Download Practice Midterm Answers 2 - The University of Chicago Booth

Erik’s First Midterm
Macroeconomics
Fall 2015
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Tuesday a.m.
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TEST GRADE BREAKDOWN
Part I:
(Stock Market Crashes: 16 points total)
____________
Part II: (Understanding Model Mechanisms: 18 points total)
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Part III: (True/False/Uncertain: 30 points total)
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Part IV: (Question on Reading: 4 points total)
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Part V: (Social Security Reform: 16 points total)
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Part VI: (Government Spending Multiplier: 16 points total)
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Total (out of 100)
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1
Exam Preamble

As always, the 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 your “own” models of the economy. While these are often
fun to read – they are also 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 in class, I am not going to test you on it.
2.
TFP (A), population, government spending (G), taxes (tc, tn), welfare programs (Tr),
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 unless told
otherwise. Throughout 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 TPF, 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). I have not defined "nonRicardian" in class yet - this just means that the expectations of future tax increases that
result from the government deficits today will not affect consumption today.
Consumption will respond to tax changes - but, only the tax changes I tell you about.
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). This
just makes our life easier.
8.
Assume that the labor market always clears - unless specifically told otherwise. In Part
IV of the exam, we will ignore the labor market completely. In that part of the exam, the
labor market may not clear - but, given the assumptions I make in that problem, the labor
market is irrelevant for the question at hand.
3
Part 1: Objective Questions: Stock Market Crashes (16 points total)
Between early 2007 and early 2010, the value of U.S. equities fell by some 30 percent. On top of
that, the value of real estate (due to the housing collapse) fell sharply. In this question, we will
assess what happens to the macro economy when there is a substantial decline in household
wealth.
When addressing this question, we are just going to analyze the decline in wealth and how that
affects the economy. In other words, we will hold everything else constant (consumer
confidence, business confidence, TFP) when the wealth falls. This is not overly realistic – one
reason stock markets may fall is our expectations about future productivity fall. But, for this
question, we are only going to focus on the effects of massive declines in U.S. wealth.
Again, assume all other exogenous variables (government spending, tax rates, transfer programs,
interest rates) are all held fixed through this example. Just focus your attention on what happens
when individuals experience a massive decline in their wealth.
Finally, assume that the decline in wealth was unexpected and that individuals expect the decline
to be permanent. In other words, individuals assume that the stock market will remain at the
2010 level going forward– this means that they will be permanently poorer relative to where they
were in 2007. At the time of the crash, many people did think it was going to be permanent.
Goal of this question: Use the models developed in class to analyze the effect of an unexpected
one-time large and permanent decline in stock market wealth (holding all else constant). Do so
by explaining the effects (if any) of such a change on the four major curves developed in class:
the labor demand curve (Nd) , the labor supply curve (Ns) , the long run aggregate supply curve
(LRAS), and the IS curve.
For each question listed below, circle whether the unexpected permanent decline in stock market
wealth will shift the curve to the right (on net), shift the curve to the left (on net), have no effect
on the curve (on net), or whether the direction of the shift is uncertain (on net). After that, provide
a 1-2 sentence reason to justify the response that you circled.
Note: This example is all about a change to PVLR (as households take a big hit to their
initial wealth). The fall in PVLR will affect household optimization. As households become
poorer, they will buy less of what makes them happy. Given our assumptions about utility
in this class, consumption and leisure make individuals happy. A sharp decline in PVLR
will affect the labor supply curve (as individuals are poorer, they will work more – i.e., take
less leisure). Additionally, as PVLR falls, they will consume less (C will fall). The fall in C
will also shift in the IS curve.
Note: The IS curve is just the graphical representation of Y = C + I + G + NX (remember,
we are ignoring NX for now) drawn in {Y,r} space. For any given r, a lower C means lower
Y. This means a decline in C will shift the IS curve to the left.
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A)
shift right
Labor demand (Nd) curve (circle one) (3 points)
shift left
no shift
direction of the shift is ambiguous
Reason: The labor demand curve shifts with changes in A and changes in K. A is fixed in
this problem (it only changes when I tell you it changes). K is fixed by assumption (read the
exam assumptions). Given A and K are fixed, there is no shift in the labor demand when
wealth increases. (Note – we will move along the labor demand curve)
B)
shift right
Labor supply (Ns) curve (circle one) (3 points)
shift left
no shift
direction of the shift is ambiguous
Reason: We went over this above. As PVLR falls, the income effect says households will
work more (they can afford less leisure time).
C)
shift right
shift left
IS Curve (circle one) (3 points)
no shift
direction of the shift is ambiguous
Reason: We went over this above. As C falls, the IS curve will shift to the left.
