Download Practice Midterm 1 Answers - The University of Chicago Booth

Erik’s First Midterm
Macroeconomics
Fall 2014
Name (print):
______ANSWERS______________________________
Name (signature):
_______________________________________
Section Registered (circle one):
Mail Folder (circle one):
Student
No Folder
Tuesday a.m.
Harper Center
Tuesday p.m.
Wednesday a.m.
Gleacher Center
Exchange
TEST GRADE BREAKDOWN
Part I: (Consumption Tax: 15 points total)
____________
Part II: (Understanding Macro Models: 16 points)
____________
Part III: (True/False/Uncertain: 45 points)
____________
Part IV: (A Preview of Inequality: 6 points)
____________
Part V: (Income Taxes and Consumption: 18 points)
____________
Total (out of 100)
____________
1
Exam Preamble

As always, that honor code rules are in effect. You know the routine. All the usual
disclaimers apply. By signing on page 1, you are pledging to adhere to the honor code
guidelines in my syllabus and the student handbook. Any discussing of the exam with
students who have yet to take the exam is a blatant violation of the honor code.

You have 1 hour and 45 minutes for the exam.
will run out of time.

Unless otherwise indicated, assume all curves are well behaved (i.e., labor supply slopes up,
labor demand slopes down, investment demand slopes down, etc).

For discussion problems, explain - but do not be wordy! (The more you say, the more likely
you will say something wrong).

Please, please, please - read ALL the information for the questions.

When you are finished, you can leave the room. However, I will start my lecture promptly at
10:30 (in the morning classes) or 8:00 (in the evening class). We will have a lecture after the
midterm.

You are allowed:
Move quickly through the exam or you
One Piece of Paper - Handwritten - Not Photo Copied - Front Side Only
A Calculator

