Fall 2012 ECON 302 – Intermediate Macroeconomics Professor Ananth Seshadri

Assignment 4 Answers

December, 2014

12.8

(a) In this question the permanent increase in government purchases will happen in the future. Basically, people try to smooth consumption by transferring current consumption and leisure since future consumption will decline (tax will increase permanently). In terms of the model, people’s wealth falls, so they reduce their private consumption demand and raise labor supply. There is no immediate direct substitution effect because G does not rise right away. So we don’t get the additional “α”-shift to the left of aggregate consumption demand curve. We also don’t get the direct shift to the right of G. So, on net, the demand curve shifts left only due to the wealth effect. The current output supply curve shifts to the right because of the increase in labor supply due to the wealth effect, and current output demand falls due to fall in consumption. As a result, real interest rate decreases, hence, investment demand increases so that the capital stock (and hence consumption) will be higher. Current investment rises and current consumption falls.

(b) The effect on the inflation rate is ambiguous. Thus, the effect on the nominal interest rate is also ambiguous, and so does the price level.

(c) It could be caused by an increased probability of a future war, or the expected policy on increased future government purchases. For example, Roosevelt and the “New Deal”, or Johnson and the “The Great Society”.

12.9 The real wage is equal to the MPL. We know the MPL schedule is unaffected by a G-shock, so all we have to worry about is the effect on labor supply.

(a) For the temporary increase in G we found that r rises, and that the level of wealth is roughly unchanged. Therefore, L rises, so MPL falls and w/P falls.

(b) For the permanent increase in Gwe found that r is unchanged, but wealth declines. Therefore, L rises, so MPL falls and w/P falls.

1 12.12

When Gt increases by 1 unit permanently, the wealth effect on households is that consump- tion decreases by 1 − α − β and increases by MPL ∗ 4L due to the increase in labor supply.

(a) This question assumes that households care about their consumption and leisure. When

Gt increases by 1 unit, consumption decreases, and leisure also decreases (they would work hard due to a negative WE). Thus households are worse off. C decreases by (1 − α − β).

(b) Note that this question assumes α and β decreases with government consumption. This means that the negative wealth effect (1 − α − β) is closed to 1 (α = 0, β = 0) when government consumption is large enough. Government should reduce its consumption until α + β = 1.

(c) Maximizing GDP is not the correct answer because government services are an input into ptoduction. Counting government consumption directly in GDP double counts, so it is inappropriate to use GDP as the target.

(d) This question is vague. Think about countries with socialism, like countries in North Europe. Government consumptions offer services to households directly, and people’s happiness in these countries are generally higher than capitalistic countries (If you are interested about this, you can goole “Index of Happiness” for more information.) In these countries, government functions well with households’ objectives. And to maxi- mize households’ utility, G should be maintained at some positive level. This is totally opposite to zero government consumption result in (b).

13.7

(a) If the elimination of deductions permits government to reduce the marginal tax rate on labor income, then there is an increase in labor income. Hence labor supply will increases, as well as output supply Y S. If this reduction on marginal tax rate also rises the after tax return on capital, then investment will increase. If it does not affect the return on capital, investment demand would not shift.

(b) There are similarities. Currently, the payroll tax provides a constant marginal tax rate on labor income, just as the proposed flat tax would. However, social security taxes provide no exemption until income exceeds a particular level ($62,700), after which the marginal tax rate falls to zero. This social security tax system results in a decreasing average tax rate as income rises. Under a flat tax, the exemption is applied to the first portion of earned income, so that the average rate increases with income. For social security tax, please refer to page 480 in the book.

2 (c) The tax law of 1986 reduced the number of tax brackets; this change was a movement (of sorts) closer to a flat tax.

13.10

(a) If real income remains the same, but nominal income increases over time, than it is possible that the marginal tax rate increases, because the nominal income jumps to a high tax level. Over time, the average marginal tax rate increases, and total real tax collection also increases.

(b) If the income bracket limits adjust with inflation level, than there is no change to the real tax collection, and the average marginal tax rate remains the same as if there is no inflation.

14.8 Government’s budget constraint is

g g g PtGt + Vt + Rt−1Bt−1 = Tt + (Mt − Mt−1) + (Bt − Bt−1).

Tt is lump-sum tax.

g (a) Assume Gt,Vt, and Mt do not change for all t. The tax cut is financed by deficit (Bt increases). The Ricradian Equivalence applies here, and there is no wealth effect on households. Since it is lump-sum tax, a tax cut has no effects on MPK and MPL. So CD,ID will not change, and output demand and output supply remain the same. As a result, r, Y, I, P, R remain the same.

(b) Assume Gt,Vt do not change for all t, but people expect Mt will increase in future. For this case, the deficit(debt) can be paid back by printing more money. However, an increase in M also drives up inflation level. Thus change in money has no aggregate wealth effect. The Ricardian Equivalence holds here. So r, Y, I remain the same. Money supply increases in future, so price level and nominal interest will increase in future, but it seems there is no effect on current price level and nominal interest rate.

(c) Assume Gt,Mt do not change, but people expect Vt decreases in future. When Vt de- creases, households’ wealth decreases in future. This is equivalent as saying the tax cut today is financed by lower transfer tomorrow, hence the same argument in the Ricardian Equivalence applies. The result is the same as in (a).

3 (d) Assume Vt,Mt do not change, but people expect Gt decreases in future. The current D S tax-cut is supported by lowering Gt, so there is positive wealth effect, C increases, L decreases. But these effects are small. Hence Y D and Y S remain roughly the same. So r, Y, I, P, R remain the same.

14.9 The two plans are identical with respect to the paths of government spending, so they would have the same implications, except for the fact that the timing of taxes would be different. Under the Reagan plan, the fact that taxes were higher in the early part of the 3-year phase in plan and lower later, implies that the tax cut would induce intertemporal substitution effects similar to question 14.5 in the textbook.