D)
shift right
Long Run Aggregate Supply (LRAS) Curve (circle one) (3 points)
shift left
no shift
direction of the shift is ambiguous
Reason: This was a little more difficult. The long run aggregate supply curve is a function
of A, K and N. A and K are fixed. The fall in wealth increases N (as labor supply shifts
right). The net effect of more people working is higher Y (but lower Y/N as real wages
fall).
Using the definition of the long run aggregate supply curve, this was straight forward. It
becomes difficult when we start to try to reconcile this with the fact that the IS curve shifted
left (implying that Y fell as C fell). The way we will reconcile these things is that other
prices in the economy will change (like P and r). We do not know how to do this yet (but
we will). The key is that r will fall (because P falls) causing I to increase (not the
autonomous part of I but the part of I that responds to interest rates) and offset the decline
in C (we will represent this as a move down the new IS curve as interest rates fall).
We will go over this in great depth during the next few weeks (after I tell you how r is set in
topic 5). For this exam, however, I just wanted you to know what way the curves shift!
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Part I (continued): Stock Market Crashes Continued (16 points total)
Continue the assumptions on the previous page (i.e., there is a large unexpected and permanent
decline in the U.S. stock market).
As macroeconomists, we are interested in not only what direction consumption will respond to a
permanent decline in wealth, we are also interested in how much consumption will respond to a
permanent decline in wealth. We refer to the quantitative impact on consumption from a
permanent decline in household wealth as the “wealth effect on consumption”.
(As an aside, when the exam is over, enter “wealth effect on consumption” into your favorite
search engine. There is a massive literature by us empirical macroeconomists trying to estimate
how much consumption responds to a permanent change in stock market wealth. This will give
you a sampling of this literature).
Instead of trying to figure out empirically how much consumption should change from a
permanent change in wealth, let’s use our model to predict how much consumption (C) should
change when there is a permanent decline in wealth.
E) Wealth Effect on Consumption (4 points)
Assume all consumers in the economy are non-liquidity constrained PIH consumers. Assume
that the average wealth holder in the economy is 50 years of age and assume that the average
length of life for those individuals is 80 years of age. Lastly, assume that consumers behave
according to the model developed in class (log utility, β = 1 and r = 0).
Given these assumptions, what should be the marginal propensity to consume (MPC) out of a
permanent and unexpected decline in household wealth for wealth holders?
Put your answer in the box. Note: your answer should be some number in the interval between 0
and 1 (potentially including 0 or 1). (4 points total). No explanation is needed.
Answer: MPC out of permanent and unexpected decline in household wealth =
0.0333
1/30 =
Intuition: This was very straight forward and comes directly from the lecture notes. A onetime permanent change in household wealth has a MPC of 1/LL (that exact sentence came
from one of the slides in Topic 4). Moreover, it was a question that was on the practice
quizzes/midterms. This was one of the easier questions on the exam and I expect most
people to have gotten this correct.
Why is the answer 1/30? In this case, the remaining length of life is 30 years. The PIH
model says that individuals will spread out the change in wealth over their remaining years
of life. There is a large literature in macroeconomics trying to estimate the wealth effect on
consumption. The answer to this helps us to understand how much will consumption be
depressed when stock markets fall? Now, if households are liquidity constrained, the effect
could be larger. This is related to some of the recent work from Amir Sufi (a Booth
professor). Amir’s work show that the MPC of housing wealth declines can be larger than
1/LL if households are liquidity constrained. Veronica Guerrieri (another Booth professor)
is also working on this topic. You can tell your friends to take Veronica’s macro class in the
winter.
6
Part II: Economic Mechanisms (18 points total – 3 points each)
For this question, circle the answer that makes the question stem true. There is only one answer
to each question. No explanation is needed.
Question A
Which of the following is unambiguously true about an unexpected permanent increase in
TFP (A)?
a. The marginal product of labor will increase.
b. The marginal utility of leisure will increase.
c. Both the marginal product of labor and marginal utility of leisure will increase.
d. Neither the marginal product of labor nor the marginal utility of leisure will increase.
An unexpected permanent increase in TFP will shift labor demand to the right. As real
wages go up, households are richer and will choose to work less. This will cause an income
effect that causes the labor supply to shift to the left. (The substitution effect is movements
along the labor supply curve).
MPN = W/P (first order condition of firm profit maximization).
We know W/P
unambiguously increased (labor demand shifts out and labor supply shifts in). So, we know
unambiguously that MPN increases.
The marginal utility of leisure depends on how much leisure household takes. Whether
leisure increases or not (employment falls or not) depends on strength of income vs.
substitution effect on labor supply. If substitution effect dominates, N increases and leisure
falls. If leisure falls, the marginal utility of leisure increases. If the income effect dominates,
N falls and leisure increases. If leisure increases, the marginal utility of leisure falls. Given
that I didn’t tell you about the strength of income effect relative to substitution effect, we
don’t know what happens to the marginal utility of leisure.