Good Luck!
2
Exam Assumptions
1.
All answers should be provided in terms of the models and discussions developed in
class. Some of you provide me with your “own” models of the economy. While these
are often fun to read – they are almost always wrong (or, at least, incomplete). So,
please try to answer the questions in terms of the models developed in class. Moreover,
this is not a philosophy class. I am testing you on the models developed in class. If we
have not talked about it in class, I am not going to test you on it.
2.
TFP, population, government spending, taxes, transfers, consumer confidence,
uncertainty, and business confidence are all held fixed, unless I specifically tell you
otherwise.
3.
The capital stock (K) is assumed to be constant through our entire analysis (aside from
one question later in the exam - for that question I will tell you to assume that K can
change). Throughout the rest of the exam, this does not mean that investment (I) is
constant. People can invest today – we will just assume that today’s investment does not
affect today’s capital stock (unless told otherwise). This assumption just makes our life
easier.
4.
All changes in TFP, taxes, government spending, etc. are assumed to be permanent and
unexpected, unless I specifically tell you otherwise. (Often, I will tell you otherwise.
This assumption is here in case I ever forget to tell you about the nature of the change in
the variable, this will be the default situation. Again, this is just to reduce any potential
exam ambiguity).
5.
Unless told otherwise, all consumers in the class are PIH (non-Ricardian) who have the
preferences developed in class (log utility, r = 0, β = 1).
6.
We will assume, for now, that NX always equals zero.
7.
Assume that changes in N have no effect on investment demand (for simplicity).
3
Part I: Consumption Tax (15 points - 3 points each)
As government budgets continue to be stressed, the talk of moving to a national sales tax arises
from time to time. In this problem, let’s discuss how an increase in consumption taxes will affect
some of the curves/markets that we have discussed so far in class.
When answering the questions, consider only the models we have built so far. For this problem,
let's assume that the labor market will always clear. There are links that you want to put in place
between various markets (i.e., aggregate supply and aggregate demand). You do not know those
links yet. For now, just think about the models we have built so far and do not try to link
aggregate supply (production) and aggregate demand (expenditure). Those links will not affect
the answers to the questions below.
When answering the questions, assume the change in the consumption tax was unexpected and
permanent (and that all consumers are non-liquidity constrained PIH consumers).
Finally, let’s assume that income effects on labor supply are large relative to the
substitution effects on labor supply in the labor market (resulting from changes in after tax
wages).
Given the above information, circle the true answer for each of the question stems.
explanation is needed.
No
Let’s start by figuring out what happened in the labor market.
Ns0
Ns1
w/p(0)
w/p(1)
ND
N0 N1
The labor supply curve will shift right (on net) because the income effect on labor supply is
large relative to the substitution effect. This will cause the following:
N* to rise (equilibrium labor will rise from N0 to N1)
Y* to rise (as N* rises)
Before tax wages will fall
After tax wages will fall (even more than before tax wages)
PVLR will fall (as after tax wages will fall)
C will fall (as after tax wages will fall).
Marginal utility of consumption will increase (because of diminishing marginal utility of
consumption as C falls).
The IS curve will shift in as C will fall.
Marginal utility of leisure will increase (as leisure falls as N increases)
4
One may ask how does the IS curve shift in as Y* shifts out? We will do this later in the
class. What will happen is that P will fall (w will change such that w/p remains at w/p(1)).
As p falls, the real money supply will increase and real interest rates will fall. The result
will be that move along the new IS curve to have an equilibrium where the new IS curve
intersects the higher level of Y* (at lower interest rates and higher investment). You do not
know about this yet – but, that is how a shift in of the IS curve can co-exist when Y* shifts
out. That is why I asked this question so you can see the dichotomy.
A.
The potential level of GDP (Y*) will:
i.
Unambiguously increase as N* increases
ii.
Unambiguously decrease
iii.
Unambiguously stay the same
iv.
Could either increase, decrease, or stay the same
B.
The marginal utility of consumption (MUC) will:
