income and substitution effects work in
the same or opposite direction (i.e., is it a tug of war or do they work in the same direction?) in
this particular case. Please include actual numbers when discussing the income and
substitution effects or points will be taken off.
NO - worse off..... Since Homer is a borrower (C > Y), he cares most about his PV of future resources
since he is financing consumption today by borrowing from the future. When r goes up, PV = (y f +
af) / (1 + r) falls and therefore Homer is poorer and should spread the pain and consume less in both
periods - this is the income effect. With numbers: PV = 250 / (1 + (-.05)) = 263.16 vs PV = 250 / (1 +
(.01)) = 247.52.
The substitution effect works in the same direction - when r goes up so does the price of current
consumption = 1+r / 1. The price of current consumption goes from .95 units of future consumption
to 1.01 units of future consumption - since the price of current consumption has gone up, Homer
should substitute away from current consumption towards future consumption.
The income effect and substitution effect work in the SAME direction since both imply Homer
should consume less in the current period!
Now Homer is having a discussion with Marge and Marge is worried
about Homer’s spending habits. Marge reads an economic textbook and
suggests to Homer that he should smooth consumption, consistent with the
life cycle theory of consumption. So Homer listens and changes his
preference to that of a perfect smoother (like our friend Dagwood).
4
d) (5 points) Recalculate Homer’s optimal bundle given his change in preferences (the real
interest rate is still 1%). Please draw a new graph and label on your diagram as point C*c.
CB* = [(1 + (0.01))(250) + 250 ] / (2 + (0.01))
CB* = 250, 250
CB* = [(1 + (0.06))(250) + 250 ] / (2 + (0.06))
CB* = 250, 250
(10 points for a completely labeled graph – be sure to label the no lending / no borrowing
points = NL/NB and the slope of each budget constraint)
e) (5 points) In steps Jerome Powell and the Fed again
and given that the economy appears to be on sound
footing, the Fed raises interest rates again so that the real
5
rate of interest rises to 0.06. Recalculate the optimal bundle for Dagwood and add this point to
your new graph and label as point C*D.
f) (10 points) Is Homer better or worse off due to the RISE in the real rate of interest? Explain
being sure to discuss exactly how the substitution and income effects play a role in Homer's
consumption
NO DIFFERENCE, SINCE HE IS AT HIS NL/NB POINT, DAG DOESN'T CARE
ABOUT FV OF PRESENT RESOURCES (HE IS NOT SAVING) NOR DOES HE CARE
ABOUT THE PV OF FUTURE RESOURCES (HE IS NOT BORROWING). SO HE
COULD CARE LESS ABOUT WHAT THE REAL INTEREST RATE IS, HE IS LIVING
PAYCHECK TO PAYCHECK LIKE MANY PEOPLE IN THE REAL WORLD DOES (I
WAS THERE FOR MANY YEARS)
ALSO, NO SUB EFFECT GIVEN THE STRICT PREFERENCES
6
We are now going to graph two savings functions for Homer and compare and contrast the slope
of each. Savings in this problem is defined as: S = Y - C.......Y is current income and C is current
consumption.
g)(25 points total) The first savings function to draw refers to the savings initially, before Homer
changes his preferences to that of a perfect smoother. Calculate the level of savings at point CA*
and label as point A on your savings diagram. Now calculate the level of savings at the point CB*
and label as point B on your savings diagram.
The second savings function is after the change in Homer’s preferences. Label as point C,
Homer's saving at point CC* and then label as point D, Homer's saving at point CD*. Connect
points C and D and we have the second savings function for Homer. Be sure to label your
diagram completely including all the shift variables that we are holding constant along any
savings function with the signs ( + or - ) above the shift variables.
PLEASE SHOW ALL WORK FOR POINTS A, B, C, AND D!
S=Y=C
POINT A: -86.2 = 250 – 336.2
POINT B: -82.78 = 250 – 332.78
POINTS C AND D ARE TRIVIAL…. Y=C = 250 FOR BOTH POINTS, SAVINGS
IS ZERO
point distribution: 15 points for correct and completely labeled graph along with 19 points
for showing all work to calculate savings for all points: A, B, C, and D.
7
2) (70 points total)
a)(10 points) What is meant by the phrase 'two percent is not enough'. In your answer, please make sure
you mention what the Fed did to fight the most previous 3 recessions and how this fact relates directly to
'two percent is not enough.' Be sure to use the Fisher equation to help support your answer!
