Erik’s Midterm
Macroeconomics
Winter 2014
Name (print): ________ ANSWERS _____________________
Name (signature): _______________________________________
Section Registered (circle one): Friday a.m. Friday p.m. Saturday a.m.
Mail Folder (circle one): Campus MBA Campus PHD Evening Weekend
TEST GRADE BREAKDOWN
Part I: (Costs of Inflation: 15 points) ____________
Part II: (Taxes and Mechanisms: 20 points)
Part III: (True/False/Uncertain: 25 points)
____________
____________
____________ Part IV: (Marginal Propensity to Consume: 8 points)
Part V: (Immigration Reform: 20 points)
Part VI: (Labor Market Analysis: 12 points)
Total (out of 100)
____________
____________
____________
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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 discussion 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. Move quickly through the exam or you 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 Friday morning class, at 3:30 in the Friday afternoon class, or at 11:00 in the Saturday morning class. We will have a lecture after the midterm.

You are allowed:
One Piece of Paper - Handwritten - Not Photo Copied - Front Side Only
A Calculator

Good Luck!
2

6.
7.
8.
Exam Assumptions
1.
2. TFP (A), population, government spending (G), taxes (t c
, t n
) , welfare programs (Tr), consumer confidence, uncertainty, and business confidence are all held fixed , unless I specifically tell you otherwise.
3.
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 almost always wrong (or, at least, incomplete). Please try to answer the questions in terms of the models developed in class. Moreover, this is not a philosophy class. I am testing you on the models developed in class. If we have not talked about it in class, I am not going to test you on it.
The capital stock (K) is assumed to be constant through our entire analysis. Throughout the rest of the exam, this does not mean that investment (I) is constant . People can invest today – we will just assume that today’s investment does not affect today’s capital stock (unless told otherwise).
This assumption just makes our life easier.
4. All changes in TFP, taxes, government spending, etc. are assumed to be permanent and unexpected, unless I specifically tell you otherwise . (Often, I will tell you otherwise. This assumption is here in case I ever forget to tell you about the nature of the change in the variable, this will be the default situation. Again, this is just to reduce any potential exam ambiguity).
5. Unless told otherwise, all consumers in the class are PIH (non-Ricardian) who have the preferences developed in class (log utility, r = 0, β = 1). I have not defined "non-Ricardian" 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.
We will assume, for now, that NX always equals zero.
Assume that changes in N have no effect on investment demand (for simplicity). This just makes our life easier.
Assume that the labor market always clears - unless specifically told otherwise.
3

Part I: Costs of 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. However, we also discussed two other distinct reasons why low stable inflation is preferred to high stable inflation.
A. Describe two distinct reasons discussed in class why we prefer a low stable inflation rate to a high stable inflation rate . Make sure to explain the intuition (3 points each) i. "Shoe Leather Costs". Shoe leather costs refer to the fact that nominal interest rates on money in really liquid form (like in your pocket) are zero. This implies that real rates are large and negative when inflation is large and positive. High inflation results in it being expensive to keep funds in liquid form for transactions. In high inflation environments, households have to incur an additional cost of converting their resources into liquid form every time they want to transact. ii. "Menu Costs". Menu costs refer to the fact that firms have to pay a cost to change their price more frequently in a high inflation environment. This also refers to the fact that firms have to spend more resources trying to think about what their optimal price is when inflation rate is high. Are people paying more for the firm's product because they like the product more or because the prices of all goods are increasing?
B. In this 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 4 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. i. 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 = 4 % from the approximation formula (i = r + π e = 4% + 0%)
Tax is paid on nominal interest rate = tax rate * nominal interest rate = 0.25 * 4 = 1%
After tax nominal interest rate = 3% (nominal interest rate - tax paid)
Expected after tax real interest rate = 3% (after tax nominal interest rate - expected inflation rate)
Expected after tax real interest rate = 3%
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ii. Given the above information, what is the expected after-tax real interest rate when the expected inflation rate is 8 percent? Show work. Put answer in box. (3 points)
Again, plugging in to the approximation formula (Supplemental Notes 1 and 2):
Nominal interest rate = 12 % (i = r + π e = 4% + 8%)
Tax is paid on nominal interest rate = tax rate * nominal interest rate = 0.25 * 12 = 3%
After tax nominal interest rate = 9% (nominal interest rate - tax paid)
Expected after tax real interest rate = 1% (after tax nominal interest rate - expected inflation rate)
Expected after tax real interest rate = 1% 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.
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Part II: Taxes and Economic Mechanisms (20 points total – 5 points each)
Consider the models developed in class. In this question, we are going to analyze what happens when there is an unexpected permanent decrease in labor income taxes (t n
) . Specifically, we are going to address what happens to the marginal utility of consumption (MU
C
), the marginal utility of leisure (MU
L
), the marginal product of labor (MPN) and the marginal product of capital
(MPK).
Below, indicate how each of these marginal variables will change (by circling the appropriate answer). Additionally, provide 1-2 sentences to explain your answer . In your answer, you should specifically discuss what is driving the changes in the marginal variables and why.
When answer the questions, we will make the following assumptions:

Households have preferences as discussed in class. We will assume they are nonliquidity constrained PIH (with log utility).

Firms maximize profits with a production function that has the features we described in class.

Real interest rates are permanently fixed (i.e., in this problem they will never change).

The capital stock is held fixed in this problem . In addition, we will continue to assume that changes in N do not affect the marginal product of capital (MPK).

All other exogenous variables (TFP, government spending, confidence, wealth, uncertainty, expectations, etc.) are held fixed.

No assumption is made about the relative strength of income and substitution effects on labor supply.
Before answering this question, let’s figure out what happens when taxes are permanently reduced.
Labor market:
Labor demand: Nothing happens. Recall, MPN= 0.7A(K/N)^.3
A is fixed (I told you that). K is fixed (I told you that). So, the labor demand curve will not shift!
Labor supply: As taxes fall, we know that after tax wages must increase—the government is taking less out of every paycheck. The substitution effect tells us that the labor supply curve will shift right—it has become relatively more expensive to take leisure so we choose to work more. As after tax wages permanently increase, PVLR must increase. Thus, we know the income effect will shift the labor supply curve to the left—as we feel permanently richer, we choose to work less. Given I told you that the income effect is small relative to the substitution effect, we know that the labor supply curve (on net) will shift right. This means, in equilibrium, that N will increase (leisure will fall) and before tax wages will fall.
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Note, that as tax rates fall, after tax wages will unambiguously go up (we are working more
- only a substitution effect can make us work more so we know after tax wages go up).
Consumption.
This is easy. We know that the present value of life time resources (PVLR) increases because as after tax wages unambiguously and permanently increase. Given the consumers are PIH, we know that a permanent increase in lifetime resources will increase household consumption today. (Note: this would occur for Keynesian and PIH liquidity-constrained consumers as well.)
Investment/Capital
We know firms optimize. In other words, firms hire capital (K) where the marginal product of capital (MPK) = the real interest rate (r). First, note that the real interest rate did not change (so
MPK cannot change in equilibrium). Also, notice that nothing else changed the MPK. Recall,
MPK = 0.3A(N/K)^0.7. A did not change and I explicitly told you that we will assume that changes in N will not affect MPK.
A) The new equilibrium marginal product of labor (MPN): i.
will definitely increase ii.
will definitely decrease iii.
will definitely stay the same iv.
is indeterminate (could either increase, decrease or stay the same)
Explanation :
Firms optimize. That means, they hire labor (N) where MPN = W/P. From above, we know that before tax wages (W/P) fell as a result of the tax change and a dominant substitution effect. The intuition is that as individuals work more, N increases. The increased N reduces MPN because of diminishing marginal product of labor.
B) The new equilibrium marginal utility of consumption (MU
C
): i.
will definitely increase ii.
will definitely decrease iii.
will definitely stay the same iv.
is indeterminate (could either increase, decrease or stay the same)
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Explanation :
As C increases, the marginal utility of consumption will fall (due to diminishing marginal utility of consumption).
C) The new equilibrium marginal utility of leisure (MU
L
): i.
will definitely increase ii.
will definitely decrease iii.
will definitely stay the same iv.
is indeterminate (could either increase, decrease or stay the same)
Explanation :
As N increases, leisure falls. Households substitute away from leisure and towards work. As a result, we know that the marginal utility of leisure will increase (as leisure falls) because of diminishing marginal utility of leisure. Notice, the marginal utility of leisure and the marginal product of labor (MPN) move in opposite directions. This has to be the case. N increasing, by definition, implies that leisure falls.
D) The marginal product of capital (MPK): i.
will definitely increase ii.
will definitely decrease iii.
will definitely stay the same iv.
is indeterminate (could either increase, decrease or stay the same)
Explanation :
As explained above, nothing changed MPK. Moreover, r is fixed and we know MPK = r. So, as a result, there is no change in MPK in this example. When we allow interest rates to change (in topic