i.
Unambiguously increase as C falls
ii.
Unambiguously decrease
iii.
Unambiguously stay the same
iv.
Could either increase, decrease, or stay the same
5
Part I: Consumption Tax (15 points - 3 points each)
C.
The marginal utility of leisure (MUL) will:
i.
Unambiguously increase We work more and take less leisure
ii.
Unambiguously decrease
iii.
Unambiguously stay the same
iv.
Could either increase, decrease, or stay the same
D.
The Investment-Savings (IS) curve (on net) will
i.
Unambiguously increase
ii.
Unambiguously decrease (shifts in) as C falls
iii.
Unambiguously stay the same
iv.
Could either increase, decrease, or stay the same
E.
Labor income tax revenues will:
i.
Unambiguously increase as N increases, Y increases and tn remains constant
ii.
Unambiguously decrease
iii.
Unambiguously stay the same
iv.
Could either increase, decrease, or stay the same
6
Part II: Understanding our Macro Models (16 points total, 4 points each)
For each of the questions below, choose the correct answer to the question stem (choose only one
answer). When answering this question, all the assumptions on page 3 hold. In particular, when I
am changing one exogenous variable I am assuming all other exogenous variables are held fixed
(unless told otherwise).
Note:
We will grade this question on a 0/4 scale. If you pick the correct answer, you get four
points.
A.
Which of the following are true about a permanent and unexpected increase in TFP (A)
today? For this sub-question, assume that the substitution effect on labor supply
dominates the income effect on labor supply.
i.
The long run aggregate supply (LRAS) curve will shift to the right today and the
labor supply (NS) curve will shift to the left today.
ii.
The labor demand (ND) curve will shift to the right today and the labor supply (NS)
curve will shift to the right today.
iii.
The long run aggregate supply (LRAS) curve will shift to the right today and the IS
curve will shift to the right today.
iv.
Answers (i) and (iii) above are true.
v.
Answers (ii) and (iii) above are true.
vi.
Answers (i), (ii) and (iii) above are true.
vii.
None of the above answers are true.
As TFP increases, in the labor market, the labor demand curve shifts right (as MPN increases)
and the labor supply curve shifts left (from the income effect on labor supply – remember, the
substitution effect is a movement along the labor supply curve). In the IS-LM market, the IS
curve shifts out as PVLR increases which causes C(.) to increase and I(.) to increase as MPK
increases. The LRAS curve must also shift out as Y* increases as a result of N* increasing (the
substitution effect dominates) and A increasing (the shock).
7
Part II: Understanding our Macro Models (16 points total, 4 points each) (continued)
B.
Which of the following are true about a permanent and unexpected increase in
government spending (G) today? For this sub-question, assume that the substitution
effect on labor supply dominates the income effect on labor supply.
i.
The IS curve will shift to the right today and the long run aggregate supply (LRAS)
curve will shift to the right today.
ii.
The IS curve will shift to the right today and the labor demand (ND) curve will shift
to the right today.
iii.
The IS curve will shift to the right today and the labor supply (NS) curve will shift to
the right today.
iv.
Answers (i) and (iii) above are true.
v.
Answers (ii) and (iii) above are true.
vi.
Answers (i), (ii) and (iii) above are true.
vii.
None of the above answers are true.
G affects only the expenditure side of the economy: Y= C+I+G+NX. Increasing G will shift out
the IS curve. It has no effect on labor demand, labor supply or the long run aggregate supply
curve (LRAS). We never had G as any part of the discussion of the labor market at any point in
the class. We will have a more detailed discussion of G in class this week.
C.
Which of the following are true about a permanent and unexpected decline in labor
income taxes today? For this sub-question, assume that the income effect on labor
supply dominates the substitution effect on labor supply.
i.
The IS curve will shift to the right today and the long run aggregate (LRAS) supply
curve will shift to the left today.
ii.
The IS curve will shift to the right today and the labor demand (ND) curve will not
change today.
iii.
The IS curve will shift to the right today and the labor supply (NS) curve will shift to
the left today.
iv.
Answers (i) and (iii) above are true.
v.
Answers (ii) and (iii) above are true.
vi.
Answers (i), (ii) and (iii) above are true.
8
vii.
None of the above answers are true.
In the labor market, as labor income taxes permanently fall, the after-tax wage must increase
