Erik’s Final
Macro
Fall 2014
Section Registered
Tues a.m.
Tues p.m.
Wed a.m.
Mail Folder (circle one):
Campus MBA
Name (print):
_______________________________________
Signature:
_______________________________________
Evening
Exchange
Other
Total Score on the Exam:
Part I
(out of 27)
_____________
Part II (out of 20)
_____________
Part III (out of 12)
_____________
Part IV (out of 10)
_____________
Part V (out of 15)
_____________
Part VI (out of 16)
_____________
TOTAL (out of 100)
_____________
1
Exam Preamble
1.
As always, honor code rules are in effect. You know the routine. All the usual disclaimers
apply. By taking this test (and signing on the previous page), you pledge that you are
adhering to the honor code outlined in the syllabus and Booth’s honor code. This implies
that you are not to discuss test questions with anyone until after the answers are
distributed. Additionally, you should not let your eyes wander around to your neighbor’s
exam. You would be surprised how much your classmates monitor each other.
2.
There are 4 pages of scrap paper at the end. If you use it, you do not have to hand it in. Do
not hand in any loose pages (the chance of them getting lost is infinite). Carolyn will not
grade scrap paper so if you do use the scrap paper, neatly re-write any graphs or
computations that you want to be graded in the space of the problem.
3.
You have 2.5 hours for the exam. Time should not be a constraint.
4.
You are allowed:
One Piece of Paper (Cheat sheet) - Handwritten - Not Photo Copied - Both Sides
Calculator
Blank macro worksheets
5.
Please, Please, Please - read all the directions and assumptions that I make for each
question. Sometimes, the assumptions (short run, long run, type of consumers, etc.) change
from question to question and make a difference for the answers!!
6.
Be concise! If you start rambling and say something wrong - we will take points off. Note:
All true/false/uncertain questions (where an explanation is needed) should be answered in 34 sentences. Be aware of that and think through your answer before you start writing.
7.
Good Luck
2
Exam Assumptions
These assumptions hold throughout the ENTIRE exam (unless told otherwise)
1)
we always start at Y*,
2)
all variables (consumption, investment, etc.) are real variables, unless otherwise stated,
3)
Capital (K) is fixed in both the short and long run, but is allowed to change in the really long
run.
4)
NX is fixed (at zero), unless otherwise instructed,
5)
no policy response takes place, unless otherwise instructed,
6)
consumers are non-liquidity constrained, non-Ricardian PIH (who have long lives such that LL is
large), unless otherwise instructed,
7)
all shocks to the economy are permanent and unexpected, unless otherwise stated,
8)
Expected inflation has no effect on money demand.
10) TFP, oil prices, consumer confidence, business confidence, changes in the stock market, changes
in population, and changes in value of leisure (i.e., all exogenous variables) only change when I
tell you they change.
**When discussing long run changes, compare the initial condition of the economy to where it will
end up in the long run (unless told otherwise).
3
Part I: Circle the True Answers (27 points total, 3 points each)
For each of the questions below, circle the one response that makes the question unambiguously true.
Questions A-E are stand-alone questions. Questions F-I are related (same question preamble).
A. Suppose there is a permanent increase in government spending (G). Suppose the economy returns
to long run equilibrium via the self-correcting mechanism. Which of the following are
unambiguously true?
Between the initial condition and the short run, the IS and AD curves will shift out (recall, Y =
C+I+G+NX). As AD shifts out, it will put upward pressure on prices. As prices increase W/P will
fall and N>N* in the labor market (move along the labor demand curve). The self-correcting
mechanism tells us that nominal wages (W) will have to increase between the short and long run for
the labor market to return to N*. As W increases, the cost of production increases and the SRAS
shifts in. This will return the AS-AD market to Y*. In the IS-LM market as P increases, M/P falls
and the LM curve shifts in returning the IS-LM market to Y*. In the long run: AD, IS shift out,
SRAS, LM shift in from their initial positions.
i.
Both the aggregate demand (AD) curve and the IS curve will be shifted right between
the initial condition and the long run.
ii.
The percentage change in the nominal money supply (M) will equal the percentage change in
prices (P) between the initial condition and the long run.
Note, there is no change in M in this example but P will increase.
iii. The percentage change in the nominal wages (W) will equal the percentage change in prices
(P) between the short run and the long run.
This is false. Between the short run and the long run, real wages will increase (which
means the percentage change in W will exceed the percentage change in P).
iv.
Both (i) and (ii) are unambiguously true.
v.
Both (i) and (iii) are unambiguously true.
vi.
Both (ii) and (iii) are unambiguously true.
vii. None of the above (i – iii) is unambiguously true.
viii. All of the above (i – iii) are unambiguously true.
4
B. Suppose there is a permanent increase in government spending (G). Suppose the Fed returns the
economy to Y* between the short run and the long run using monetary policy. Which of the
following are unambiguously true?
