Erik’s Midterm Macroeconomics

Winter 2012

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TEST GRADE BREAKDOWN

Part I: (Consumption Tax: 15 points total) ____________

Part II: (True/False/Uncertain: 50 points total) ____________

Part III: (Social Security: 15 points total) ____________

Part IV: (Labor Market Analysis: 20 points) ____________

Total (out of 100) ____________

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Exam Preamble

As always, that honor code rules are in effect. You know the routine. All the usual disclaimers apply. By signing on page 1, you are pledging to adhere to the honor code guidelines in my syllabus and the student handbook. Any discussing of the exam with students who have yet to take the exam is a blatant violation of the honor code.

You have 1 hour and 45 minutes for the exam. 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 morning class) or 8:00 (in the evening class). We will have a lecture after the midterm.

You are allowed:

One Piece of Paper - Handwritten - Not Photo Copied - Front Side OnlyA Calculator

Good Luck!

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Exam Assumptions

1. All answers should be provided in terms of the models and discussions developed in class. Some of you provide me with your “own” models of the economy. While these are often fun to read – they are 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 (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 (aside from one question later in the exam - for that question I will tell you to assume that K can change). Throughout the rest of the exam, this does not mean that investment (I) is constant. People can invest today – we will just assume that today’s investment does not affect today’s capital stock (unless told otherwise). This assumption just makes our life easier.

4. All changes in TPF (A), taxes (tn), government spending (G), etc. are assumed to be permanent and unexpected, unless I specifically tell you otherwise. (Often, I will tell you otherwise. This assumption is here in case I ever forget to tell you about the nature of the change in the variable, this will be the default situation. Again, this is just to reduce any potential exam ambiguity).

5. Unless told otherwise, all consumers in the class are PIH (non-Ricardian) who have the preferences developed in class (log utility, r = 0, β = 1).

6. We will assume, for now, that NX always equals zero.

7. Assume that changes in N have no effect on investment demand (for simplicity).

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Part 1: Consumption Tax (15 points - 3 points each)

As government budgets continue to be stressed, some policymakers have proposed moving to a national sales tax. In this problem, let’s discuss how an increase in consumption taxes will affect some of the curves/markets that we have discussed so far in class.

When answering the questions, consider only the models we have built so far. For this problem, let's assume that the labor market will always clear. It may avoid over-thinking on the part of some of you (if you have read ahead).

When answering the questions, assume the change in the consumption tax was unexpected and permanent (and that all consumers are non-liquidity constrained PIH consumers).

Finally, let’s assume that income effects on labor supply are large relative to the substitution effects on labor supply in the labor market (resulting from changes in after tax wages).

Given the above information, circle the true answer for each of the question stems. No explanation is needed.

Let’s start by figuring out what happened in the labor market.

Ns0

Ns1

w/p(0)

w/p(1) ND

N0 N1

The labor supply curve will shift right (on net) because the income effect on labor supply is large relative to the substitution effect. This will cause the following:

N* to rise (equilibrium labor will rise from N0 to N1)Y* to rise (as N* rises)Before tax wages will fallAfter tax wages will fall (even more than before tax wages)PVLR will fall (as after tax wages will fall)C will fall (as after tax wages will fall).Marginal utility of consumption will increase (because of diminishing marginal utility of consumption as C falls).The IS curve will shift in as C will fall.Marginal utility of leisure will increase (as leisure falls as N increases)

One may ask how does the IS curve shift in as Y* shifts out? We will do this later in the class. What will happen is that P will fall (w will change such that w/p remains at w/p(1)). As p falls, the real money supply will increase and real interest rates will fall. The result will be that move along the new IS curve to have an equilibrium where the new IS curve intersects the higher level of Y* (at lower interest rates and higher investment). You do not know about this yet – but, that is how a shift in of the IS curve can co-exist when Y* shifts out. That is why I asked this question so you can see the dichotomy.