(that’s the policy). The income effect shifts the labor supply curve left. The substitution effect
shifts the labor supply curve right. Because we told you the income effect dominates, the labor
supply curve shifts on net to the left. This means before-tax wages increase and N* falls. There is
no effect on labor demand. In the IS-LM market, consumption increases as PVLR increases. This
causes the IS curve to shift out. With regard to the long run aggregate supply curve (LRAS), it
must shift in as N* falls (from the labor supply curve shifting in).
9
Part II: Understanding our Macro Models (16 points total, 4 points each) (continued)
D.
Which of the following are true about a permanent and unexpected increase in labor
income taxes starting tomorrow? For this sub-question, assume that the substitution
effect on labor supply equals the income effect on labor supply. Also, assume that
households many remaining periods of their life (LL is large).
i.
The IS curve will shift to the right today and the labor supply (NS) curve will shift to
the left today.
ii.
The IS curve will shift to the right today but the labor supply (NS) curve will not
change today.
iii.
The IS curve will not change today and the labor supply (NS) curve will not change
today.
iv.
Answers (a) and (c) above are true.
v.
Answers (b) and (c) above are true.
vi.
Answers (a), (b) and (c) above are true.
vii.
None of the above answers are true.
As labor income taxes increase, after-tax wages must fall (that’s the policy). The income effect
tells us the labor supply curve will shift out. There is no substitution effect on this economy today
because taxes do not change until tomorrow. The income effect will occur if individuals are
forward looking – they know their PVLR will fall. There is no substitution effect today because
the tax rate will not change today. Tomorrow there will be a substitution effect (but not today).
As a result, the labor supply curve will definitely shift out (because people are poorer). This
means that N* increases and W/P falls (today). As PVLR decreases, consumption must fall - we
are permanently poorer (again if consumers are forward looking). This causes the IS curve to
shift in. As N* increases today, the LRAS curve must shift out today. None of these answers
are correct.
We also gave credit for (iii). Some people thought that the tax cut wasn't announced today.
In that case, nothing would happen today. In the question, I should have said it was
announced today. If it was announced today, then the answer above is the correct answer.
If it was announced tomorrow (and enancted tomorrow), nothing happens today. So, we
will give credit for (iii).
10
Part III: True/False/Uncertain: Explanation Determines the Grade
(5 points each - 45 points total)
Each of the parts below sets up a scenario (in italics) and ends with a statement. In this section,
you are to discuss whether that final statement is True, False or Uncertain.
As on the practice exams - explanation determines all of your grade! I will give no credit for
writing true when the answer is true but your logic is wrong. Each of your answers should be at
most 3-4 sentences. To receive full credit, you need to be explicit about the mechanism that is
driving your results. Finally, if it is a two pronged question (where I asked you about two
separate things like employment and wages), you need to address both parts to get full credit!
Each question is worth 5 points each.
Please write as clearly as you can – it makes it so much easier for us to follow your logic! If we
cannot read your writing (or follow your logic), we will deduct points.
A.
Across many developing economies, the working age population often changes due to
changing fertility rates. As economies grow rapidly, fertility rates usually start to
decline.
If income effects are large relative to substitution effects on labor supply, a permanent
decline in the working age population will – on net – shift the labor supply (NS) curve to
the left.
True. This was just like one of the practice quiz questions. The answer is the same if the income
effects are large or small. The labor supply curve (Ns) will shift in as working age population
falls. This will increase W/P for those remaining in the work force. As the remaining households
are richer, they will work less. This is a second shift left of the labor supply curve. The size of
the income effect determines how far left the second shift is. But, regardless, the two shifts go in
the same direction. It is unambiguous that the labor supply curve will shift left as the working
age population falls. (Note the substitution effects – in this case – are just movements along the
new labor supply curves!)
B.