Between the initial condition and the short run, the IS and AD curves will shift out (recall, Y =
C+I+G+NX). As AD shifts out, it will put upward pressure on prices. As prices increase W/P will
fall and N>N* in the labor market. The Fed will decrease the money supply, which will shift in the
AD curve (recall, the aggregate demand curve is the IS-LM market in one curve) and return the
AS-AD market to Y*. As AD shifts in, prices will fall to their original level. In the labor market, as
prices fall, W/P increases back to their original level until N= N*. In the IS-LM market, the LM
curve shifts in as M falls.
In the long run: IS is shifted right, the LM curve is shifted left, and the AD does not move from its
initial position. Note: nominal wages W do not change (the correction in W/P between the short and
long run comes from price movements) so the percentage change in nominal wages is 0 AND prices
also have a 0 percentage change between the initial condition and long run because the price
increases from the demand shock between the initial condition and the short run are completely
unwound by Fed policy between the short and long run.
Recall, our formula for the velocity of money %∆V=%∆P + %∆Y -%∆M. Between the initial
condition and the long run, prices do not change (the AD curve is in its initial position), Y does not
change (the policy is to return the economy to Y*). What happens to M? The policy is to reduce M.
Thus, the velocity of money increases.
i.
Both the aggregate demand (AD) curve and the IS curve will be shifted right between the
initial condition and the long run.
ii.
The velocity of money (V) will fall between the initial condition and the long run.
iii. The percentage change in the nominal wages (W) will equal the percentage change in
prices (P) between the initial condition and the long run. (Nominal wages do not change
and prices also do not change between the initial condition and long run)
iv.
Both (i) and (ii) are unambiguously true.
v.
Both (i) and (iii) are unambiguously true.
vi.
Both (ii) and (iii) are unambiguously true.
vii. None of the above (i – iii) is unambiguously true.
viii. All of the above (i – iii) are unambiguously true.
.
5
Part I (continued): Circle the True Answers (27 points total, 3 points each)
C. Suppose the Fed unexpectedly buys a large amount of bonds on the open market. Suppose the
economy corrects itself in the long run through the self-correcting mechanism. Which of the
following are unambiguously true?
What happens when the Fed buys bonds on the open market? It increases the money supply (M).
This will shift out the LM curve (M/P) and the AD curve. As the AD curve shifts out, prices will
increase. As prices increase, W/P will decrease. This means N>N*.
Between the short run and the long run, the self-correcting mechanism tells us that W will increase.
As W increases, production becomes more expensive and the SRAS will shift left. This will return
the economy to Y* in the AS-AD market. In the IS-LM market, as P increases from the shift in of
the SRAS curve, the LM curve will shift in, returning the economy to Y*. In the long run: the AD is
shifted right, the SRAS is shifted left, and the IS and LM curves do not move. There is no change
to the IS curve because there is no change in C(.), I(.), or G.
Recall, our formula for the velocity of money %∆V=%∆P + %∆Y -%∆M. Between the initial
condition and the long run, we know nothing happens to Y so we can concentrate on M and P.
Prices increase (the AD curve shifts right, the SRAS curve shifts left), and M increases (that is the
initial shock). What is the relative magnitude of these changes? The changes to M and P must be of
equal magnitude. How do we know this? The LM curve returns to its initial position. Thus, there is
no change in the velocity of money.
i.
There will be no change in the IS curve or the LM curve between the initial condition and the
long run. True
ii.
There will be no change in consumption (C) and investment (I) between the initial condition
and the long run. True
iii. The velocity of money (V) will fall between the initial condition and the long run. False
iv.
Both (i) and (ii) are unambiguously true.
v.
Both (i) and (iii) are unambiguously true.
vi.
Both (ii) and (iii) are unambiguously true.
vii. None of the above (i – iii) is unambiguously true.
viii. All of the above (i – iii) are unambiguously true.
6
D. Suppose there is a permanent and unexpected decrease in labor income tax rates. Suppose the Fed
has a policy goal of keeping P close to P0. As always, assume the Fed policy takes place between
the short run and the long run. Finally, assume that the income effect on labor supply is equal to
the substitution effect on labor supply. Which of the following are unambiguously true?
As labor income taxes decrease, after tax wages will increase (you keep more of your take-home
pay). As after tax wages increase permanently, PVLR will increase.
Let’s start in the labor market. We gave you a simplifying assumption—that the income and
substitution effects are of equal magnitude—thus, we know that the labor supply curve will not
shift, on net.
As PVLR increases, consumption (C) will increase. As C increases, the IS and AD curves will
shift right. As AD shifts right, prices will increase. As P increases, W/P will decrease and N>N*.
If the Fed wants to stabilize prices, it will decrease the money supply (M). As M decreases, AD
and LM curves will shift left until the AD curve is in its original position where P*=P 0 and
Y=Y*. As the AD curve shifts left, prices will decrease. This means, W/P will increase (back to
its original level) until the labor market returns to N*.
i.