5), we will see that the answer to this question will change. However, with fixed interest rates, there is no change in MPK.
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Part III: True/False/Uncertain: Explanation Determines the Grade
(30 points total - 5 points each)
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 each.
Please write as clearly as you can – it makes it so much easier for us to follow your logic! If we cannot read your writing (or follow your logic), we will deduct points.
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 model of the economy developed in class. Suppose that income effects on labor supply are small relative to substitution effects. Finally, suppose that TFP is held fixed.
An unexpected permanent increase in government spending (G) will unambiguously shift the labor supply curve to the right causing both the equilibrium amount of N to increase and the equilibrium amount of before-tax real wages (W/P) to fall.
False. Changes in G DO NOT affect the labor market.
It does not affect labor demand. Recall, firms optimize—they hire labor where MPN=W/P. From our Cobb-Douglas production function: MPN=0.7A(K/N)^0.3. We can clearly see that only A and
K affect labor demand and neither of those variables are changing.
It does not affect labor supply. Recall, only tax rates, shocks to PVLR, shocks to the value of leisure, and population dynamics affect the labor supply curve. . Changes in G (by itself) will have NO effect on the labor market. That is what I am testing in this example. To get full credit, you need to have said that “changes in G will not affect the labor market”. Any other answer is wrong (or incomplete).
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Notice, some of you said “the decline in G could affect TFP and affect labor demand”. However, that is not what I was asking. That is a change in TFP and in this example, we are holding TFP constant.
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!
B. Consider the model put forth in class. Suppose that there is an unexpected and
permanent decline in labor income taxes (t n
). 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 (t n
) will unambiguously shift both the IS curve to the right and the long run aggregate supply (LRAS) curve to the right.
Many of you missed this. This is false. A permanent decline in tax rates was discussed in Part II.
The only difference here is that INCOME effects dominate. As income effects dominate, N will fall.
We know this is true because the substation effect tells us the labor supply curve will shift right and the income effect tells us the labor supply curve will shift left—if the income effect dominates the labor supply curve will shift left, reducing N.
As N falls, Y* falls as you can clearly see from our production function (Y = AK .3
N .7
). Given there is no change in A or K, Y* must fall as N* falls (due to the strong income effect). Remember, the long run aggregate supply (LRAS) curve is just Y*. So, in essence, I am asking you about Y* when
I ask about the long run aggregate supply curve.
What happens to the IS curve? As after tax wages permanently increase as a result of the permanent tax change, PVLR must increase. As PVLR increases and consumers are PIH (or even if they are Keynesean), we know that consumption must increase. (You also saw this in Part II). The
IS curve is the expenditure side of the economy. Y= C+I+G+NX. As one of its components (C) increases, that shifts the IS curve to the right.
While it is true that the IS curve will shift right, it is NOT true that the long run aggregate supply curve will shift right. It will shift left. So, the whole answer is false. In order to get full credit you needed to say: i.
ii.
N* falls.
Y* (long run aggregate supply curve) falls.
Some of you thought the long run aggregate supply curve was the labor supply curve. While it is true that the labor supply curve shifted left, I did not ask you about the labor supply curve. You need to show us in this answer that you knew that the long run aggregate supply curve is a different curve than the labor supply curve.
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C. Consider the labor market developed in class. Suppose that both TFP (A) permanently increases and the marginal tax rate on labor income (t n
) 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
(A) coupled with a sharp decline in labor income taxes (t n
) would unambiguously increase equilibrium before tax real wages (W/P), unambiguously increase equilibrium after tax real wages, and unambiguously have no effect on equilibrium hours worked 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):

From MPN = 0.7A(K/N)^.3, we know the labor demand curve shifts out.