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Question B
Suppose you were told the following about the economy after a shock hit:



Output went down
Employment did not change
After tax wages went down
What type of shock(s) could have generated this type of pattern in the data?
a. An decrease in TFP
b. An increase in TFP
c. An increase in labor income taxes
d. A fall in labor income taxes
e. Both (a) and (c) can be true
f.
Both (b) and (d) can be true
A decrease in TFP will unambiguously cause W/P to fall. Given that taxes didn’t change,
this means that after tax wages will unambiguously falls. So, we know, from wages falling
that it could be a decrease in TFP and NOT an increase in TFP. This rules out (b) and (f).
A decrease in TFP could cause N to remain the same if income and substitution effects
cancel. We also know that this would also cause Y to fall (As A falls and no change in N).
So, we know that a permanent decline in TFP with income and substitution effects canceling
could generate this data. So, we know that the answer is either (a) or (e).
We also know that tax changes CANNOT generate these patterns. For tax changes, Y
could only move when N moves (given A and K are fixed with tax changes). In this
example, we see Y fell and N didn’t change. No tax change can generate this pattern. So,
(c) and (d) cannot be true.
Given all of this, we know that (a) is the only true answer.
8
Part II (continued): Economic Mechanisms (18 points total – 3 points each)
Question C
Suppose you were told the following about the economy after a shock hit:



Output went up
Employment went up
After tax wages went up
What type of shock(s) could have generated this type of pattern in the data?
a. An decrease in TFP
b. An increase in TFP
c. An increase in labor income taxes
d. A fall in labor income taxes
e. Both (a) and (c) can be true
f.
Both (b) and (d) can be true
g. None of the answers are true.
We know that a permanent increase in TFP can generate this data if the substitution effect
is large relative to the income effect. A positive TFP shock will cause Y, N and W/P to
increase.
We also know that a permanent fall in labor income taxes can cause N and Y to increase if
the substitution effect is large relative to the income effect.
Also, we know that a
permanent decline in labor income taxes will cause after tax wages to rise (that is why
people are working more).
Given this, both (b) and (d) can be true.
Question D
Suppose the income effect and substitution effects are similar order of magnitude (such that
the two effects cancel). Which of the following is true about an unexpected permanent
decline in consumption taxes?
a. Before tax wages (W/P) will rise
b. Employment (N) will rise
c. GDP (Y) will rise
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d. Output per worker (Y/N) will rise
e. All of the above are true.
f.
None of the above are true.
A permanent decline in consumption taxes has the identical implications of a permanent
decline in income taxes. If the income effect equals the substitution effect, then (on net) the
labor supply curve will not shift (it will shift right and then shift back to the left to the
original position). So, N will not change, Y will not change (because A, K are fixed), before
tax wages will not change, MPN will not change, and Y/N will not change. After tax wages
will unambiguously increase and, as a result, C will unambiguously increase.
Given the above answers listed, none of the answers are true.
10
Part II (continued): Economic Mechanisms (18 points total – 3 points each)
Question E
In our class, we talked a lot about income and substitution effects of wage changes on labor
supply. Suppose the economy experiences an unexpected and permanent increase in labor
income taxes. Which of the following is true?
a. Whether employment increases or decreases depends upon whether the income effect or
substitution effect dominates.
b. Whether consumption increases or decreases depends upon whether the income effect or
substitution effect dominates.
c. Both (a) and (b) are true.
d. Neither (a) nor (b) are true.
This was pretty straight forward and was one of the easier questions in this section. A
permanent increase in labor income taxes could increase or decrease employment
depending on the strength of the income or substitution effect. However, an increase in
labor income taxes will unambiguously cause after tax wages to fall. This will
unambiguously cause PVLR to fall. Given we have PIH consumers (as our base), this will
unambiguously cause consumption to fall. So, while the change in N is ambiguous, the
change in C is not. C will unambiguously fall.
Question F
Suppose you were told the following about economies A and B.


A given change in real interest rates has a larger effect on investment in economy A
relative to economy B.
The substitution effect of an after tax real wage change on labor supply is larger in
economy A relative to economy B.
Which of the following are true about economy A relative to economy B?
A. Economy A has a steeper IS curve and a flatter labor supply curve relative to economy B.
B. Economy A has a flatter IS curve and a flatter labor supply curve relative to economy B.
C. Economy A has a steeper IS curve and a steeper labor supply curve relative to economy
B.
D. Economy A has a flatter IS curve and a steeper labor supply curve relative to economy B.
I like this question. The first bullet point implies that economy A has a FLAT IS curve
(given that a change in r will have a big effect on investment). The second bullet point
implies that the labor supply curve is also flat given that a change in W/P will have a large
effect on labor supply (N). So, economy A has both a flatter IS curve and a flatter labor
supply curve.