The potential level of output (Y*) will increase in the short run False, no change in A, K or
N*
ii.
The IS curve and the AD curve will shift to the left between the short run and the long run.
False. Only the AD curve shifts back in the short run. The IS curve stays shifted to the
right.
iii. Both the money demand curve and the money supply curve will shift left between the
short run and the long run. True. As Y falls between short run and long run, money
demand will shift left. As LM shifts in between short run and long run, we know that
M/P falls (the LM curve is only shifted by M/P). M/P is the money supply curve.
iv.
Both (i) and (ii) are unambiguously true.
v.
Both (i) and (iii) are unambiguously true.
vi.
Both (ii) and (iii) are unambiguously true.
vii. None of the above (i – iii) is unambiguously true.
viii. All of the above (i – iii) are unambiguously true.
7
Part I (continued): Circle the True Answers (27 points total, 3 points each)
E. Suppose the economy starts at Y*. Suppose oil prices permanently increase. Assume that prices
(P) rise in the short run. For simplicity, further assume that there is no income effect on labor
supply. Lastly, assume the economy returns to long run equilibrium via the self- correcting
mechanism. Which of the following is unambiguously true?
Think of an increase in oil prices is similar to a fall in TFP.
In the labor market, we know that the labor demand curve will shift left (the marginal productivity
of labor falls) and (W/P)* will fall in the long run. We told you there are no income effects on labor
supply, thus the labor supply curve does not move. We know that W/P2* will be < W/P0* and N2*
<N0*. As W/P* falls, we know that PVLR must fall.
What happens to the LRAS curve? It unambiguously shifts left as oil prices increase and N* falls.
Production becomes more expensive so the SRAS curve will shift in. As PVLR permanently falls,
Consumption will fall. The autonomous part of Investment will also fall (capital and oil are
complements in production) as capital becomes less productive. The fall in C(.) and I(.) will cause
AD to shift left. It is given that prices will increase in the short run so you know the magnitude of
the shift left of the SRAS curve will be greater than the magnitude of the shift left of the AD curve.
Both shifts will cause Y < Y0* but it is unclear if Y<Y1*. That depends on how much W/P falls in
the short run (because P rises) relative to the fall in W/P in the long run. There is no way to pin
down this given the data I have provided. So, whether Y1 < or > Y1* is ambiguous.
i.
Y in the short run will be larger than the new Y*. False – as discussed above – we do not
know where N is relative to N*(new) in the short run. So, we do not know where Y in
the short run is relative to new Y*.
ii.
Prices (P) in the short run will be higher than P in the long run. False - Given that we do not
know where Y (short run) is relative to Y (new long run), we cannot say nominal wages
will increase or decrease between short run and long run. So, we do not know what way
SRAS will shift between short run and long run. So, we do not know whether prices
will go up or down between short run and long run.
iii. The labor supply curve will shift right between the short run and the long run. False – the
labor supply curve does not move in this example.
iv.
Both (i) and (ii) are unambiguously true.
v.
Both (i) and (iii) are unambiguously true.
vi.
Both (ii) and (iii) are unambiguously true.
vii. None of the above (i – iii) is unambiguously true.
viii. All of the above (i – iii) are unambiguously true.
8
9
Part I (continued): Circle the True Answers (27 points total, 3 points each)
Parts F-I (Questions F – I all have the following background information)
Suppose that Y < Y* in the short run. For each of the following questions, circle the answer that makes
the question true. Again, there is only one true answer to each of the question stems. (Note: It does not
matter why Y is currently lower than the potential level (Y*) when answering the questions below).
For parts F-I, we will assume that:


Consumers are standard non-liquidity constrained (non-Ricardian) PIH consumers.
No policy takes place to return the economy to Y* (i.e., the economy corrects itself).
This is actually a pretty simple question. When Y < Y*, N is below N*. This means that real wages
are too high (we are in short run disequilibrium). Eventually, nominal wages (W) will fall to clear
the labor market. This will shift the SRAS to the right and prices will fall. The fall in prices will
shift out M/P and lower r. The lower r will increase investment. All of this will take place between
the short run and the long run. This question was just a question on the mechanics of the selfcorrecting mechanism.
Note – it does not matter why Y < Y* (demand shock or a supply shock). All we know is that the
labor market is in disequilibrium. If it is in disequilibrium, the self-correcting mechanism will kick
in.
F.
Which of the following is true about real wages (W/P) in the short run relative to real wages
(W/P*) in the long run (assuming Y < Y* in the short run)?
i.
Real wages in the short run will be higher than real wages in the long run.
ii. Real wages in the short run will be lower than real wages in the long run.
iii. Real wages in the short run will be the same as the real wages in the long run.
iv. It is uncertain whether real wages in the short run will be higher or lower than real wages in
the long run.
G.