TWO PERCENT IS NOT ENOUGH REFERS TO THE INFLATION TARGET OF TWO
PERCENT NOT BEING ENOUGH
The Fed lowered the federal funds rate by an average of 5.97 % to fight the most previous 3
recessions
IF r* is low, around .5%, then the Fed only has 3% of bullets (given inflation target) - if the neutral
funds rate stays at 3%, the fed will not have enough ammunition (bullets = 3%) to fight the next
recession, this is a BIG DEAL!
iff* = r* + π* ....... 2.5% = .5% + 2%
IF YOU RAISE INFLATION TARGET THE FED CAN 'BUY' BULLETS TO FIGHT NEXT
RECESSION - SAY TO 4% - THAT WOULD GIVE THEM 5% OF RECESSION FIGHTING
BULLETS!
iff* = r* + π* ....... 4.5% = .5% + 4%
b)(40 points, 20 for explanation and 20 points for correct and completely labeled diagram) We discussed in
detail why the Fed had more bullets (to fight recessions) back in the new economy days (mid to late 1990s)
relative to the present (now). Using a savings, investment diagram, explain what has changed since the new
economy. Label as point A, the conditions during the new economy (you should know the r* back in the
new economy) and then label as point B, the conditions now (again, you should know the r* presently). Be
sure to explain in detail exactly what has happened, in the context of your diagram, since the new economy
years. Finish your explanation with what this means for monetary policy in terms of bullets to fight the
next recession…. Use the Taylor Rule to show how many bullets the Fed had in the new economy days
and compare to how many bullets the Fed has now. What does r* mean exactly??
Write your Essay here followed by your graph – make sure you refer to your graph throughout your essay.
8
20 points for correct and completely labeled graph
More room for your essay….
9
Use the MW table below to answer the following questions:
c)(10 points) What is the rate of inflation between 1960 abd 1961? Please take answer to 4 decimal places?
Price index 1960: 1.00 / P = 5.30…….
.1887
Price index 1961: 1.15 / P = 6.03…….
.1907
Percent change: 1.05988 % equal inflation between 1960 – 1961
d)(10 points) What would the minimum wage need to be in 2021 to equal the real purchasing power of the
minimum wage 20 years ago in 1991?
price index in 2021.... 7.25/P21 = 4.19…. P10 = 1.7303
4.90 =MW21 / 1.7303…… MW15 = $ 8.48
10
3. (60 points total).
An economy’s aggregate production function is given by Y = A·K·N – N2. The marginal
product of labor for this production function is MPN = A·K – 2N.
(a) (10 points) Assume that A = 8 and K = 9. Suppose that the labor supply function for
this economy is given by NS = 3 + w. Find the equilibrium real wage rate, the full
employment level of employment, and the full-employment level of output for this
economy.
w = 8 x 9 - 2[3 + w]
3w = 66
w = 22, N = 25, Y = 1175
Y = 8 x 9 x 25 - 252
Draw a production function and labor market diagram vertically as we did in class and
label this initial equilibrium point as point A.
A correct and completely labeled diagram is worth 20 points (remember to put shift
variables in parentheses next to the relevant functions).
11
(b) (10 points) Suppose that the corporate tax rate goes down and this results in firms
investing in more capital so that capital (K) rises to 10 (from 9). Also, suppose that
improvements in business efficiency goes up as businesses can now collaborate on
projects remotely, raising technology (A) to 11 (from 8). In addition, the government
stimulus has made the labor force more apathetic so that the Labor force Participation
Rate (LFPR) has fallen, decreasing labor supply so that labor supply is now: NS = 1 + w
Find the equilibrium real wage rate, the full employment level of employment, and the
full-employment level of output for this economy and label on your diagrams as point B.
w = 11 x 10 – 2[1 + w]
3w = 108
w = 36, N = 37, Y = 2701
Y = 11 x 10 x 37 - 372
(c) (10 points) Explain exactly why the profit maximizing level of labor has changed
given the increase in total factor productivity. Again 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 = 25, MPN = 11 x 10 – 2 (25) = 60 = MPN and w needed to attract 25 workers is
25 = 1 + w….w=24
So MPN > w….. 60>24….HIRE!
for every worker you hire MPN falls by 2 - in order to hire one worker you need to
increase the price of leisure or the real wage by 1 – when you hire 12 more workers,
MPN falls by 24 to equal 36 and wages go up by 12 to equal 36, Back to profit
maximization!
d)(10 points) Are workers better off or worse off due to the increase in K and A? What
has happened to the government’s income tax revenue and why? Corporate tax revenue?
Workers are better off for two reasons– more of them working (37 vs 25) and the
real wage has risen from 22 to 36.
Income tax revenue rises since more are working and wages have risen
Corporate Tax revenue – went up – profits have risen!
12
4)(60 points) A closed economy has full employment level of output (Y) of 2,500. Government purchases,
G, are 300, taxes (T) are 500. Desired consumption (Cd) and investment (Id) are:
Cd = 600 + 0.5(Y –T) - 600r
Id = 630 - 400r
a) (5 points) Solve for the desired savings function in intercept - slope form (note, the intercept is an
integer).
S = 2500 - [600 + .5(2500 - 500) - 600r] - 300
S = 600 + 600r
b) (5 points) Now solve for the goods market clearing interest rate. Please show all work.
Draw a desired savings/investment diagram locating this initial equilibrium and point A on the next page
.
600 + 600r = 630 - 400r .............r = .03, S = I = 618
A correct and completely labeled diagram is worth 20 points
13
We now have two shocks that occur simultaneously:
i) a change in the desired investment function – it is now:
Id = 650 - 400r
ii) a change in the consumption function:
Cd = 620 + 0.5(Y –T) - 600r
c) (5 points) Name three reasons why the savings function would change the way it did.