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A. The potential level of GDP will:

a. Unambiguously increase (see above, N* increases)b. Unambiguously decreasec. Unambiguously stay the samed. Could increase, decrease, or stay the same

B. The marginal utility of consumption will:

a. Unambiguously increase (see above, C falls)b. Unambiguously decreasec. Unambiguously stay the samed. Could increase, decrease, or stay the same

C. The marginal utility of leisure will:

a. Unambiguously increase (see above, N increases so leisure falls)b. Unambiguously decreasec. Unambiguously stay the samed. Could increase, decrease, or stay the same

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Part 1: Consumption Tax (15 points - 3 points each)

D. The IS curve (on net) will

a. Unambiguously shift rightb. Unambiguously shift left (as C(.) falls)c. Unambiguously not shift d. Could shift right, shift left or not shift at all

E. Income tax revenues will:

a. Unambiguously increase (as Y increases and income tax rates (tn) remain fixed)

b. Unambiguously decreasec. Unambiguously stay the samed. Could increase, decrease, or stay the same

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Part II: True/False/Uncertain: Explanation Determines the Grade (50 points total)

Each of the question stems sets up a scenario (in italics) and ends with a statement. In this section, you are to discuss whether that final statement is True, False or Uncertain.

As on the practice exams - explanation determines all of your grade! I will give no credit for writing true when the answer is true but your logic is wrong. Each of your answers should be at most 3-4 sentences. To receive full credit, you need to be explicit about the mechanism that is driving your results. Finally, if it is a two-pronged question (where I asked you about two separate things like employment and wages), you need to address both parts to get full credit! Each question is worth 5 points each.

Please write as clearly as you can – it makes it so much easier for us to follow your logic! If we cannot read your writing or follow your logic, we will deduct points.

A. In many developing economies, the working age population often changes due to changing fertility rates. As economies grow, fertility rates usually start to decline.

If income effects are large relative to substitution effects on labor supply, a permanent decline in the working age population will – on net – shift the labor supply curve to the left.

True. This was just like one of the practice quiz questions. The answer is the same if the income effects are large or small. The labor supply curve (Ns) will shift in as working age population falls. This will increase W/P for those remaining in the work force. As the remaining households are richer, they will work less. This is a second shift left of the labor supply curve. The size of the income effect determines how far left the second shift is. But, regardless, the two shifts go in the same direction. It is unambiguous that the labor supply curve will shift left as the working age population falls. (Note the substitution effects – in this case – are just movements along the new labor supply curves!)

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B. We have spent a lot of time talking about the Cobb-Douglas production function in class. However, nothing says that such a given production function is always going to be a good representation of the macroeconomic environment.

Instead of Cobb-Douglas, let’s consider the following production function:

According to this production function, TFP and labor are substitutes.

The answer is false. A and N are complements. You can answer this via math. Given this production function, the MPN is:

Some of you forgot how to take the derivative of a ln. Note: the derivative of ln(N) is (1/N).

Given this production function, you can see that as A increases, the marginal product of labor unambiguously increases. This fact, by definition, is what complementary across the inputs means. As A increases, the marginal product of labor increases.

A perfect answer to this question discussed MPN. If your answer did not discuss MPN, you did not receive full points.

In terms of intuition, you can look at the production function and see that as A increases, a unit of labor is more valuable. A and N reinforce each other in the production function.

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C. We have spent a lot of time talking about the Cobb-Douglas production function in class. However, nothing says that such a production function is always going to be a good representation of the macroeconomic environment.

Suppose instead that we have the following production function:

According to this production function, TFP and capital are substitutes.

The answer is True. A and K are substitutes in this production function. You can answer this via math. Given this production function, the MPK is:

(Note the derivative of (1/K) is -(1/K)2).

Given this production function, you can see that as A increases, the marginal product of capital unambiguously falls. This fact, by definition, is what substitutability across the inputs means. As A increases, the marginal product of capital falls.

In terms of intuition, you can look at the production function and see that K is in the denominator of the production function while A and N are in the numerator. You can get higher production by lowering K or increasing A or N.