Suppose TFP (A) increases permanently starting today. Assume further that real interest
rates are permanently held fixed. In this question, we will let the capital stock (K) adjust
optimally (if firms desire). Also, for simplicity, we will assume that income and
substitution effects on labor supply cancel such that N is remained fixed through the
problem.
Given firm profit maximization (as described in class), a permanent increase in TFP
(starting today) will result in an increased marginal product of capital (MPK) tomorrow.
False. MPK = r (that is the first order condition of firm optimization – ignoring depreciation,
etc.). If r is fixed, MPK will remain constant. How does this happen? As A goes up, MPK goes
up. Firms respond by investing more today (lowering MPK by increasing the capital stock). This
is the key assumption of the firm’s problem – they maximize profits such that the marginal
11
benefit of investment equals the marginal cost of investment. If the marginal costs do not change,
than the marginal benefits cannot change.
Part II: True/False/Uncertain: Explanation Determines the Grade (continued)
C.
Consider the labor market developed in class. Assume income effects are small relative to
substitution effects. Since 2000, the U.S. economy has experienced both large increases
in TFP and declining marginal tax rates on income.
Theoretically, our model of the labor market predicts that a permanent increase in TFP
coupled with a permanent decline in labor income tax rates would unambiguously
increase both the amount of workers in the economy (N) and the after tax wage.
True!
Analyze each shift separately.
An increase in TFP will increase both W/P and N (if income effects are small). Given that tax
rates are fixed (if we are looking only at the TFP change, after tax wages would also increase).
A fall in taxes rates would shift labor supply curve to the right which would increase N and
increase AFTER tax wages (that is why we are working more).
So, in both cases, N increases and after tax wages increases. So, when you put the two shocks
together, both effects will reinforce each other.
If you said that the change in after tax wages was ambiguous, you did not receive the full points.
D.
Economists and demographers have long predicted that there will be a sharp decline in
the work force starting in 2013 as baby boomers start to retire. Such predictions have
been widely publicized during the last decade.
According to the standard PIH theory developed in class, we should see a sharp increase in
consumption for those remaining in the work force between 2012 (prior to the baby
boomers starting to retire) and 2014 (after they start retiring).
False. This was a harder problem. If consumers are truly PIH, the change in demographics
would have been forecast in advance. So, even though W/P would increase (as the baby
boomers retire), the change should already have been incorporated into their consumption plan
today (mean consumption would not change when it actually occurs). You could have told me
that it would have increased if people were liquidity constrained. That is fine – but you would
have needed to say that.
12
E.
Assume income effects are small relative to substitution effects.
Consider the models developed in class. A permanent increase in TFP will reduce the
equilibrium unemployment rate in the economy.
False. In our model, the labor market is in equilibrium so there is no unemployment. What effect
would an increase in TFP have in our labor market? The labor demand curve would shift out (as
the marginal productivity of labor increases) and the labor supply curve would shift in (from the
income effect). Our market would reach a new equilibrium!
13
Part II: True/False/Uncertain: Explanation Determines the Grade (continued)
For parts F and G, consider the following information.
During the late 1990s and early 2000s, we saw large run ups in stock market wealth. For
simplicity, let’s refer to the run up in stock market wealth as being a magnitude of X dollars.
For simplicity, let’s assume that there is only one individual in the economy and that individual
owns stocks. This individual is expected to live 25 more years (i.e., LL = 25). From the
perspective of today’s individual, suppose the stock market unexpectedly increased by X today
(measured in dollars).
Lastly, assume that this representative individual in the economy is a non-liquidity constrained
PIH consumer of the type modeled in class (has log utility, β=1, r = 0, etc.).
F.
Given the above information, if the individual believes that the unexpected increase in the
stock market today of X was permanent (i.e., increase by X dollars today and remain
constant at that new level forever), their annual consumption today (C) should increase