11
Part III: True/False/Uncertain: Explanation Determines the Grade (30 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. Any more than the fourth sentence will be ignored (unless it is wrong - in
that case we will deduct points). Lastly, to receive full credit, you need to be explicit about the
mechanism that is driving your results. Each question is worth 5 points.
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.
Some questions have multiple parts within the question stem such as: "Suppose the economy is
hit with an increase in "z". If "z" increases, then both "x" and "y" will increase." For those
questions, you will need to discuss both parts to get full credit. In other words, you will have to
discuss whether the increase in "z" will cause "x" to increase and then separately discuss whether
it will cause "y" to increase.
Lastly, you should consider your analysis in terms of the models developed in class. Note: all
assumptions on page 3 of the exam hold unless I tell you otherwise.
A.
Consider the equilibrium model of the labor market developed in class.
If the income effect is small relative to the substitution effect, a reduction in labor income
taxes can reduce the unemployment rate.
False. There is no effect on unemployment in equilibrium! Our model – in equilibrium –
tells about changes in N, but not changes in unemployment. So, it is true that N will
increase. It is not true that unemployment will fall.
B.
Consider the equilibrium model of the labor market developed in class. Suppose that the
substitution effect on labor supply is very large relative to the income effect on labor
supply.
A permanent increase in TFP (A) will cause both the labor demand curve to shift to the
right and the labor supply curve to shift to the right.
False. An increase in TFP will cause labor demand to shift right. This will lead to a
substitution effect that will cause a movement along labor supply shift. The income effect
will cause the labor supply curve to shift left. Nothing will make labor supply curve shift
right (in this example).
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Part III: True/False/Uncertain: Explanation Determines the Grade (continued)
Each of your answers should only be at most 3-4 sentences. We will not read any more than 4
(regular) sentences!
C.
Consider an aggregate economy that can be represented with a Cobb-Douglas
production technology. Assume TFP is held fixed.
A doubling of both capital (K) and labor (N) will cause output per worker (Y/N) to
exactly double.
False. This came from quizzes and practice quizzes. 0.7 Y/N = MPN = 0.7 * A * (K/N)0.3.
If we double K and double N, the ratio of K/N does not change. Given the ratio doesn’t
change, MPN doesn’t change. Given that MPN doesn’t change, Y/N doesn’t change.
Alternatively, doubling both K and N doubles Y, so the ratio of Y/N does not change.
D.
Consider the discussions of the economy built in class.
Both a zero inflation rate and a zero unemployment rate are desirable policy goals.
False. We talked about this in week 1. A zero unemployment rate is not a desirable policy
goal because we think frictional unemployment is good and structural unemployment is
necessary; they are indicators of a varied and evolving economy. A zero inflation rate is
not always a desirable policy goal for two reasons (that we talked about). First, we like a
little inflation to “grease the wheels of the labor market” allowing firms to reduce real
wages without cutting nominal wages. Second, having a target inflation rate of higher than
zero percent gives wiggle room when nominal interest rates are close to zero.
E.
Consider the model put forth in class. Suppose that there is an unexpected and
permanent decline in labor income taxes (tn). Suppose further that income effects on
labor supply are large relative to the substitution effects on labor supply.
A permanent decline in labor income taxes (tn) will unambiguously shift both the IS
curve to the right and the long run aggregate supply (LRAS) curve to the right.
False.
A permanent decline in labor income taxes will unambiguously increase
consumption (see above answers) which will shift the IS curve to the right. However, if the
income effect dominates the substitution effect on labor supply, a permanent decline in
labor income taxes may make people work less (N falls). This will cause a leftward shift in
the LRAS (remember LRAS is Y* = A K0.3 (N*)0.7
13
Part III: True/False/Uncertain: Explanation Determines the Grade (continued)
Each of your answers should only be at most 3-4 sentences. We will not read any more than 4
(regular) sentences!
F.
Consider the equilibrium labor market developed in class. Suppose that both TFP
permanently increases and the marginal tax rate on labor income permanently declines.
Lastly, assume that income effects on labor supply exactly offset substitution effects on
labor supply.
Theoretically, our model of the labor market predicts that a permanent increase in TFP
coupled with a sharp decline in labor income taxes would unambiguously increase
equilibrium before tax real wages, unambiguously increase equilibrium after tax real
wages, and unambiguously have no effect on equilibrium hours worked (N) in the
population (N).
True. How do you approach this problem? The key is to take each shock individually and
put the effects together at the end.
Shock 1: TFP increases permanently (only):



W/P increases (before tax wages).
(1-tn) (W/P) increases (after tax wages) (tax rates are held fixed – we are only
looking at TFP shock).
N does not change (income and substitution effects offset)
Shock 2: Tax rates fall permanently (only)



W/P does not change (before tax wages – income effect and substitution effects
offset)
(1-tn)(W/P) increases (after tax wages – because tax rate falls)
N does not change (income effect and substitution effects offset).