A perfect answer to this question would have discussed MPK. If your answer did not discuss MPK, you did not receive full points.

Note – this production function is not overly realistic. Capital and labor are also substitutes. I picked this production function to show you some production function where capital and labor are substitutes (which is the intuition that many of you have at the firm level).

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D. Consider the labor market developed in class. Assume income effects are small relative to substitution effects. During the last 10 years, the U.S. economy has experienced both

large increases in TFP and declining marginal tax rates on income.

Theoretically, our model of the labor market predicts that a permanent increase in TFP coupled with a decline in labor income tax rates would unambiguously increase both the amount of workers in the economy (N) and the after tax wage.

True!

Analyze each shift separately.

An increase in TFP will increase both W/P and N (if income effects are small). Given that tax rates are fixed (if we are looking only at the TFP change, after tax wages would also increase).

A fall in taxes rates would shift labor supply curve to the right which would increase N and increase AFTER tax wages (that is why we are working more).

So, in both cases, N increases and after tax wages increases. So, when you put the two shocks together, both effects will reinforce each other.

If you said that the change in after tax wages was ambiguous, you did not receive the full points.

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Part II: True/False/Uncertain: Explanation Determines the Grade (continued)

E. Economists and demographers have long predicted that there will be a sharp decline in the work force starting in 2013 as baby boomers start to retire. Such predictions have been widely publicized during the last decade.

According to the standard PIH theory developed in class, we should see a sharp increase in consumption (C) for those remaining in the work force between 2012 (prior to the baby boomers starting to retire) and 2014 (after they start retiring).

False. This was a harder problem. If consumers are truly PIH, the change in demographics would have been forecast in advance. So, even though W/P would increase (as the baby boomers retire), the change should already have been incorporated into their consumption plan today (mean consumption would not change when it actually occurs). You could have told me that it would have increased if people were liquidity constrained. That is fine – but you would have needed to say that.

F. Economists are always looking for ways to predict future economic activity. One way we do this (as discussed in the supplemental notes), is by looking at firm inventories.

A rise in firm inventories is always a reliable signal that the economy is heading into a recession.

False. This was from the supplemental notes. Increases in UNPLANNED inventories are good predictors of recessions. However, increases in PLANNED inventories are good predictors of future economic growth. All of this is in the supplemental notes.

A perfect answer would have discussed unplanned and planned inventories. If your response mentioned only one, you did not receive full points.

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Part II: True/False/Uncertain: Explanation Determines the Grade (continued)

For parts G and H, consider the following information.

During the late 1990s and early 2000s, we saw large run ups in stock market wealth. For simplicity, let’s refer to the run up in stock market wealth as being a magnitude of X dollars.

For simplicity, let’s assume that there is only one individual in the economy and that individual owns stocks. This individual is expected to live 25 more years (i.e., LL = 25). From the perspective of today’s individual, suppose the stock market unexpectedly increased by X today (measured in dollars).

Lastly, assume that this representative individual in the economy is a non-liquidity constrained PIH consumer of the type modeled in class (has log utility, β=1, r = 0, etc.).

G. Given the above information, if the individual believes that the unexpected increase in the stock market today of X was permanent (i.e., increase by X dollars today and remain constant at that new level forever), their annual consumption today (C) should increase by X/25 dollars.

True. Households will take the increase in wealth and spread it over the remaining periods of their life. If they get an extra $250 today, the will take that $250 and spread it over the remaining periods of their life (25 years) thereby increasing their consumption by $10 per year. When we estimate the MPC out of permanent wealth changes, our estimates are roughly in the 0.03-0.04 range (roughly consistent with LL being 25-30 years for the average stock owner).

H. Given the above information, if the individual believes that the unexpected increase in the stock market today of X was temporary (i.e., increase by X dollars today and decrease by X dollars tomorrow such that the total change in the stock market value is zero over the next 25 years), their annual consumption today (C) should increase by X/25 dollars.