Which of the following are true about investment (I) in the short run relative to investment (I) in
the long run (assuming Y < Y* in the short run)?
I will increase between the short run and the long run (via the self-correcting mechanism). See
above.
10
i.
Investment in the short run will be higher than investment in the long run.
ii. Investment in the short run will be lower than investment in the long run.
iii. Investment in the short run will be the same as the investment in the long run.
iv. It is uncertain whether investment in the short run will be higher or lower than investment in
the long run.
11
Part I (continued): Circle the True Answers (27 points total, 3 points each)
H.
Which of the following are true about the money demand curve in the short run relative to the
money demand curve in the long run (assuming Y < Y* in the short run)?
i.
The money demand curve in the short run will be to the right of the money demand curve in
the long run.
ii. The money demand curve in the short run will be to the left of the money demand curve
in the long run. Y will increase between SR and LR – so, money demand will shift right
iii. There will be no change in the money demand curve between the short run and the long run.
iv. It is uncertain whether the money demand curve in the short run will be to the right or the left
of the money demand curve in the long run.
I.
Which of the following are true about the aggregate demand (AD) curve in the short run relative to
the aggregate demand curve in the long run (assuming Y < Y* in the short run)?
The self-correcting mechanism does not affect the AD curve.
i.
The aggregate demand curve in the short run will be to the right of the aggregate demand
curve in the long run.
ii. The aggregate demand curve in the short run will be to the left of the aggregate demand curve
in the long run.
iii. There will be no change in the aggregate demand curve between the short run and the
long run.
iv. It is uncertain whether the aggregate demand curve in the short run will be to the right or the
left of the aggregate demand curve in the long run.
12
Part II: True/False/Uncertain (20 points – 5 points each)
As usual, your explanation determines your entire grade! No credit will be given for writing true when
the answer is true but your logic is wrong.
Unless told otherwise, all the assumptions at the beginning of the exam hold. These questions will be
essentially graded on a 0/2/5 scale. Answers that are perfectly correct will receive 5 points. All other
answers will be given either 0 or 2 points (depending on whether or not there is any correct intuition or
not). Again, almost all of these questions have a clear answer (true, false or uncertain) given the models
developed in class (and given the exam assumptions described on the first page).
NOTE: YOU MUST EXPLAIN YOUR ANSWERS: If I give you a math question in True/False form,
you must provide the correct answer to get full credit. If I ask a two part answer, you must tell me
whether both parts – independently – are true, false or ambiguous.
A.
Suppose there is a permanent increase in TFP (A). Suppose income effects are small relative to
substitution effects.
If there a permanent increase in TFP (A), the labor supply curve (Ns) will shift – on net – to the
right when income effects are small relative to substitution effects.
False – The increase in TFP will cause the labor demand curve to shift out (recall Y=AK.3N.7 and A
increases). As the labor demand curve shifts out, W/P will increase permanently which means
PVLR will increase. As PVLR increases, the income effect tells us people will work less. No matter
the strength of the income effect relative to the substitution effect, as PVLR increases, the income
effects will always cause the labor supply curve to shift to the left (or not shift at all) – it will never
shift to the right from an increase in TFP. The strength of the income effect relative to the
substitution effect has to do with the movement up the labor supply curve (which increases N) and
the shift in of the labor supply (which decreases N).
B.
Consider a closed economy (NX=0). For simplicity, assume there are no income effects on labor
supply from changes in consumer confidence. Otherwise, assume our standard assumptions hold
(in particular, we will assume that consumers are non-Ricardian PIH).
In the short run, a permanent decline in consumer confidence will unambiguously cause
consumption (C) to fall, unambiguously cause GDP (Y) to fall, and unambiguously cause
household savings (SHH) to rise.
True—Total household savings will increase in the short run. How do we know this? Let’s start
with our simplest identity-- S=I. What happens to I? We know I increases as r falls. So we
know S (total savings) has to increase. SGOV actually decreases as T falls (T = tnY – as Y
falls, T falls – this increases government deficits and lowers government saving). For S
(SGOV + SHH) to increase, SHH must have increased.
13
Part II: True/False/Uncertain (20 points – 5 points each)
C.
Consider the models developed in class.
There are many parameters in our model that
determine by how much output will change in the short run for a given change in an exogenous
variable. One such parameter is the transaction demand for money.
A permanent increase in government spending will result in a larger change in output in the short
run if the transaction demand of money is higher.
False. A higher transaction demand for money means a steeper LM curve. The slope of the LM
curve is determined by the transaction demand for money. If an increases in income really
increases money demand, it will really cause r to increase – that is a steep LM curve. In the short
run, a change in the IS curve will have a smaller effect on Y (and a bigger change in r which means
more crowding out) when the LM curve is steeper. This was very similar in spirit to a question on
the practice final.
D.
Suppose both government spending (G) and TFP (A) permanently increased. Suppose we start at
Y* and all standard assumptions hold. Lastly, assume that prices are fixed in the short run and
the economy will correct itself via the self-correcting mechanism.