Since taxes will be lower in the future, for a given value of the after tax real interest rate, consumption demand today will be unaffected, but labor supply will decrease now and increase later through a simple intertemporal substitution effect. This is intuitively clear since the disincentive to work now is stronger than the disincentive to work in the future.

The net effect of this is that the aggregate supply curve today will shift to the left while the aggregate demand curve remains the same. Relative to the end of the phase-in period, the earlier period would be characterized by lower employment, output and investment and a higher real interest rate. An immediate tax-cut to the long-run tax rates would have induced no intertemporal effects of that kind.

14.10 The implicit but realistic assumption here is that retired people don’t have wage and must rely on their savings. Suppose now the government allocates part of its tax revenues as social security.

(a) People now know that they will receive more transfer when they retire, and thus can save less for the future. Once saving rate decreases, according to our model (Solow growth model in Ch11), we know that the steady state capital will decrease. That is, in the long run, the stock of capital decreases.

(b) The pay-as-you-go (PAYG) tax system collect tax from labor income and transfer it to the social security fund. In other words, PAYG system supports retirees by current young workers. The fully-funded social security system invests its funds in some financial assets, such as equity and stocks, and use its financial return to pay the social security. If being operated perfectly, a fully funded social security system does not rely on tax revenue. In PYAG, people are taxed now but they know this part of wealth will be paid back when they retire. In other words, people are forced to save for future, and hence their saving on other parts will decrease, since they mentally have already saved

4 in the form of tax. So the saving rate in PAYG should be lower than it in a fully funded system. The stock of capital under PAYG is lower than it under a fully funded system.

15.6 The figure in this question is the same as the Figure 15.5 in the book.

(a) As in Fig15.5, Y S decreases, while Y D does not shift. CAB decreases, but consumption does not change.

(b) This is the same case as a closed economy. The interest goes up due to the decrease in Y S. CD decreases a little bit due to the temporary wealth effect.

(c) Y S will shift to left, but in a less amount, because domestic production is now less affected by local supply shock (as implied in the question).

15.7 Now there are only two countries in the economy. As a result, one must be a borrower (CAB< 0) and the other be a lender (CAB> 0). With out loss of generality, suppose a bad supply shock hits A. If A is a borrower, now he would like to borrow more (Y S shifts to left, CAB decreases), and this drives up the interest rate. Note now there are only two countries, the world interest rate is determined only by A and B. If A is originally a lender, due to a bad shock, A would like to lend less, and this also drives up the interest rate.

15.9 The answer is in Ex2, Handout 10.

Additional Problem 1 The answer is in page 600, and 604-605 in the book. The absolute from of IRP is i j i εt j εt (1 + R ) i = (1 + R ) j εt+1 εt+1 or rewrite i i i εt+1 = εt + 4εt, we can get 1 + Ri 1 + Rj = , (1) 4εi 4εj 1 + εi 1 + εj which is the equation in the very top on page 605. The relative form of IRP is Eq(16.3), or equivalently Eq(16.6) in the book. To derive the relative form of IRP, we need to use an approximation rule: 1 + x ≈ x − y if x and y are small. 1 + y

5 Applying this rule, Eq(1) becomes

4εi 4εj Ri − ≈ Rj − , εi εj rearrange, we get 4εj 4εi Rj − Ri ≈ − , εj εi which is Eq(16.3).

Additional Problem 2

In this question, a rise in Gt also increases MPK. This may affect investment demand. Note that ID today depends on MPK tomorrow.

D (a) Gt rises permanently, hence MPK rise permanently as well. I shifts to right.  4C = −α(SE) − (1 − α − β) + MPL ∗ 4L(WE) D  D 4Y = 4I = 4I ⇒ 4Y = β+MPL∗4L+4I ,  4G = 1

where 4I is the increase in investment demand due to higher MPK tomorrow.

S 4Y = β + MPL ∗ 4L + 4Y ,

where 4Y is the increase due to higher MPK today. Note that 4Y is not equal to 4I . D S It is not clear which shifts more. If we assume that 4Y ≈ 4I , then 4Y ≈ 4Y , the real interest remains the same. The graph is the same as Figure 12.5 in the book.

D (b) A temporary increase in Gt today only affect MPK today, hence I does not shift. And the wealth effect is small, so we can ignore it.  4C = −α(SE), no wealth effect  4Y D = 4I = 0 ⇒ 4Y D = 1 − α.  4G = 1

S 4Y = β + 4Y

S D Since α + β < 1, and assume 4Y is not large, so that 4Y < 4Y . As the result, the interest rate rises a little bit. The graph is the same as Figure 12.3 in the book.

(c) The answer is already in (a) and (b). For a permanent change in Gt, WE in consumption is −(1 − α − β) + MPL ∗ 4L; for a temporary change, WE is small and can be ignored.

(d) The answer is similar to problem 12.12. α + β must less than 1, and Gt = 0.

6 Additional Problem 3 To have current account balance be counter-cyclical, the productivity shock must affect the investment demand, and the resulting shift in Y D is larger than the shift in Y S. Since

CAB=St − P (It + GIt), when there is a good productivity shock, both national saving St, and domestic private investment It increases, and we want It increases more than St so change in CAB is negative.

An example is in Ex1 (a large country case), Handout 10: a permanent shock which increases MPK forever. In this case, Y D shifts more than Y S in response to a good shock, and CAB decreases (counter-cyclical), output increases, the interest rate also increases a little. Thus C, I, Y, r are all procyclical and CAB is counter-cyclical. These match data, except the interest rate. Recall that the long term interest rate is weakly counter-cyclical in the data (see Figure 9.10 in the book).

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