False, a temporary change in wealth has ZERO effect on consumption. The wealth comes today and goes away tomorrow – a household’s PVLR is unchanged so consumption should not respond. If households are non-liquidity constrained PIH, temporary wealth changes have NO effect on their consumption.

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Part II: True/False/Uncertain: Explanation Determines the Grade (continued)

I. Suppose TFP increases permanently starting today. Assume further that real interest rates are permanently held fixed. In this question, we will let the capital stock (K) adjust optimally (if firms desire).

Given firm profit maximization (as described in class), a permanent increase in TFP (starting today) will result in an increased marginal product of capital tomorrow.

False. MPK = r (that is the first order condition of firm optimization – ignoring depreciation, etc.). If r is fixed, MPK will remain constant. How does this happen? As A goes up, MPK goes up. Firms respond by investing more today (lowering MPK by increasing the capital stock). This is the key assumption of the firm’s problem – they maximize profits such that the marginal benefit of investment equals the marginal cost of investment. If the marginal costs do not change, than the marginal benefits cannot change.

J. In class, we discussed the role of interest rates (r) on consumer spending (C). When answering the question, focus your attention on the two period model we built in class. Further, assume that households are non-liquidity constrained PIH.

If households are net borrowers, a permanent increase in interest rates (r) today will unambiguously cause both consumption today (Ct) and consumption tomorrow (Ct+1) to fall.

False. As discussed in the supplemental notes, an increase in interest rates will cause:

Substitution Effect: Consumption today will fall and consumption tomorrow will increase.

Income Effect: Consumption today and tomorrow will fall (if households are net borrowers).

If households are net borrowers, a rise in interest rates will make households poorer because they will have higher interest payments (higher debt service).

So, consumption today will definitely fall but the effect on consumption tomorrow is ambiguous.

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Part III: Social Security (15 points-5 points each)

On both practice exams, I outlined how our model of consumption could be used to think about winners and losers from a social security system. If you used the practice exams as a study aid, this question should be extremely easy for you. If not, you are going to have to do some thinking.

The set up of the model is similar to one of the practice exam. Suppose individuals live four periods and earn income in each period as follows:

Y1 = 35 Y2 = 50 Y3 = 80 Y4 = 15 (where Yi = gross income in period i).

Note: This lifecycle pattern of income is typical for many households (earnings grow over working years (periods 1-3) and falls sharply in retirement (period 4).

Suppose, a social security system is placed on this economy where:

Taxes: T1 = 7 T2 = 10 T3 = 16 T4 = 0 Transfers: Tr1 = 0 Tr2 = 0 Tr3 = 0 Tr4 = 33

Individuals pay 20% income tax on their gross earnings during their working years to the social security system and get all of that money back in retirement (let's assume the system is actuarially fair). Also, assume that interest rates (r) are zero (so there is no need to discount).

Also assume that initial wealth (Wealth0 = 0).

Finally, let's assume all types of consumers (PIH, Keynesians, Liquidity Constrained PIH) accrue utility over their lifecycle such that:

Total Utility = ln(C1) + ln(C2) + ln(C3) + ln(C4) (where Ci is consumption in period i).

Note: As in class, liquidity constraints are defined as individuals not being allowed to have negative wealth (Wealtht ≥ 0).

Given these assumptions, we can assess whether a social security system increases the utility, decreases the utility, or keeps the utility the same for different types of consumers (relative to the environment where there is no social security system).

For each type of consumer circle the answer that makes the statement true. Then, to receive full credit, provide a 1 or 2 sentence intuitive explanation for your answer (i.e., use words NOT math). Be precise to get full credit. Why is the consumer made better off or worse off?

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Part III: Social Security (15 points - 5 points each)

A. Relative to the world without a social security system, implementing the above social security system ___________ the utility of non-liquidity constrained PIH consumers.