Given these changes, interest rates (r) will unambiguously increase in the long run (relative to the
initial condition) and investment will unambiguously fall in the long run (relative to the initial
condition).
False - I will not unambiguously fall in the long run. The increase in A, will increase I(.). I = I(.) dI r. The increase in r will lower I. The increase in MPK will cause I to increase. The net effect is
ambiguous.
Note: In order to receive full credit, you also had to say that r unambiguously increases. The
increase in G will increase r in the long run. The increase in TFP (where prices are fixed in the
short run), will also increase r in the long run. So, combined, they will definitely increase r in the
long run.
14
Part III: Government Spending Multipliers (12 points - 4 points each)
There was a big discussion among economists during the last recession about whether to stimulate the
economy with changes in taxes or changes in government spending (G). The people who preferred
government spending said that the response of output to changes in government spending are much higher
than the response of output to changes in taxes (in other words, they are suggesting that the government
spending multiplier is bigger). In this question, we will address that hypothesis in a very simple model.
Suppose the true tax process is T = T0 + tnY, where T0 is like a tax rebate (which we will assume goes to
all individuals regardless of their labor income) and tn is our standard labor income tax.
Given that, suppose the economy can be defined as follows:
C
I
G
T
=
=
=
=
a + b (Yd)
I(.) – dI r
G
T 0 + tn Y
NX = Transfers = 0
For simplicity, we will further assume that interest rates (r) are held fixed throughout and prices (P) are
held fixed throughout. The latter assumption is just to make our life easier by ignoring the supply side.
The former assumption (that interest rates are fixed) is not crazy when the economy is at the zero lower
bound.
A.
According to this model, derive the government spending multiplier algebraically.
words, you answer will solve for dY/dG in symbols).
(In other
Note: Something like this was on one of the practice midterms with numbers. Additionally, this
came directly from supplemental notes 4. You goal is to get things algebraically in one equation
with one unknown.
To answer this problem, all you need do is solve for Y using algebra.
Y
=C+I+G
= a + b(Y-T) + I(.) - dI r + G
= a + bY - bT + I(.) - dI r + G
= a + bY - b (T0 + tn Y) + I(.) - dI r + G
= a + bY - b T0 - b tn Y + I(.) - dI r + G
= [a - b T0 + I(.) - dI r + G ] + bY- b tn Y
= [a - b T0 + I(.) - dI r + G ] + b(1- tn)Y
15
Y - b(1- tn)Y = [a - b T0 + I(.) - dI r + G ]
Y
=
[a - b T0 + I(.) - dI r + G ] * [1/(1-b(1-tn))]
To get the government spending multiplier, take the partial derivative of the above expression with
regard to G: 1*[1/(1-b(1-tn))]
The government spending multiplier (just like in the notes) is:
1
1  b(1  tn )
The government spending multiplier is just the coefficient on G in the above expression for Y (the
derivative of Y with respect to G is the just the coefficient in front of G - this is similar to if we had
an equation that says Y = 5X, dY/dX would equal 5.)
16
Part III: Government Spending Multipliers (12 points- 4 points each)
B.
As the fraction of households who are liquidity constrained increases, what happens to the
government spending multiplier? (Circle one)
i)
It will increase
ii) It will decrease
iii) It will not change
Given our discussion in class, how do we represent this in terms of our model (equations on the
previous page)? What is the intuition for why the multiplier will or will not change? Your
explanation should be no more than 3-4 sentences.
The fraction of liquidity constrained individuals in our model is measured by b (think of our
discussion of the government spending multipliers in class). If the tax rate (tn) was equal to zero,
the multiplier would be 1/(1-b). (Note – I find it easier sometimes to set the tax rate equal to zero to
build intuition). Basically, how much extra kick you get from a $1 increase in government spending
depends on the fraction of liquidity constrained individuals (or Keynesians) in the economy. This is
because current expenditure should not affect C(.) if PVLR does not change. However, a
temporary change in Y will further increase C if people are liquidity constrained. That is where
the extra kick from government spending comes from (given that Y* and real wages will not change
in the long run - so PVLR will not change). We need some people to be liquidity constrained (or
Keynesians) to get the extra kick.
C.
According to this simple model, is the tax rebate multiplier (dY/dT 0) bigger, smaller, or the same
as the government spending multiplier (dY/dG) (in absolute value)? If it differs, explain the
intuition for why it differs. If it is the same, explain the intuition for why it is the same.
Note: When answering this question, you should use words and not math. Make sure you say
whether the tax rebate multiplier is bigger, smaller, or the same.
Note: The absolute value part is important to keep track of. The tax rebate multiplier is
negative (raising T0 will lower GDP). The government spending multiplier is positive
(raising G will increase GDP). I want to know the relative effect on the economy of a
cut of T0 by $1 compared to an increase of G by the same amount.