Net effect is the two effects together. Wages (both after tax and before tax) raise and N does
not change.
This is how we will explore all multiple changes to exogenous variables in our class. We will
do them separately and then put them together at the end. If the effects reinforce each
other, we know what will happen. If they go in opposite directions, our results will be
ambiguous. In this case, the shocks reinforced each other.
14
Part IV: Reading (4 points)
As part of the reading this week, I had you listen to another radio piece from This American Life.
In Act 1 of the episode “How to Create a Job”, the episode was devoted to whether governments
can actually “create jobs”. All politicians claim that they if you elect them they will “create
jobs”. The episode starts (act 1) with a case study of one U.S. state. The governor of that state
ran on a platform of job creation. He was elected. The episode starts by focusing on how one
would ever be able to assess whether the governor’s policies had any effect on job creation.
This question is simple. Just name the state on which the case study (Act 1 of the episode) was
based. Put your answer in the box. Your answer should just be the name of a state. No further
explanation is needed.
Hint: This is extremely easy question if you attempted the reading. You didn’t even have to
listen to the episode (although, you should). If you just clicked on the link describing the
episode, you would have seen the answer.
Wisconsin
15
Part V – Understanding Social Security (16 points total)
In this example, we are going to examine the potential benefits and costs of a social security
system (paying taxes when young so as to get transfers when older) for different types of
consumers. At this point, we will not discuss the budgetary consequences (we will do that in
class this week). What we will do is assess how social security will affect lifetime utility for
different types of consumers by changing the way disposable income is allocated over time.
Here is the problem. All consumers live 4 periods. They work extensively during the first three
periods of their life and only work a little bit in their fourth period. You can consider the fourth
period to be like retirement. All consumers start their life with zero wealth (Wealth0 = 0).
We will assume that the true utility function of all consumers is log utility. For simplicity, we
will further assume that β = 1 and r = 0 (there is no discounting of money or utility over the
lifecycle). Given that, all consumers have a true total utility of:
Total Utility = ln(C1) + ln(C2) + ln(C3) + ln(C4)
(where Ci is consumption in period i).
The three types of consumers are:



Non-liquidity constrained PIH consumers (optimizing consumers as modeled in class).
Liquidity constrained PIH consumers (PIH consumers who cannot have negative wealth)
Keynesian consumers (who set C = disposable income in each period).
Lastly, here is the gross income (before taxes and transfers) profile of households over their life:
Y1 = 70
Y2 = 100
Y3 = 160
Y4 = 30 (where Yi = gross income in period i).
A.
In the first example, we will assume that there are no taxes or transfers such that gross
income equals disposable income (T = Tr = 0). This will be our baseline situation.
Given the above gross income path and the assumption that taxes and transfers are zero, what
would be the observed level of consumption for each type of consumer in each period of their
life. Fill in the grid below with your answers. Note: consumers can consume partial units (if
necessary). No work is needed (5 points total: a mistake with one consumer will lose 3 points,
mistakes with two consumers will lose 4 points, mistakes with all consumers will lose 5 points.)
This was pretty straight forward given the practice quizzes and the practice exams. So, I
am just going to quickly go through the answers.
PIH (non-liquidity constrained) set C = PVLR/LL
In this example, PVLR (the sum of disposable income) = 360 implying a C in each period of
90.
The liquidity constrained PIH consumers are a little more difficult. They want to consume
90 in period 1 but are prevented from borrowing. As a result, the maximum they can
consume is 70 (their disposable income). After that, they take the remaining PVLR and
16
figure out their optimal consumption (in this case it is 96.67 (290/3)). Given that current
income in period 2 is greater than their desired consumption, the liquidity constraint does
not bind. The household will carry 3.33 units of saving into period 3 and start the problem
over. In this case (carrying that method forward), we see that the liquidity constrained PIH
is able to smooth their consumption over periods 2-4 (at 96.67 units).
The Keynesians are the easiest. They just set C = disposable income. Notice, that if we
computed total utility for each household (taking the log of consumption in each period and
summing them together as described above), the PIH (non-liquidity constrained) consumers
will have the highest utility and the Keynesians have the lowest utility. Given these
preferences, variable consumption is bad and stable consumption is good (because of
diminishing marginal utility of consumption).
The question you should ask is: why do Keynesians do what they do? That is a great
question! The way that we model such households is that they are extremely short-sighted.
David Laibson (a professor at Harvard) has spent much of his early career trying to come
up with rational models to explain the consumption patterns of such Keynesian households.
The bottom line of his research is that they just cannot commit to their consumption plans
(they know they need to save but find themselves unable to do so). Ex-post, they regret not
saving – but ex-ante, they cannot commit themselves to save more.
Here is a summary of the consumption decisions:
Period
Consumer
1
2
3
4
Non-Liquidity Constrained PIH
90
90
90
90
Liquidity Constrained PIH
70
96.67
96.67
Keynesians
70
100
160
96.67
30
17
Part V (continued) – Understanding Social Security (16 points total)
B.