Increases Decreases Keeps The Same

Explanation:

This was straight from the practice exam. The reason is that the social security program has NO effect on the consumption of the non-liquidity constrained PIH. The key to PIH consumers who are not liquidity constrained is the total lifetime resources. Conditional on lifetime resources, PIH non-liquidity constrained households can always allocate their consumption to maximize their utility. In this case, PVLR does not change. As a result, the optimal allocation of the spending over their life does not change. So, the social security program does not alter the wellbeing of PIH (non-liquidity constrained) in any way.

B. Relative to the world without a social security system, implementing the above social security system ___________ the utility of liquidity constrained PIH consumers.

Increases Decreases Keeps The Same

Explanation:

This was straight from the practice exam. Liquidity constrained PIH households in this example have lower utility because they consume too little when their young (relative to their optimal). Because their income profiles are steep (earn more late in life relative to early in their life), they are constrained because they cannot borrow when young (move resources forward in their life). The social security system, however, taxes people when they are young. This makes the disposable income of young workers even LOWER than it was before. As a result, consumption is even lower for young households after the social security program (because taxes are levied on young households). So social security programs actually make liquidity constrained households worse off. I wrote a paper on this a few years ago. You can find it on my web page. It is entitled “Social Security and Unsecured Debt” (because some young people are liquidity constrained, social security increases the incentives to borrow on credit cards at high interest rates).

To get full credit, you need to mention that the social security program exasperates the liquidity constrained (making the households more constrained when young) which lowers their utility.

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C. Relative to the world without a social security system, implementing the above social security system ___________ the utility of Keynesian consumers.

Increases Decreases Keeps The Same

Explanation:

The utility of Keynesians increases because they actually have a big increase in consumption during retirement. Without the social security program, Keynesians consume very little in retirement. That makes their utility much lower than otherwise. The reason we have a social security program is to increase the utility of Keynesians. There are other reasons for the social security system (provide annuity to people to insure against longevity risk). But, the main rational for forced saving programs is that some people are unable to save on their own for their retirement (Keynesians).

*Notice, this is a separate issue from the fully funded social security system debate.* 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. (There is an insurance aspect to social security in that it also provides an annuity insuring households with respect to their length of life. But, we could always create an annuity market that does that for private wealth. When we talk about why we have a social security system, the only justification is that some people are Keynesians.)

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Part IV – Analysis of the Labor Markets (20 points total)

In this part of the exam, I am trying to gauge how much you have internalized about the labor market. You must show your work to receive any credit. Put your answers in the box.

Suppose the following equations represent an economy’s labor market:

Labor supply: NS = 200 + 10 ((1-tn)*W/P)2

Labor demand: ND = 1000 – 5 (W/P)2

where (W/P) represents the before tax real wage (in dollars per hour) and (tn) represents the tax on household wages (an hourly income tax).

Additional assumptions that hold through all parts of the question:

i. Refer to N as both the number of workers 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. ***

Part A: No Tax Equilibrium

A) Assuming tn = 0, what is the equilibrium number of workers (jobs) in the economy? Round your answer to the nearest number of workers (jobs). (3 points)

I am going to do part (A) and (B) together.

This first part was easy. You have two equations (labor demand and labor supply) and two unknowns (N and W/P). Use the two equations to solve for the two unknowns.

Step 1) 200 + 10 ((1-tn)W/P)2 = 1000 – 5(W/P)2 (solve for equilibrium W/P)

15 (W/P)2 = 800 (assuming tn = 0)

W/P = 7.30

Step 2) 1000 – 5 (7.30)2 = NN = 733 (or 734 depending at what stage you rounded)

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Part V – Analysis of the Labor Markets (continued)

B) Assuming tn = 0, what is the equilibrium hourly after tax wage (measured in dollars/hour) in this economy? Round your answer to the nearest cent (i.e., $xx.xx/hour). (3 points)

W/P = 7.30

C) Now assume that tn = 0.2. What would be the equilibrium hourly after tax wage (measured in dollars/hour) received by the household if tn = 0.2? Round your answer to the nearest cent (i.e., $xx.xx/hour). Hint: Make sure you keep track of your parentheses! (3 points)

Let’s start by graphing an increase in labor income taxes on a market (remember there is no income effect). This will make our discussion easier below. Remember, from the previous problem that N*0 = 733 and W/P (initial) = $7.30.