W/P increases (before tax wages).

After-tax wages increase. We define after tax wages as (1-tn) (W/P). We know W/P
 increases as a result of the shock so (1tn)(W/P) must increase. (tax rates are held fixed – we are only looking at TFP shock.
N does not change. Why? Let’s think about what happens as a result of the increase in W/P from the TFP shock. The income effect tells us the labor supply curve will shift in as PVLR increases and we feel permanently richer. Recall, the substitution effect here is a movement along the labor demand curve. If the income and substitution effects permanently offset each other, the labor supply curve will shift in enough for the new equilibrium to be pinned at the initial N* with higher wages.
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Shock 2: Tax rates fall permanently (only)

(1-tn)(W/P) increases (after tax wages – because tax rate falls)

The income effect tells us the labor supply curve will shift left. The substitution effect tells us the labor supply curve will shift right. If they perfectly offset each other, then, on-net the labor supply curve does not shift.

W/P does not change (before tax wages – income effect and substitution effects offset)


N does not change (income effect and substitution effects offset).
Now let’s take the 2 shocks together. We know from the tax analysis that when the substitution and income effects perfectly offset—nothing happens (on-net) in the labor market. So, we can simply look at the effects from the shock in TFP. After-tax wages (both after tax and before tax) increase 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.
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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!
D.
Some have argued that during recent years, there has been a large expansion of government transfers (Tr) to the household sector. Consider the models built in class.
Suppose there was a large unexpected permanent increase in government transfers
(Tr). Lastly, suppose nothing else changes with respect to government spending (G) or tax rates.
Theoretically, our models predict that a large unexpected permanent increase in government transfers (Tr) will shift the IS curve to the right and the labor supply curve to the left.
True. This was easy. A permanent increase in Tr will increase disposable income. Recall we define disposable income as Yd = (Y + Tr – taxes). As Yd increases C will increase. This is true regardless of the type of consumer. Transfers are like a negative tax.
What happens to the IS curve? Recall, we define the IS curve as the expenditure side of the economy: Y= C+I+G+NX. The increase in C will shift the IS curve to the right.
Additionally, as transfers go up, there could be both an income effect that shifts the labor supply curve to the left and a substitution effect that shifts it left (if the transfers are only provided if people do not work). This problem came straight from the Supplemental Notes on Transfers.
E. Recently, there has been a large amount of discussion surrounding "economic uncertainty". Consider the models built in class.
An increase in uncertainty will steepen the IS curve.
True. As we talked about in class, an increase in uncertainty steepens the investment demand curve. As firms are more uncertain about the future, they are less responsive with respect to their investment decisions to changes in real interest rates today. Put another way, you need to bribe a firm more with lower interest rates to get them to do a given amount of investment when times are uncertain (and they do not want to invest). The IS curve is the graphical representation of the
Y=C+I+G drawn in {Y,r} space. The IS curve inherits the slope of the investment demand curve
(it is the only component of C, I and G that responds to changes in real interest rate rates). So, it is true that an increase in uncertainty will steepen the IS curve.
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14

Part IV: The Marginal Propensity To Consume (8 Points Total)
In class, we discussed the consumption behavior of different types of consumers. In this question, we will explore that behavior. Given the information below, compute the marginal propensity to consume (MPC) out of the temporary income change. Put your answer in the box below.
Assumptions:

All consumers in the economy follow the permanent income hypothesis (PIH) but are bound by liquidity constraints such that the consumer's wealth can never be negative in any period (i.e., Wealth t
≥ 0).

Individuals have initial wealth ( Wealth
0
) = 10.

Individuals have log utility with β = 1 and r = 0.

Individuals live two periods. Where income in period 1 is: ( Y t
) = 30. Where income in period 2 is: ( Y t+1
) = 50.