In the next example, we will illustrate what happens when we implement a social security
system in this hypothetical economy. Our social security system will be crude, but it will
approximate the true system.
The social security payments in period 4 (a transfer) will be financed through taxes on working
households when they are in periods 1 – 3. For this example, we will assume that that social
security system is fully funded in the sense that all social security payments are financed with
social security taxes (instead of debt).
Formally, we will assume the following pattern of taxes and transfers:
Taxes:
Transfers:
T1 = 14
Tr1 = 0
T2 = 20
Tr2 = 0
T3 = 32
Tr3 = 0
T4 = 0
Tr4 = 66
Note: The taxes are roughly 20% of gross income during periods 1 – 3 and then households get
all those taxes paid back (in the form of a transfer) in period 4. Assuming r = 0, this
works out exactly to ensure that the amount of taxes paid in exactly equals the transfer
payment paid out.
Given the above gross income path and the assumption on taxes and transfers, what would be the
observed level of consumption for each type of consumer in each period of their life? Fill in the
grid below with your answers. No work is needed (5 points total – same grading as in part A).
Note – using the same procedure as above, I will just quickly give you the answers. Note, all
you need do for this part is compute disposable income in each period which is income –
taxes + transfers. Again, notice, that total income over the life time (PVLR) did not change
with our tax and transfer program.
Period
Consumer
1
2
3
4
Non-Liquidity Constrained PIH
90
90
90
90
Liquidity Constrained PIH
56
80
112
112
Keynesians
56
80
128
96
18
Part V (continued) – Understanding Social Security (16 points total)
C.
As discussed in the first part of the question, all three consumers have log utility such
that their total lifetime utility is just the sum of log utility in each period of their life (Total Utility
= ln(C1) + ln(C2) + ln(C3) + ln(C4) (where Ci is consumption in period i)).
Given how total utility is defined, we are going to ask whether the social security program we
considered increases, decreases, or keeps the same total lifetime utility for each of our three
consumers. For each consumer below, circle whether lifetime utility will increase, decrease, or
stay the same. After, you will give a (roughly) 2-3 sentence explanation for your answer. The
first sentence should be related to math (computing the total utility of each consumer with and
without social security). The remaining sentence should provide some intuition. (6 points total
– 2 points each).
i
The social security program will _______ the total lifetime utility of non-liquidity
constrained PIH consumers: (circle 1)
increase
decrease
keep the same
Given that the consumption pattern (in any period) did not change, non-liquidity
constrained PIH households are no better off and no worse off from the social security
program.
[Mathematically, Total Utility Before = ln(90) + ln(90) + ln(90) + ln(90)
Total Utility After = ln(90) + ln(90) + ln(90) + ln(90)]
Given that the social security program forced them to save when they are young – they
could undo the social security program by borrowing more. Their lifetime consumption
profile is unaltered (assuming what they put in is what they got out).
ii
The social security program will _______ the total lifetime utility of liquidity
constrained PIH consumers: (circle 1)
increase
decrease
keep the same
The social security program decreases total utility of liquidity constrained households (the
way we set up the problem). The reason is that the consumption profile of these households
became MORE variable. The social security program forced these households to SAVE
when they were young (by putting money into the social security program). Yet, these
households want to BORROW when young. By forcing them to save when they actually
want to borrow, this kind of transfer program decreases their total lifetime utility.
[Mathematically,
Total Utility Before = ln(70) + ln(96.67) + ln(96.67) + ln(96.67) = ln(70 * 96.67 * 96.67 *
96.67) = ln(63,296,174.41)
Total Utility After = ln(56) + ln(80) + ln(112) + ln(112) = ln(56 * 80 * 112 * 122) =
ln(56,197,120)
63,296,174.41 > 56,197,120, therefore Total Utility Before > Total Utility After]
19
iii
The social security program will _______ the total lifetime utility of Keynesian
consumers: (circle 1)
increase
decrease
keep the same
Explanation:
The social security program makes the Keynesian households better off. This is one of the
main reasons we have a social security system. We are afraid that households will not be
able to plan for their own retirement sufficiently on their own (i.e., they are Keynesian).
Given this, we force them to save when young and give them money back when they are
retired. This type of policy makes them strictly better off.
[Mathematically,
Total Utility Before = ln(70) + ln(100) + ln(160) + ln(30) = ln(70 * 100 * 160 * 30) =
ln(33,600,000)
Total Utility After = ln(56) + ln(80) + ln(128) + ln(96) = ln(56*80*128*96) = ln(55,050,240)
55,050,240 > 33,600,000, therefore Total Utility After > Total Utility Before]
The main economic justification for a social security system is the belief that a portion of the
population is Keynesian. If there were no liquidity constraints, we could have a social
security system where PIH consumers are no worse off and Keynesians are strictly better
off. The existence of liquidity constraints make the cost-benefit analysis more complicated.