by X/25 dollars.
True. Households will take the increase in wealth and spread it over the remaining periods of
their life. If they get an extra $250 today, the will take that $250 and spread it over the remaining
periods of their life (25 years) thereby increasing their consumption by $10 per year. When we
estimate the MPC out of permanent wealth changes, our estimates are roughly in the 0.03-0.04
range (roughly consistent with LL being 25-30 years for the average stock owner).
G.
Given the above information, if the individual believes that the unexpected increase in the
stock market today of X was temporary (i.e., increase by X dollars today and decrease
by X dollars tomorrow such that the total change in the stock market value is zero over
the next 30 years), their annual consumption today (C) should increase by X/25 dollars.
False, a temporary change in wealth has ZERO effect on consumption. The wealth comes today
and goes away tomorrow – a household’s PVLR is unchanged so consumption should not
respond. If households are non-liquidity constrained PIH, temporary wealth changes have NO
effect on their consumption.
14
Part II: True/False/Uncertain: Explanation Determines the Grade (continued)
H.
Over the past few weeks, Kansas has made the news with respect to early outcomes of
their "Economic Experiment". In 2010, Kansas cut labor income taxes dramatically
across the board. The plan was for the tax cut to stimulate employment and "pay for
itself" (raising more tax revenue). The net result was no change in employment growth
(relative to neighboring states that didn't cut taxes) and massive deficits.
In this question, we will consider how a large decline in labor income taxes will effect
government budget deficits. Throughout the problem, assume all other exogenous
variables are held fixed (i.e., A, G, Tr, etc.).
According to the models developed in class, a large decline in labor income taxes will
unambiguously reduce tax revenues if the income effects on labor supply are roughly the
same magnitude as the substitution effects on labor supply.
TRUE. Tax Revenues = Y * tn. First, what happens to tn? The policy is that tn falls. What
happens to Y? To determine what happens to Y, we must determine what happens to N*. As
labor income taxes fall, taking leisure has become relatively more expensive, thus the substitution
effect tells us that the labor supply curve must shift out. As labor income taxes fall, after-tax
wages rise (that is the policy) which means PVLR must increase. As PVLR increases, the income
effect says we feel rich and work less—shifting in the labor supply curve. We told you the
income and substitution effects are roughly the same which means the labor supply curve is
roughly in the initial position and N* has not changed. Thus, Y has not changed. If Y has not
changed and tn has decreased, it is easy to sign the effect on tax revenues—they must have
declined.
I.
Some have argued that during recent years, there has been a large expansion of
government transfers (Tr) to the household sector. Consider the models built in class.
Suppose there was a large unexpected permanent increase in government transfers (Tr).
Lastly, suppose nothing else changes with respect to government spending (G) or tax
rates.
Theoretically, our models predict that a large unexpected permanent increase in
government transfers (Tr) will shift the IS curve to the right and the labor supply curve to
the left.
TRUE. In this case, the policy causes the income and substitution effect to move in the same
direction. Let’s do the income effect first, as transfers increase, we feel richer and work less
shifting in the labor supply curve. As transfers increase, taking leisure has become relatively less
expensive (Uncle Sam is paying us to stay at home!). That means we want to work less, shifting
in the labor supply curve. Thus, both effects shift the labor supply curve in. As transfers
permanently
increase,
consumption
increases
shifting
out
the
IS
curve.
15
Part IV: A Preview of Our Inequality Discussion (6 points total)
In Topic 4, we are going to have a discussion of inequality. One common discussion in the
inequality literature is that rich individuals own the capital and that the return to capital (real
interest rates) have been high relative to the growth rate in wages.
In this problem, we will consider the implications of an increase in real interest rates on share of
income going to capital owners using the model we have developed (holding all else equal). In
particular, we will assume our Cobb-Douglas production function holds such that:
Y  AK  N 1
Assume that α is fixed over time. Additionally, we will assume that firms maximize profits and