Assume taxes and transfers are zero such that total income equals disposable income.
Question:
Given the above information, you can solve for the individual's lifetime consumption profile ( C
1
) and ( C
2
). Take that profile as given. Suppose at the beginning of period 1, the individual unexpectedly receives an increase of 20 in their income in period 1 (and no expected change in their income in period 2). What is the marginal propensity to consume (MPC) out of the unexpected change in income today?
Hint: The marginal propensity to consume is defined as the fraction of the increase in income today (20) that is consumed today. As a result, your answer should range between 0 and 1.
Show your work to receive full credit.
To answer this question, let’s start with what the consumption profile will look like prior to the unexpected temporary income.
Prior to the unexpected income, initial wealth = 10, Y
1
= 30, and Y
2
= 50. Total life time resources will equal 90. According to the PIH without liquidity constraints, the household would like to consume 45 in each period of his life. However, given they face a liquidity constraint (wealth can never be negative), the most that the household could consume in period 1 is 40 (his 10 of initial wealth plus the 30 of income earned in period 1). So, prior to the unexpected income increase, the household would have a consumption profile of C
1
= 40 and C
2
= 50.
Now, consider what will happen when the household receives an extra 20 of income in period 1.
Now, the household has initial wealth = 10, Y
1
= 50 (30 initially plus the extra 20), and Y
2
= 50.
Total life time resources will equal 110. According to the PIH without liquidity constraints, the
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household would like to consume 55 in each period of his life. In this case, the household can actually achieve their desired consumption. The household now has 60 units of resources available in period 1 (10 of initial wealth and Y
1
= 50). Given that the household only wants to consume 55 and they have 60 units of resources, they will save 5 for tomorrow.
The above analysis implies the household will only consume 15 of the 20 units of extra income today
(they will save 5 for tomorrow). So, the MPC out of the 20 units of income today will be 0.75
(15/20).
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Part V – Analyzing Immigration (20 points total)
One argument in favor of allowing more low-skilled immigrants into the U.S. is that such a policy will increase government revenues (more legal workers means more people that the government can tax). Proponents of this view say that the increase in low-skilled immigration can help raise revenues for the government without the government having to raise the tax rate on existing U.S. workers.
Most economists, however, find this argument flawed (at least partially). Allowing immigration of low-skilled workers, we argue, is exactly like imposing a tax on the existing (native) population of low-skilled workers. In this question, we will see how immigration can act like a tax on low-skilled workers. (For now, we will take the extreme assumption that immigrants only pay taxes and do not receive any transfers. For simplicity, we will ignore all transfers!).
General Assumptions to be used through all parts of this question (parts A and B)
Suppose the following equations represent an economy’s low-skilled labor market:
Total Labor supply: N
S
= (low skilled population/20) * (5 + 0.2 ( (1-t n
)W/P )
2
)
Total Labor demand: N
D
= 2500 – 6 (W/P)
2 where (W/P) represents the before tax real wage and (t n
) represents the tax on household wages
(income tax).
Additional assumptions that hold through all parts of the question: i. Refer to N as both the number of low-skilled workers actually working and the number of jobs in the economy (i.e., we are assuming that every worker has one job). ii. Assume every job has the workers working exactly 40 hours per week. iii. Assume that the before-tax wage is measured in dollars per hour (such that 40 *
W/P is an individual’s weekly before tax earnings). iv. *** Assume that there are no income effects on labor supply. *** v. Weekly total tax revenues of the government (from all workers) = N * tax rate * before tax wage * 40 (each worker pays t n
percent of their before tax weekly earnings to the government). vi. It is ok to have fraction of people working (there is no need to round N to the nearest number). In other words, do not round N!
17