C1. Relative to the government spending multiplier, the tax rebate multiplier is (circle one):
i.
Bigger
ii) Smaller
iii) The Same Size
C2. Provide a brief explanation for the intuition as to why the tax and government spending
multipliers would or would not differ.
17
To obtain the tax rebate multiplier, take the partial derivative of the identity for Y (above) with
respect to T0. (which is = -b*[1/(1-b(1-tn))]).
b
1  b(1  tn ) .
The tax rebate multiplier is just the coefficient on To which is
The tax rebate multiplier is smaller than the government spending multiplier (in absolute value).
The reason is that 0 < b < 1. The first dollar of government spending has a direct effect on Y (we
build more missiles when the government wants them.) For tax rebates, the first dollar of rebate
does not have a direct effect on Y. It only has a b * one dollar effect on Y (through C). So, the fact
that tax rebates have an effect on Y indirectly (via C) while G has a direct effect on Y is the reason
the government spending multiplier exceeds the tax rebate multiplier (in absolute value).
18
Part IV: Policy in Action (10 points total)
On January 25th, 2012, the Federal Reserve Board of Governors issued a press release outlining their
monetary policy goals (i.e., the beginning of their policy of “forward guidance”). The press release
issued the following statement:
"In setting monetary policy, the committee seeks to mitigate deviations of inflation from its longer-run
goal and deviations of employment from the Committee's assessment of its maximum level. These
objectives are generally complementary. However, under circumstances in which the Committee judges
that the objectives are not complementary, (we will follow) a balanced approach in promoting them".
A.
With the above quote in mind and given what we have learned in class, under what conditions are
the objectives of the Fed "generally complementary"? Your answer should not be more than one
or two sentence. Also, given the context of our class, your answer should be as broad as possible.
(4 points)
When Bernanke (in 2012) referred to objectives as “generally complementary,” he is referring to
demand shocks such as changes in C(.) or I(.) or G that only affect the AD curve. In this world, the
Fed can undo the demand shocks by changing M maintaining both Price and Output (employment)
stability. With demand shocks there is complentarity between its policy objectives.
B.
With the above quote in mind and given what we have learned in class, under what conditions are
the objectives of the Fed "not complementary"? Your answer should not be more than one or two
sentence. Also, given the context of our class, your answer should be as broad as possible. (4
points)
When Bernanke (in 2012) referred to conditions where the objectives are “not complementary,” he
is referring to supply shocks. In this world, the Fed cannot undo the supply shock (shifts in SRAS)
because they do not control the supply side of the economy. In this case, they can target prices
(Volker) or output (Burns) - but not both perfectly. Bernanke is saying that they will target some
combination of both.
C.
Forward guidance is one “new” type of monetary policy tool implemented in recent years.
Quantitative Easing is another monetary policy tool used in recent years. We talked about
Quantitative Easing in class. In words, describe the policy of Quantitative Easing. How does it
differ from traditional open market operations? Your answer should not be more than 2 or 3 wellconstructed sentences. (2 points)
19
From Investopedia: “Quantitative Easing: An unconventional monetary policy in which a central
bank purchases government securities or other securities from the market in order to lower interest
rates and increase the money supply. Quantitative easing increases the money supply by flooding
financial institutions with capital in an effort to promote increased lending and liquidity.
Quantitative easing is considered when short-term interest rates are at or approaching zero, and
does not involve the printing of new banknotes.”
Basically, we gave you credit if you said that through Quantitative Easing, Central Banks (1) target
long interest rates as opposed to short rates (this is how I mostly defined it) or (2) buy/sell non
treasury bills (mortgage securities/other assets) instead of treasury bills.
20
Part V: Inflation (15 points total)
Understanding why we care about inflation is one of the main goals of this class. In class, we
talked about the fact that high inflation is associated empirically with volatile inflation. The
increased uncertainty surrounding inflation can reduce economic activity. We also talked about
two other costs which make us prefer low stable inflation rates relative to high stable inflation
(“menu” costs and “shoe-leather” costs
A.
i.
In this part of the question, I want us to explore another cost of a high stable inflation rate
(relative to a low stable inflation rate). Because of time constraints, we did not talk
about this reason in class. The cost arises from the fact the U.S. tax code is set up so that
it taxes nominal interest earnings. The taxation of nominal interest rates can actually
discourage saving in high inflationary environments. To examine this cost of high stable
inflation, we will use the following information.

Consider a world where before-tax real interest rates are always fixed at 6 percent.

Also consider a world where there is no inflation uncertainty such that expected inflation
always equals actual inflation.

Finally, suppose the tax rate on nominal interest income is always 25 percent.

Note: To keep the grading simple, use the approximation formula when going between
real and nominal interest rates.
