Question

7. Consider an economy in which the marginal product of labor MPN is MPN=284-2N where N is the amount of labor used. The amount of labor supplied, NS, is given by NS=22+12w+2T, where w is the real wage and T is a lump-sum tax levied on individuals.

a)      Use the concepts of income effect and substitution effect to explain why an increase in lump-sum taxes will increase the amount of labor supplied.

b)      Suppose that T=25. What are the equilibrium values of employment and the real wage?

c)       With T remaining equal to 35, the government passes minimum-wage legislation that requires firms to pay a real wage greater than or equal to 7. What are the resulting values of employment and the real wage?

Answer 1

Q7)

a) If the limp-sum taxes will increase. There will be an income effect on labour supply, not a substitution effect(since the real wage will not change). An increase in the lump-sum tax will reduce a worker's wealth, so labour supply will increase.

b) Given, MPN = 284 - 2N, NS = 22 + 12W + 2T

If T = 25. Then

NS = 22 + 12W + (2*25)

NS = 72 + 12W

Labour demand is given by W = MNP = 284 -2N, or 2N = 284 -W, so N = 142 - W/2

Setting labour supply equal labour demad gives,

72 + 12W = 142 -W/2

or, 12W + W/2 = 142 - 72

or, 25W/2 = 70

or, 25W = 140

or, W = 140/25

or, W = 5.6

with W = 5.6,

N = 72 + 12(5.6)

N = 139.2

c)

NS = 92+ 12 (w) 02-+62 IL T-35 then NSE 23+ (2x35) + 12W =92 + 12 W Labau demand is given by W= MNP 284-2N ar 2N = 284-w ar, N= 142 - W/ 2020/3/19 13:43 so, Ns > N with minimum wage wat N will be 1385, which is less befane gouvement impases minimum wage which was 14o. Setting Labar supply = Labar demand gives = = - 142-W/2 = 92+12W 142 - 92 = 12W+ W/2 50 = 25W 10o = 25 W Car N8 = 142-w/ 8 = 142-2 = 140 Since the quilibrium real wage is a belaw the minimum wage, the minimum is binding with w = 7, N=142- 7/2 Y N = 138.5