Part V: Immigration Question (continued) (A1 – A2)
Part A
Additional assumptions for part A (only) : t n
= 0.2 (labor income taxes equals 20%).
Working age population (population) = 2000
Note: These latter two assumptions imply that in part A:
Total Labor supply: N
S
= (100) * (5 + 0.128 ( W/P ) 2 )
(Note: To get the new labor supply curve, just set (working age population) = 2000 and set t n
=
0.2 and do some algebra).
Put all answers in the box. You must show work to receive both partial and full credit!
A1. Given the above information, what is the equilibrium before tax wage in this economy.
[Express your answer as $XX.XX per hour]. (2 points)
N
S
= N
D
(100) * (5 + 0.128 (W/P) 2 ) = 2500 – 6 (W/P) 2
500 + 12.8 (W/P) 2 = 2500 – 6 (W/P) 2
18.8 (W/P) 2 = 2000
(W/P) 2 = 106.38
(W/P)
N
= 10.31
= 1860.59
(W/P)(1-t n
) = 8.25
(equilibrium before tax wage)
(equilibrium employment) (some got 1861.70 depending on how the wage was rounded – that is fine)
(after tax wage)
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A2. Given the above information, what is the total weekly tax revenues (earned from all workers) paid to the government. [Express your answer as $XXXX.XX per week.] (3 points)
As defined above, total weekly tax revenues =
N * (W/P) * (t n
) * 40 = 1860.59 * 10.31 * (0.2) * 40 = 153,461.46 (some got 153,553.02 depending on how the wage was rounded to get N*).
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Part V: Immigration Question (continued) (B1 – B2)
Part B
Additional assumptions for part B (only) : t n
= 0.2 (labor income taxes equal 20%).
Working age population (population) = 2200
In this part of the problem, the income tax rate is still 20%, but the government allowed the low skilled working age population to increase by 10% - via immigration (from 2000 to 2200).
Put all answers in the box. You must show work to receive both partial and full credit!
B1. Given the above information, by how much did hourly after tax wages change as the government increased the working age population. [Express your answer as the change in $XX.XX per hour (after tax) and be sure to indicate the sign of the change ]. (5 points)
N
S
= N
D
(110) * (5 + 0.128 (W/P) 2 ) = 2500 – 6 (W/P) 2
550 + 14.08 (W/P) 2 = 2500 – 6 (W/P) 2
20.08 (W/P) 2 = 1950
(W/P) 2 = 97.11
(W/P) = 9.85 (equilibrium before tax wage)
N = 1917.33
(W/P)(1-t n
) = 7.88
(equilibrium employment)
(after tax wage)
The change in after tax wages would be 8.25 – 7.88 = $0.37 per hour
You could have expressed the change in weekly hours per week (multiply the number by 40). That would have been fine as well.
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B2. Given the above information, by how much did government tax revenues change as the government increased the working age population. [Express your answer as the change in total weekly tax revenues collected by the government and be sure to indicate the sign of the change.
Again, express the change in dollars (not percent).]. (5 points)
As defined above, total weekly tax revenues =
N * (W/P) * (t n
) * 40 = 1917.33 * 9.85 * (0.2) * 40 = 151,085.60
In this problem, total tax revenues actually fall! The reason is that even though N increases, after tax wages fall. The decline in tax revenues would be 153,461.46 - 151,085.60
= 2,375.86 (some got a decline of 2,467.36 or so depending on rounding)
In order to get full credit, you must report that tax revenues actually fell. That must be clear from your answer.
Part B (continued)
B3. As after tax wages change, individuals will change their desired labor supply because of a substitution effect (the price of leisure will change). In this example, what is the change in N that results from ONLY the substitution effect due to after tax wages changing as the government increases the working age population. [Express your answer as the change in
N (i.e., number of workers) and be sure to indicate the sign of the change ]. (5 points)
The substitution effect from an increase in population – as discussed in class – is the difference in labor supply that results from the change in before tax wages. To compute this, we start by calculating how much labor would be supplied if population increased and real wages did not change.
Step 1:
N
S
= (110) * (5 + 0.128 (W/P) 2 ) = (110) * (5 + 0.128 (10.31) 2 ) = 2046.65
Then we compare this to the labor supply at the new equilibrium wage (we did this above).
Step 2:
N
S
= (110) * (5 + 0.128 (W/P) 2 ) = (110) * (5 + 0.128 (9.85) 2 ) = 1917.33
The substitution effect implies that N would fall (as before tax wages fall): 128.67
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Part VI: Labor Markets in Recent Periods (12 points total - 4 points each)
Open up any newspaper and you will hear discussions surrounding the effect of declining housing market wealth on economic activity. Or, how increased uncertainty (over economic policies and future TFP) is hindering economic activity. Or, how we have suddenly reduced our expectation of future economic growth. In this question, I want us to think about these factors viewed through the lens of our labor market analysis.
For these problems, we will make the following assumptions:

The labor market will always clear.