Given the above information, what is the expected after-tax real interest rate when the
expected inflation rate is 0 percent? Show work. Put answer in box. (3 points)
Nominal interest rate = 6 % from the approximation formula (i = r + πe = 6% + 0%)
Tax is paid on nominal interest rate = tax rate * nominal interest rate = 0.25 * 6 = 1.5%
After tax nominal interest rate = 4.5% (nominal interest rate - tax paid)
Expected after tax real interest rate = 4.5% (after tax nominal interest rate - expected
inflation rate)
Expected after tax real interest rate = 4.5%
ii.
Given the above information, what is the expected after-tax real interest rate when the
expected inflation rate is 10 percent? Show work. Put answer in box. (3 points)
Again, plugging in to the approximation formula (Supplemental Notes 1 and 2):
Nominal interest rate = 16% (i = r + πe = 6% + 10%)
Tax is paid on nominal interest rate = tax rate * nominal interest rate = 0.25 * 16 = 4%
After tax nominal interest rate = 12% (nominal interest rate - tax paid)
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Expected after tax real interest rate = 2% (after tax nominal interest rate - expected
inflation rate)
Expected after tax real interest rate = 2%
iii.
Why is it that a high stable inflation rate can discourage savings behavior? (3 points)
Because nominal interest rates are taxable (not real interest rates), a high inflation rate increases a
household's tax burden. This reduces the real return on savings potentially causing households to
save less. A high inflation rate implies a "higher tax" on savings because we only tax nominal
interest payments.
22
Part V: Inflation (Continued)
B.
As we talked about in class, we can sometimes use the yield curve to back out the market’s
expectation of expected inflation (with some assumptions).
Suppose you were given the following data (all of these are real data from last week).
One Year Treasury Rate (i0,1) = 0.13
Two Year Treasury Rate (i0,2) = 0.49
Three Year Treasury Rate (i0,3) = 0.90
Five Year Treasury Rate (i0,5) = 1.52
Let’s make the following assumptions for this problem. Let’s assume that expected annual real
rates are zero percent in all future periods (i.e., r0,1 = r1,2 = r2,3 … r4,5 = 0). Let’s also assume that
U.S. Treasuries have no risk premium (ρ = 0 for all periods). Finally, let’s assume the treasury
market is perfectly competitive such that arbitrage will ensure that the expected return is
equalized across government securities of different maturities.
Given the above assumptions, what is the expected average annualized inflation rate in this
economy between period 3 (three years from now) and period 5 (five years from now)?
You must show your work to get full credit. Put your answer in the box. Answers will be
graded on a 0/3 scale. So be careful with your math. (3 points)
First we use our arbitrage conditions to solve for the nominal interest rate between periods 3 and 5.
As an investor, you should be indifferent between investing in a five year security starting in year 0
(today) or investing in a 3 year security in year 0 (today) and then re-investing in a two-year
security beginning in year 3 and ending at beginning of year 5.
(1+ i0,5)5=(1+i0,3)3 (1+i3,5)2
Plugging in (1+.0152)5=(1+.009)3(1+i3,5)2
So i3,5 = (1.0497)1/2 – 1 = .02457 or 2.457%
We told you to assume r3.5 = 0. Using the approximation formula: r3.5 = i3,5 - π3,5 – ρ3,5.
Thus, π3,5 = 2.457%.
If people believe real rates will be close to zero, the yield curve expects very LOW inflation rate
over the next few years! If people believe real rates will be much above zero, the expected inflation
rate is much lower. If people believe the real rates are below zero, the expected inflation rate would
be higher.
C.
In class, we talked about why inflation expectations are self-fulfilling within an economy. Using
the models developed in class (in words), describe why inflation expectations are self-fulfilling.
Be precise. However, you answer should not be more than four well-constructed sentences. (3
points total).
Let’s consider the worker’s problem. If a worker anticipates that inflation will increase, he may
negotiate with his employer for a preemptive cost of living adjustment (an increase in nominal
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wages). As nominal wages (a major input price for firms) increases, it becomes more expensive for
firms to produce, causing the SRAS curve to shift left causing prices to increase.
The firm response (contracting production or increasing product prices) can also happen in
anticipation of any of their input prices increasing (absent actual negotiation with workers for
COLA increases).
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Part VI: Quantitatively Analyzing a Permanent Increase in TFP (16 points)
In this question, we will analyze a permanent increase in TFP (A) within the United States in the really
long run (i.e., we are going to also allow the capital stock (K) to change). When answering, we will use
the concepts of the model we build in class. Throughout this question, we will also assume:
(1)
There are no income effects on labor supply.
(2)
The labor market always clears (we are never in the short run).
(3)
Interest rates are fixed in this example throughout all periods (rt = rt+1). We do this for simplicity.
(4)
You can hire fractions of workers (i.e., N in equilibrium need not be a whole number).
example, N could equal X.XX.
(5)
The user cost of capital is only determined by the real interest rate.
Suppose we are currently in period t.