Notice, this is a separate issue from the fully funded social security system debate (we may
talk about that in class after the midterm). This problem assumes what you put in is what
you get out. If that is not the case, the analysis will change. But, if we went to a fully
funded social security system (what you put in is what you get out) – the only justification
for such a policy is the existence of Keynesians (and to provide insurance for longevity risk).
This is really cool (potentially my favorite exam question of all time). My guess is that you
will not be able to think about the social security debate the same way after doing this
question (which just uses some of the simple tools that we have developed in the class).
20
Part VI – Government Spending Multipliers (16 points total)
We are often interested in how much government spending will increase GDP during a recession.
There was a huge topic of debate around this issue during the 2009 recession (and some are still
calling for more government stimulus today).
What is the logic of the Keynesian consumption multiplier? In this question, we will sketch were
the logic comes from. In answering this question, I want you to ignore completely the supply
(production) side of the economy. In topic 6, we will fill in the missing links between this
question and the supply side of the economy. However, for this question, we will ignore it (this
basically comes down to the assumption that prices will adjust and nominal wages could be fixed
- but, we will ignore those price changes for this question - the original Keynesian theories also
ignored such forces).
Here are the fundamentals of this economy:
C = a + b Yd
(Assume a = 7,000 and b = 0.25)
I = I0 - dI r
(Assume I0 = 2,500 and dI = 1,000)
G =G
(Assume G = 500)
T = tn Y
(Assume tn = 0.2)
We will additionally assume that government transfers (Tr) and net exports (NX) always equal
zero. Finally, assume that interest rates are permanently fixed at 0% (i.e., 0.00).
Note: These functions look very similar to the demand side model we developed in class.

The investment function has an "autonomous" component and a component that varies
with real interest rates.

Total tax revenues (T) are a function of the tax rate on income (tn) and income (Y).

The key equation is the consumption function. This consumption function also has two
components: an "autonomous" component and a part that depends on current disposable
income. The parameter "b" is akin to the Keynesian marginal propensity to consume.
You should think of the autonomous part of the consumption function responding to
permanent changes in after tax resources (“a” is something like PVLR/LL). The
marginal propensity to consume represents how people response to current income,
holding lifetime resources fixed. For our non-liquidity constrained PVLR households, b
would equal zero (current income would have no effect on consumption once you control
for lifetime resources). b is greater than zero to the extent that people are either liquidity
constrained or Keynesians. Liquidity constrained PIH consumers and Keynesians will
respond to current income even after conditioning on lifetime resources.
21
Part VI – Government Spending Multipliers (16 points total)
A)
Given the above information, what is the level of GDP that would exist in this economy?
Again, you should only focus on the demand side of the economy. Put your answer in
the box. You must show your work to get full credit. (4 points total)
Hint:
Your answer should be a number. Using what you know, you should be able to express
the above information in terms of one equation and one unknown (Y).
Solve that
equation for Y.
Before giving the numerical answer to the problem, let me solve this problem algebraically.
The algebraic answer will provide all the intuition we need.
Here is what we know:
Y = C + I + G (+NX) – but we set NX = 0 in the problem.
(1)
We have algebraic expressions for C, I and G. Substitute those into (1).
Y = a + b (Yd) + I0 – dI r + G
(2)
We know that disposable income Yd is Y – T + Tr. I actually gave you the definition of
disposable income in question III in case you forgot. So, the next step is to substitute the
definition of disposable income into (2) knowing that Tr = 0 and T = tnY.
Y = a + b (Y - tnY) + I0 – dI r + G
(3)
The next step is just to solve (3) for Y. We have one equation (i.e., (3)) and one unknown
(i.e., Y).
Y
1
 a  I 0  d I r  G 
1  b(1  tn )
(4)
Notice, once I write this equation in this form, you can easy see that the simple government
spending multiplier is:
Y
1

G 1  b(1  tn )
(5)
What is the idea behind the government spending multiplier? To start, let’s set tn = 0. In
this case, the multiplier is only a function of the marginal propensity to consume out of
current income (b) holding lifetime resources (a) constant. If the government temporarily
spends a dollar today (by hiring a construction worker to build a bridge – for example),
consumption in the economy (C) will increase by b * $1 (the construction worker will spend
b percent of that dollar – that is what the marginal propensity to consume out of current
income would imply). Why would the construction worker spend b percent? Perhaps he is
Keynesian or perhaps he is liquidity constrained. Once the construction worker increases
22
their consumption worker by b*$1 at a restaurant, the restaurant owner will increase their
consumption by b * b*$1 (or b2 * $1). They will spend b percent of b*$1. This process will
continue …. The net change in consumption will be:
C  [b  b 2  b3  ........b  ]* G 
b
* G
1 b
(6)
Where ΔG is the increase in government spending and b/(1-b) is the infinite sum of b being
raised to successively higher powers (that is just a geeky math fact).