The exam assumptions (page 2) hold throughout this question (i.e, capital is fixed, all exogenous variables are held fixed unless told otherwise , etc.).

Households are risk averse (such that they do not like uncertainty).

Households maximize utility over consumption today, consumption in the future, leisure today, and leisure in the future.

Labor demand is only a function of current TFP (not future TFP or uncertainty) .
Given this, today's labor demand will remain fixed through this example.
Circle the correct answer for each of the following questions. No further explanation is needed.
Hint: The way I set up this problem, all the action is on labor supply.
Overview
All three of the problems I outlined will shift the labor supply curve to the right.
Notice, the labor demand curve will not shift with any of the changes. Why? MPN =
0.7A(K/N)^0.3. I told you in the "Hint" that I am holding today's TFP fixed in all examples and I mentioned that only today's TFP will affect labor demand.
The substitution effect in these problems is reflected in the a movement along the labor demand curve. So, all the shifts occur because of an income effect on labor supply.
In these cases,e either PVLR falls or uncertainty increases resulting in precautionary behavior. When today's wealth falls, PVLR falls (even though there is no direct substitution effect). We should work more when wealth falls. When future income falls, we are poorer (even if wages do not change today). There is no direct substitution effect, only an income effect. Likewise, when uncertainty goes up, we can protect our self from the uncertainty by working more today.
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Given there is no direct substitution effect (only the income effect is shifting the labor supply curve), nothing is ambiguous. All of these are just incentives for people to work more.
Why did I write this problem? Because there is a discussion in many macro models that people should actually be working more in this recession because of the declines in wealth and increase in uncertainty. There is some evidence that older workers have delayed retirement (consistent with part A) of the example. The uncertainty story is more nuanced. While workers want to work more with uncertainty - firms may want to hire less. I shut this channel down in our example (by assuming labor demand is not a function of uncertainty). In the real world, however, this is likely an unrealistic assumption. But, models that have the uncertainty effect on labor demand being small - still get an uncertainty effect on labor supply where workers want to work more. The goal was to show you that there are currently economic forces that should increase the labor supply of existing workers (all else equal).
A. An unexpected permanent fall in household wealth (housing wealth and stock wealth) will: a. b. c. d. e.
Unambiguously cause equilibrium labor (N*) to fall and before tax real wages
(W/P) to rise.
Unambiguously cause equilibrium labor (N*) to fall and before tax real wages
(W/P) to fall.
Unambiguously cause equilibrium labor (N*) to rise and before tax real wages
(W/P) to rise.
Unambiguously cause equilibrium labor (N*) to rise and before tax real wages (W/P) to fall.
The effect on equilibrium labor (N*) and before tax real wages (W/P) depends on the relative strength of income and substitution effects on labor supply.
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Part VI: Labor Markets in Recent Periods (12 points total - 4 points each)
B. Individual expectations that TFP will be lower in the future (holding today's TFP fixed) will: a. Unambiguously cause equilibrium labor (N*) to fall and before tax real wages
(W/P) to rise. b. Unambiguously cause equilibrium labor (N*) to fall and before tax real wages
(W/P) to fall. c. d. e.
Unambiguously cause equilibrium labor (N*) to rise and before tax real wages
(W/P) to rise.
Unambiguously cause equilibrium labor (N*) to rise and before tax real wages (W/P) to fall.
The effect on equilibrium labor (N*) and before tax real wages (W/P) depends on the relative strength of income and substitution effects on labor supply.
C. An increase in individual's uncertainty about future TFP (holding today's TFP and the expected level of future TFP fixed) will: a. Unambiguously cause equilibrium labor (N*) to fall and before tax real wages
(W/P) to rise. b. Unambiguously cause equilibrium labor (N*) to fall and before tax real wages
(W/P) to fall. c. Unambiguously cause equilibrium labor (N*) to rise and before tax real wages
(W/P) to rise. d. Unambiguously cause equilibrium labor (N*) to rise and before tax real wages (W/P) to fall. e. The effect on equilibrium labor (N*) and before tax real wages (W/P) depends on the relative strength of income and substitution effects on labor supply.
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