There are four……a (wealth) rises, yf, af, and CC rises.
d) (5 points) Resolve for the goods market clearing interest rate and the associated levels of desired savings
and investment.
New Savings function: S = 2500 - [620 + .5(2500 - 500) - 600r] - 300
S = 580 + 600r
580 + 600r = 650 - 400r
r = .07 I = S = 622
Add this development to your diagram and label as point B.
e) (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. When rates
change, explain what happens to saving and investment (be specific) and why?
@ r = .03, S = 598 and I = 638.....S < I ......Y - C - G < I ......Y < C + I + G..2500 < 2540...SINCE C + I
+ G is greater than Y, r must rise to decrease C and I to get back to equilibrium... when r rises by .04,
C falls by -600 x .04 = 24, I falls by -400 x .04 = 16, back to equilibrium where Y = C + I + G (2500 =
2500) or S = I (622 = 622)
f)(10 points) Are your results consistent with the conditions in the US economy shortly after (before the
recovery) the pandemic hit the economy? Why or why not?
NO - NOT REALLY - THE SHOCK TO CONSUMPTION IS POSITIVE (SHOULD BE
NEGATIVE) - LOWER WEALTH AND CC
INVESTMENT - NO, THE SHOCK IS POSITIVE, SHOULD BE NEGATIVE ANIMAL SPIRITS
HAVE FALLEN…NEGATIVE IMPACT ON INVESTMENT
14
5. (70 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 = 260 – 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 = 260 - 5K.........K* = 47
15
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 20 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 MPK f = 290 – 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 = 290 - 5K ..........K* = 52
16
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 = 47, uc = 30, MPK = 290 - 5(47) = 55, since uc= 30 is LESS than MPK=55, we need to BUY 5
golf carts to get back to profit maximization where uc = MPK = 30 when K=52 - for every cart we
buy. MPK falls by 5, when we buy 5, MPK falls by 5 x 5 = 25....from 55 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 50. 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 = 50 .... MPK = 290 - 5(50) = 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 I dC.
A completely labeled and correct diagram is worth 20 points (make sure you include the relevant
shift variables in parentheses or points will be taken off).
17
6. (60 points total) We assume that the world consists of two large open economies, USA and China.
USA Initial Conditions
Cd = 410 + 0.5(Y-T) – 300rw
Id = 460 – 200rw
Y = 2400
T = 200
G =500
China Initial Conditions
Cd = 500 + .5(YF – TF) – 300rw
Id = 400 – 200rw
Y = 2000
T = 400
G = 300
a) (10 points) What is the equilibrium interest rate that clears the international goods market? Show all
work
USA
S = 2400 - [410 + .5(2400 - 200) - 300 r ] - 500
S = 390 + 300r
CHINA
S = 2000 - [500 + .5(2000 - 400) - 300 r ] - 300
S = 400 + 300r
[390 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0
-70 + 1000r = 0 .............r* = .07
18
b) (5 points) Now calculate the levels of desired savings and investment for each country at this equilibrium
world real interest rate .
USA
S = 390 + 300(.07) = 411
I = 460 - 200(.07) = 446
NX = -35
CHINA
S = 400 + 300(.07) = 421
I = 400 - 200(.07) = 386
NX = + 35
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 absorption in each country to its income. Explain.
USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the
income we generate Y.
Absorption in the US is 2435, Y = 2400, Absorption in China is 1965, Y =2000.
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.
20 points for correct and completely labeled diagrams
We now have a change in conditions: China experiences some economic growth and their output rises to
2100. All else remains the same.
19
d) (5 points) Resolve for the world real interest rate that clears the international goods market 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)
NEW SAVINGS FOR CHINA
S = 2100 - [500 + .5(2100 - 400) - 300 r ] - 300
S = 450 + 300r
{390 + 300r] - [460 - 200r] + [450 + 300r] - [400 - 200r] = 0
-20 + 1000r = 0 .............r* = .02
USA
S = 390 + 300(.02) = 396
I = 460 - 200(.02) = 456
NX = -60
CHINA
S = 450 + 300(.02) = 456
I = 400 - 200(.02) = 396
NX = +60
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.
NO , things are getting worse - we are spending even more beyond our means - trade deficit has risen
from 35 to 60... US has NOT gone to AA.
f)(10 points) We know that world output has gone up by 100 and we also know, via the equation below that
the world's absorption has to rise by 100 (right hand side of the equation below). Explain where this 100 in
additional output was absorbed in each country. Use specific numbers.
Yus + YChina = [C + I + G] US + [C + I + G] China
Real interest rates have fallen by .05... from .07 to .02. As a result, Consumption and Investment in
both the US and China will rise.... for the US, C rises by -300 x -.05 = 15, I in US rises by 10, Same
for China - so the fall in r causes absorption to go up by a total of 50 plus the increase in C in China
due to higher output.. .since mpc = .50 in China, an increase of 100 in Y results in an increase in C by
50. Total increase = 100!
20
21
22