are price takers in the aggregate economy (as we did in class).
For this question, I want you to discuss whether the following statement (in italics) is true, false,
or uncertain given the model we developed in class. Use equations from class to prove your
answer. The use of equations to prove your point will determine your entire grade.
Question:
Hint:
According to the model developed in class, an increase in real interest rates will
increase the share of income flowing to capital owners in the economy.
Marginal product equations and some algebra will be needed. Make sure you define the
share of income going to capital owners in your answer. Label all equations clearly!
Also, circle whether you think the answer is true, false or uncertain (it will help us with
grading) before launching into equations to defend your answer.
The above statement is:
True
False
Uncertain
(circle one)
Here is the only correct answer to this question as stated.
This was pretty easy to do from the intuition. It may be slightly harder to do with the math. The
intuition is simple. α is the share of income going to capital owners (this is how we defined alpha
and 1-alpha in the Cobb-Douglas (CD) production function). In the problem, I told you alpha
was constant. So, you know, by definition, that the share of income going to capital owners must
be fixed in the CD production function no matter what happens to TFP or r or after-tax wages or
what. So, the answer is that r will have no effect on the share of income going to capital owners.
Here is the math to prove it.
Share of income going to capital owners = (r*K)/Y. (r*K) is the amount of capital in the
economy (owned by the capital owners) times the rate of return on capital. This is analogous to
the share of income going to workers being ((W/P)*N)/Y.
Lets use the share of income going to capital owners equation: (r*K)/Y.
Using firm optimization, we know that r = MPK = αA(N/K)1-α
16
Now, lets do some algebra:
Share of income going to capital owners = (αA(N/K)1-αK)/Y = α Y/Y = α.
Given that I told you alpha was fixed, you know that the share of income going to capital owners
will also be fixed. The reason is that as r goes up, K will go down. The CD production function
implies that the percentage increase in r will exactly equal the percentage decline in K/Y leaving
the share of income going to capital owners unchanged. This is a particular assumption with the
CD production function.
Also, for those that studied, this came directly from supplemental notes 2 (on the aggregate
production function).
Update
There was some confusion between Carolyn and I as to the wording of the question. She thought
the wording of the question was "According to the model developed in class, an increase in real
interest rates will NOT increase the share of income flowing to capital owners in the economy."
Notice, there word "NOT" was added to Carolyn's interpretation (it was just on oversight on her
part). This caused some confusion in her grading. She was looking for an answer of true. So,
she gave lots of credit to people who wrote true. The actual answer was false. So people who
got full credit really should have gotten LESS than full credit. No-one got zero on this question.
She gave out scores of 2/4/6. Given there was so little variation in the actual scoring, we decided
to just through-out the question as opposed to re-grading the question for the entire class. Also,
since there was so little points at stake, there was no real effect on anyone's course grade (whether
they would have gotten it completely right or completely wrong). Remember, throwing the
question out only matters if your performance on this question would have differed dramatically
from the rest of the exam (because we just re-weighted the rest of the exam). Given the grades
Carolyn recorded, all the 6's and 4's would have moved to 2, many of the 2's would have moved
to either 4 or 6 (depending on how well they explained their answers). We recomputed
everyone's grade assuming this alternate grading scheme (moving the 6's to 2's and moving the
2's/4's to 6's). We found that dropping the question (which is what we did) barely changed the
relative ranking of the midterm performance relative to the alternate (i.e., true) grading scheme.
Given that, we just dropped the question. It will have zero affect on people's course grade.
17
Part V: Income Taxes and Consumption (18 points total - 3 points each)
During both the 2001 and 2008 recessions, tax policy was put front and center as a way to
stimulate the economy. In this question, we will explore different policies to stimulate
consumption using the models we have built in class. Formally, we will make the following
assumptions:

All individuals live three periods (t = 1, t = 2, and t = 3).

All consumers have log utility over consumption with β = 1 and r = 0, such that:
U (C1 , C2 , C3 )  ln(C1 )  ln(C2 )  ln(C3 )

There are no transfers implying disposable income is after tax income (Yd = (1-tn) Y)

All individuals are liquidity constrained PIH. The liquidity constraint is defined such that
wealth must always be non-negative (Wealtht ≥ 0 for all t).

Baseline parameters. Initial wealth (Wealth0) = 90 and labor income tax (tn) = 0.2.

Assume pre-tax income evolves over time such that all individuals have income:
Y1 = 140, Y2 = 185, and Y3 = 185. (Don't forget to adjust for taxes!)
Note: When answering the questions, you can report consumption in each period up to one
significant digit after the decimal (if need) (i.e., XXX.X).
A.
Given the baseline assumptions, what is the consumption of individuals in this economy
in period 1? Briefly show your work. Put your answer in the box (3 points).
Consumers are PIH, we want to first solve for their lifetime pot of money, PVLR.
PVLR = 90 + .8(140+185+185) = 498
Now, divide by LL to get consumption in each period.
C1 = 498/3 = 166 (which is desired consumption. Given that our available resources in period 1
is 0.8*140 + 90, we know that our available resources exceed our desired consumption and we
are not liquidity constrained).
C1 = 166
B.
Suppose there is a housing market collapse such that initial wealth falls from W 0 = 90 to
W0 = 18. Notice, the wealth decline occurs before people make their consumption
decision in period 1. Further, assume households think the decline is permanent. Given
this assumption, what is the new level of consumption for individuals in this economy
in period 1? Briefly show your work. Put your answer in the box (3 points).
Consumers are PIH, we want to first solve for their lifetime pot of money, PVLR.
PVLR = 18 + .8(140+185+185) = 426
Now, divide by LL to get our optimal consumption in each period.
18
C1 = 426/3 = 142 however, remember we have a wealth constraint such that wealth can’t be
negative. Our available wealth to consume in period 1 is equal to our initial wealth plus our
disposable income in that period = 18 + .8*140 = 130. Therefore, although we would like to
consume 142, we are liquidity constrained and can only consume up to our constraint: 130.
C1 = 130
19
Part V: Income Taxes and Consumption (18 points) (continued)
C.
Suppose that wealth remains at its new level such that W0 = 18 (as in part B). Now
suppose the government wants to stimulate the economy by unexpectedly cutting taxes
permanently such that tn falls from 0.2 to 0.1 (i.e., tn = 0.1 for all periods). Given this,
what is the new level of consumption for individuals in this economy in period 1?
Briefly show your work. Put your answer in the box (3 points).
Consumers are PIH, we want to first solve for their lifetime pot of money, PVLR.
PVLR = 18 + .9(140+185+185) = 477
Now, divide by LL to get our optimal consumption in each period.
C1 = 477/3 = 159
Remember, our constraint dictates that we can consume up to 18+ .9*140 = 144.
Thus, we consume up to our constraint in the first period, 144.
C1 = 144
D.
Some politicians found it hard to pass a permanent tax cut. Instead they talked about
passing a temporary tax cut. Suppose that wealth remains at its new level such that W0 =
18 (as in part B). Now suppose the government wants to stimulate the economy by
unexpectedly cutting taxes temporarily such that tn falls from 0.2 to 0.1 only in period
(i.e., tn = 0.1 in period 1). In all other periods, tn is expected to remain at 0.2 Given this,
what is the new level of consumption for individuals in this economy in period 1?
Briefly show your work. Put your answer in the box (3 points).
PVLR = 18 + .9(140)+0.8(185+185) = 440
Desired consumption is 146.66.
However, we are constrained to consume at most 144 (18 + .9*140)
C1 = 144
E.
Some politicians talked about "Mortgage Debt Relief" instead of tax cuts to stimulate the
economy. In essence, this is equivalent to increasing household wealth. Suppose that
policy makers could forgive debt such that initial wealth in the economy is now 69 (i.e.,
Wealth0 = 69). Notice, this increase in wealth of 51 is about the same cost as a
permanent tax cut of 10% (as in part C). Supposing tax rates permanently remain at 0.2,
what is the new level of consumption for individuals in this economy in period 1 when
initial wealth is increased to 69? Briefly show your work. Put your answer in the box (3
points).
20
Consumers are PIH, we want to first solve for their lifetime pot of money, PVLR.
PVLR = 69 + .8(140+185+185) = 477
Now, divide by LL to get our optimal consumption in each period.
C1 = 477/3 = 159
Remember, our constraint dictates that we can consume up to 69+ .8*140 = 181.
Thus, our constraint does not bind and we can consume up to our optimal allocation, 159.
C1 = 159
Part V: Income Taxes and Consumption (18 points) (continued)
F.
The permanent tax cut (Part C) cost roughly the same amount as the debt forgiveness
policy (Part E). Both gave individuals an increase in lifetime resources of about 50.
Why did the consumption response in period 1 differ so dramatically between the two
policies? Provide the intuition for your answer! (3 points)
In part C, consumers are still liquidity constrained so they can not follow their
optimal consumption path. By giving people more money upfront it relaxes their
constraint more resulting in more spending. That is why many politicians (and
some economists) were arguing for “debt forgiveness” as opposed to tax cuts to
jump start consumer spending. My colleague Amir Sufi was one such academic
economist supporting these proposals.
____________________________________________________
(No Need to Write Below This Line)
21
Scrap Paper 1
22
Scrap Paper 2
23
Scrap Paper 3
24
Scrap Paper 4
25