For
Suppose the following facts about the economy hold:
Aggregate production function:
Y = A K0.5 N0.5
Labor Supply Curve:
W/P = N0.5
Initial conditions:
Kt = 625 ; At = 2
Depreciation rate:
δ = 0.05
(real wage = square root of N)
Note: You must show all your work to get full credit. Each of these questions can be answered with
either one or two equations. You need to show the equations to get full credit. Additionally, the
responsibility is on you to make sure we can follow your work. Some of the parts build on each other. It
is up to you to make sure we can follow what you are doing so as to give you partial credit (if it is
deserved). Place your answers in the box.
A.
What is the level of N* in this economy in period t? In other words, what is N*t? (4 points)
Optimality requires W/P = MPN (firms equate the marginal product of labor to the real wage)
Step 1: derive the MPN from the definition of Y – this should be easy for all of you
MPN = .5A(K/N).5
Note: This is just the labor demand curve.
Step 2: Set A and K to their assigned values (given in the problem). Derive the labor demand
curve as function of just N and W/P.
Where A = 2, K = 625:
W/P = (625/N).5
Step 3: Equate labor demand (given in step 2) with labor supply (given in the problem). From this,
you can solve for N*, the equilibrium amount of N.
If W/P = N.5 then N.5 = (625/N).5 (here we equate the supply and demand curve)
Which is equivalent to: N.5 = 25/N.5 (this is just algebra)
Which is equivalent to: N = 25
25
Part VI: Quantitatively Analyzing a Permanent Increase in TFP (16 points)
B.
What is the level of r in this economy in period t? In other words, what is rt?
(4 points)
To get the bulk of the credit, all you had to do was realize that MPK = r (from firm optimization).
Step 1: Solve for MPK
User cost of capital is only tied to the interest rate. Optimality requires r = MPK
MPK = .5A(N/K).5
Step 2: Put in the given values of A and K and put in the equilibrium value of N. Then solve for r.
Where A = 2 K = 625 N = 25:
r = MPK = (25/625).5 = .2 or 20%
C.
Suppose TFP (A) increases between periods t and t+1 from 2 to 2.1. By how much would the
marginal product of capital (MPK) change in response to the TFP (A) change? In other words,
what is ∆MPKt, t+1? (4 points)
This was based solely on intuition. No math was needed. So, we graded this pretty tough (like a
T/F/U problem in part 2). MPK = r. If r is fixed, MPK will not change. There was a question on
the midterm (or practice midterm) exactly like this. No partial credit was given for this. It was a
concept we were testing.
Interest rates are fixed so there is no change in MPK. MPKt = MPKt+1 = .2 (as solved in part B)
26
Part VI: Quantitatively Analyzing a Permanent Increase in TFP (16 points)
D.
Suppose TFP (A) increases between periods t and t+1 from 2 to 2.1. What is the optimal level of
investment (It+1) after the increase in TFP? (4 points)
Note: Do not forget to account for depreciation.
Note: We will assume that the labor market will also clear in period t+1.
With the change in A, we need to solve for the new level of I, K, and N.
Start with Investment since r is fixed at .2 as solved in B. Set r = MPK
Where MPK = .5(2.1)*(.95*625 + I)-.5*(N).5 = .2 (note Kt+1 = (1-δ)Kt + It)
Which is equivalent to: 1/(.95*625 + I).5 = .19/(N).5
Which is equivalent to: (N).5=(.95*625 + I).5 *.19
Which is equivalent to: N = (.95*625 + I)*.036
Which is equivalent to: N/.036 -593.75 = I now we have Investment in terms of labor
Now solve for new MPN:
MPN = .5*2.1(593.75 + N/.036 -593.75).5(N)-.5
And we know W/P = N.5 because you must equate the labor demand and labor supply curves
So N.5 = .5*2.1(N/.036).5(N)-.5
So N = 1.05(N/.036).5
So N2= 30.625N
So N = 30.625
You plug this back into: (30.625)/.036 -593.75 = I
Which means I =
256.94
Which means Kt+1 = .95(625) + 256.94 = 850.69
Sanity check, we want MPK = .2
Which means MPKt+1 = .5*(2.1)*( 850.69)-.5(30.625).5 = .199 which is ~.2
27
Worksheet
LRAS
Ns
SRAS
P0
W0/P0
ND
AD
Y0*
N *0
NOTES
LRAS
LM
r0
IS
Y0*
28
Worksheet
LRAS
Ns
SRAS
P0
W0/P0
ND
AD
Y0*
N *0
NOTES
LRAS
LM
r0
IS
Y0*
29
Worksheet
LRAS
Ns
SRAS
P0
W0/P0
ND
AD
Y0*
N *0
NOTES
LRAS
LM
r0
IS
Y0*
30
Worksheet
LRAS
Ns
SRAS
P0
W0/P0
ND
AD
Y0*
N *0
NOTES
LRAS
LM
r0
IS
Y0*
31