N`S(tn = 0.2)NS(tn=0)

1W/P (new)

ZW/P (initial) 0 ($7.30)

NZ N*1 N*0

(733)

In this part, you are to find the new AFTER TAX wage. That is (1-0.2) * W/P(new).

Given the labor demand and labor supply curves above, you solve for W/P (new) and N*1 (the new equilibrium amount of workers). The key is substituting tn = 0.2 into the labor supply equation.

Step 1) 200 + 10 ((1-tn)W/P)2 = 1000 – 5(W/P)2 (solve for equilibrium W/P)

11.4 (W/P)2 = 800 (assuming tn = 0.2)

W/P = 8.38

Step 2) 1000 – 5 (8.34)2 = NN = 649

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Step 3) Compute after tax wage: 0.8 * 8.38 = $6.70

Summarize, the imposition of the tax lowered the after tax wage. As after tax wages fall, you and I work less (substitution effect). As we work less, we become more valuable to the firm and, as a result, they pay us more (pre-tax).

D) After the imposition of the tax, the change in labor supply can be split into two substitution effects: a decrease in labor supply coming from a decline in after tax wages due to the increased tax rate (holding before tax wages constant) and an increase in labor supply coming from an increase in pretax wages (holding the tax rate constant).

Compared to the no tax equilibrium (found in part A), what would be the change in the number of workers in the economy that would result only from the substitution effect induced by the change in the tax rate? Round your answer to the nearest number of workers. Make sure you label the sign of the change correctly! (4 points)

I loved this question. Basically, I know ask you to decompose the fall in N (from N*(0) to N*(1)) into two substation effects. The first substitution effect is the effect solely due to the tax change (holding W/P at its initial level). This is represented as the difference between N*(0) and N(Z) (using the notation of the graph above).

What is N(Z)?

Solve the labor supply curve for tn = 0.2 and W/P = $7.30

N(Z) = 200 + 10 ((1-tn)W/P)2

= 200 + 10 (0.8 * 7.30)2

= 541

This means that if there was no change in before tax wages, N = 541 (lower than N*(1) found above).

What is the substitution effect due to only the tax change?

541 – 733 = -192

N would fall by 192 if there were no change in W/P (but, as we saw above, there is a change in W/P)

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E) After the imposition of the tax, the change in labor supply can be split into two substitution effects: a decrease in labor supply coming from a decline in after tax wages due to the increased tax rate (holding before tax wages constant) and an increase in labor supply coming from an increase in pretax wages (holding the tax rate constant).

What would be the change in the number of workers in the economy that would result only from the substitution effect induced by the change in the before tax wage (holding the tax rate constant at its new level)? Round your answer to the nearest number of workers. Make sure you label the sign of the change correctly! (4 points)

Given B1 and B2, this was simple. How much of the change in labor supply is due to the change in W/P (holding taxes constant at their new level). This is the difference from N (Z)

(solved in B2) and N*(1) (solved in B1)

649 – 541 = 108

N increases by 108 due to the increase in W/P. The two effects together give us the movement from N*(0) to N*(1).

I liked this problem. It was pretty easy – but, it tested intuition. That is why I liked it.

F) In total, what would be the amount of cyclical unemployment (in terms of number of workers) that would result from the imposition of the tax? Round your answer to the nearest number of workers. (3 points)

The answer is ZERO. There is no cyclical unemployment in this model, we moved from an initial equilibrium to a new equilibrium. As long as we are in equilibrium, there is no cyclical unemployment.

Note: Some of you assumed that wages were sticky and the unemployment was the movement from N*0 to Nz. That is fine (because I didn't specify). But, to get full credit you would have had to (1) state that you were assuming sticky wages (because without sticky wages there would be no unemployment) and (2) correctly compute the difference between N*0 and Nz (no other answer would make sense).

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