So, the total change in Y is going to be the sum of the change in consumption and the initial
change in G (I does not change in this problem because there is no change to I0 and r).
Y  C  G 
b
1
G  G 
G
(1  b)
(1  b)
(7)
From (7) you can see that Y will change by 1/(1-b) for every change dollar change in G.
Remember, that we assumed that tax rates were zero when we computed (6) and (7). This
was to show you some simple intuition. In the real world, every time someone earns a
dollar, the government takes tn percent of it. That means the “spending multiplier” gets
reduced because the government is taking a part of the income that is being generated.
That is why the tax rate shows up the government spending multiplier in (5). Higher tax
rates mean lower government spending multipliers.
Ok, with that in mind, we can answer the question. What I am going to do is just use
equation (4) above. You may have started with (1) and ended up with (4) using numbers.
The most common mistake people make is not including taxes in the government spending
multiplier.
Y
1
1
1
 a  I 0  d I r  G  
7000  2500  0  500  10, 000
1  b(1  tn )
1  0.25(1  0.2)
0.8
Y  12,500
This question was graded on a 0/2/4 scale. Perfect answers were graded as 4’s. Any
mistake – even a simple math mistake was graded as 2. Most people did not properly
substitute the tax function into disposable income (and keep track of the negative signs). As
long as some real attempt was made using the Y= C + I + G equation, people got at least 2
points. (A real attempt means substituting in actual equations).
23
B)
Given the above information, what is the government spending multiplier? The
government spending multiplier is Y / G . In other words, how much will GDP
increase today from a $1 increase in government spending today? Your answer
should be a number. Put it in the box. You must show work to get full credit. (4
points total)
Again, using (5) above, the government spending multiplier is 1/0.8 = 1.25.
Notice - this question really didn't have much to do with government spending. The
real essence of this question deals with the marginal propensity to consume out of
current income (b) and the marginal tax rate (tn).
Notice - some of you might think you needed calculus to answer the above question.
That is not true. You could have computed the answer to the question using brute
force (basically, just re-compute the answer when government spending increased
by $1 (from 500 to 501)). The level of Y in the economy would increase from 12,500
to 12,501.25 as G increases from 500 to 501 and all else was held equal. ΔY/ΔG =
(12,501.25 - 12,500)/(501-500) = 1.25/1 = 1.25.
This was graded as a 0/1/2/4 question. If you got 1.25 (with some sort of work), you
got 4 points. If you only made your answer 1/(1-b) and did not adjust for taxes
(multiplier = 1.33), you got either (2) or (4) points. You would have gotten (4)
points if you didn’t adjust for taxes in part (A) – in that case, it is just a carry
through mistake and we will not penalize you twice. Your (A) answer would have to
be 13,333.33 in order for us to count a carry through mistake. If you got (A) correct
and put 1.33 for (B) you will get (2) points. If you put 0.8 (the inverse of the
multiplier) you also got two points. You missed the fact that the increase gets
amplified through household consumption. Any other answer will only yield 0/1
points depending on work provided.
24
Part VI – Government Spending Multipliers (16 points total)
C)
I now want to build some intuition of what determines the simple Keynesian
government spending multiplier. For each of the variables below, circle the
correct answer with respect to how a change in the variable will increase the
government spending multiplier ( Y / G ). (8 points total - 2 points each)
Note: As discussed above – only the marginal propensity to consume out of current
income (b) and the marginal tax rate affect the government spending multiplier.
Note: We will cap the maximum points you can lose in this problem (conditional on
not leaving it blank) at 10 points (out of the full 16 – so, at a minimum people should
get at least 6 points on this question if they attempted it seriously).
(i)
The autonomous part of consumption (“a”):
a.
b.
c.
(ii)
The marginal propensity to consume out of current disposable income (“b”).
a.
b.
c.
(iii)
An increase in “b” will increase the government spending multiplier.
A decrease in “b” will increase the government spending multiplier.
A change in “b” will have no effect on the government spending
multiplier.
The autonomous part of investment (I0):
a.
b.
c.
(iv)
An increase in “a” will increase the government spending multiplier.
A decrease in “a” will increase the government spending multiplier.
A change in “a” will have no effect on the government spending
multiplier.
An increase in I0 will increase the government spending multiplier.
A decrease in I0 will increase the government spending multiplier.
A change in I0 will have no effect on the government spending
multiplier.
The marginal tax rate on income (tn).
a.
b.
c.
An increase in tn will increase the government spending multiplier.
A decrease in tn will increase the government spending multiplier.
A change in tn will have no effect on the government spending
multiplier.
25
Scrap Paper 1
26
Scrap Paper 2
27
Scrap Paper 3
28
Scrap Paper 4
29