Topics in Macroeconomics 2 Econ 2004

Transcription

1 Topics in Macroeconomics 2 Econ 2004 Practice Questions for Master Class 2 on Monay, March 2n, 2009 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) D 2) B 3) B 4) A 5) A 6) C 7) D 8) D 9) C 10) D 11) B 12) A 13) C 14) A 15) B 16) D 17) B 18) C 19) B 20) B 21) B 22) D 23) A 24) B 25) D 26) D 27) C 28) C 29) A 30) B

2 SHORT Problems 31) Using a iagram show that, if the consumer prefers more to less, then inifference curves cannot cross. Proof by contraiction: Consier the two hypothetical inifference curves in Figure 4.1. Point A is on both inifference curves, I 1 an I 2. By construction, the consumer is inifferent between A an B, as both points are on I 2. As well, the consumer is inifferent between A an C, as both points are on I 1. But at point C, the consumer has more consumption an more leisure than at point B. As long as the consumer prefers more to less, he or she must strictly prefer C to A. We, therefore, contraict the hypothesis that two inifference curves can cross. C B C A I 2 I 1 l Figure ) Why might hours worke by the representative consumer ecrease when the real wage increases? This woul occur if the income effect ominates the substitution effect

3 33) Suppose that the government imposes a proportional tax on the representative consumer s wage income. That is, the consumer s wage income is w(1-t)(h-l), where t is the tax rate. What effect oes the income tax have on consumption an labour supply? Explain your results in terms of income an substitution effects an represent it in a iagram. When the government imposes a proportional tax on wage income, the consumer s buget constraint is now given by: C = w 1 t)( h l) + π T (, where t is the tax rate on wage income. In Figure 4.3, the buget constraint for t = 0, is FGH. When t > 0, the buget constraint is EGH. The slope of the original buget line is w, while the slope of the new buget line is (1 t)w. Initially, the consumer picks the point A on the original buget line. After the tax has been impose, the consumer picks point B. The substitution effect of the imposition of the tax is to move the consumer from point A to point D on the original inifference curve. The point D is at the tangent point of inifference curve, I 1, with a line segment that is parallel to EG. The pure substitution effect inuces the consumer to reuce consumption an increase leisure (work less). The tax also makes the consumer worse off, in that he or she can no longer be on inifference curve, I 1, but must move to the less preferre inifference curve, I 2. This pure income effect moves the consumer to point B, which has less consumption an less leisure than point D, because both consumption an leisure are normal goos. The net effect of the tax is to reuce consumption, but the irection of the net effect on leisure is ambiguous. Figure 4.3 shows the case in which the substitution effect on leisure ominates the income effect. In this case, leisure increases an hours worke fall. Although consumption must fall, hours worke may rise, fall, or remain the same. C F A E D I 1 B G H I 2 l Figure 4.3

4 34) Show that the consumer is better off with a lump-sum tax rather than a proportional tax on wage income (as in question 33) given that either tax yiels the same revenue for the government. You will nee a iagram to show this. In Figure 4.4, with a proportional tax on wage income, the consumer s buget constraint is C = w(1 t)(h l) + π, (1) where t is the tax rate. In Figure 4.4, the buget constraint is DEF, an the consumer chooses point A, where C = C 1 an l = l 1. ow, suppose that the government taxes the consumer lump-sum, an the total tax the consumer pays with the lump-sum tax is the same as it was with the proportional tax, so that the lump-sum tax is T = wt(h l 1 ). The consumer s buget constraint is now C = w(h l) + π wt(h l 1 ). (2) Figure 4.4 shows the buget constraint (2), which is DGH. ote that the new buget constraint is steeper than the ol one, an that point A is on the new buget constraint, because if (C 1, l 1 ) satisfies (1) it must also satisfy (2). Thus, the consumer will now choose point B, which must be on a higher inifference curve than A, so the consumer is better off with a lump-sum tax than with a proportional tax. The proportional tax istorts economic ecisions an is therefore less efficient in extracting the same revenue that a lump-sum tax can generate.

5 35) Suppose that the government imposes a proucer tax. That is, the firm pays t units of consumption goos to the government for each unit of output it prouces. Determine the effect of this tax on the firm s eman for labour. The firm chooses its labour input,,so as to maximize profits. When there is no tax, profits for the firm are given by π = zf ) ( w. Profits are the ifference between revenue an costs. In the left panel in Figure 4.7, the revenue function is zf ( ) an the cost function is the straight line, w. The firm maximizes profits by choosing the quantity of labour where the slope of the revenue function equals the slope of the cost function: MP = w. The firm s eman for labour curve is the marginal prouct of labour scheule in the right panel of Figure 4.7. With a tax that is proportional to the firm s output, the firm s profits are given by: π = ) w = (1 t) t ) w where the term (1 t) ) is the after-tax revenue function, an as before, w is the cost function. In the left panel of Figure 4.7, the tax acts to shift own the revenue function for the firm an reuces the slope of the revenue function. As before, the firm will maximize profits by choosing the quantity of labour input where the slope of the revenue function is equal to the slope of the cost function, but the slope of the revenue function is ( 1 t)mp, so the firm chooses the quantity of labour where ( 1 t ) MP = w. In the right panel of Figure 4.7, the labour eman curve is now, ) ( 1 t)mp, an the labour eman curve has shifte own. The tax acts to reuce the after-tax marginal prouct of labour, an the firm will hire less labour at any given real wage. Revenues, Costs w ) (1 t) ) w MP ( 1 t)mp Figure 4.7

6 36) Suppose that the government subsiizes employment. That is, the government pays s units of consumption goos to the firm for each unit of labour that the firm hires. Determine the effect of this subsiy on the firm s eman for labour. The firm chooses its labour input so as to maximize profits. When there is no subsiy, profits for the firm are given by π = zf ) ( w. Profits are the ifference between revenue an costs. In the left panel in Figure 4.7, the revenue function is zf ( ) an the cost function is the straight line, w. The firm maximizes profits by choosing the quantity of labour where the slope of the revenue function equals the slope of the cost function: MP = w. The firm s eman for labour curve is the marginal prouct of labour scheule in the right panel of Figure 4.8. With an employment subsiy, the firm s profits are given by: π = zf ( ) ( w s) where the term zf ( ) is the unchange revenue function, an (w-s) is the cost function. The subsiy acts to reuce the cost of each unit of labour by the amount of the subsiy, s. In the left panel of Figure 4.8, the subsiy acts to shift own the cost function for the firm by reucing its slope. As before, the firm will maximize profits by choosing the quantity of labour input where the slope of the revenue function is equal to the slope of the cost function, (t-s), so the firm chooses the quantity of labour where MP = w s. In the right panel of Figure 4.8, the labour eman curve is now MP + s, an the labour eman curve has shifte up. The subsiy acts to reuce the marginal cost of labour, an the firm will hire more labour at any given real wage. Revenues, Costs w ( w s) ) w MP + s MP Figure 4.8