1.  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.

(a)   If the lump-sum tax is increased, there’s an income effect on labor supply, not a substitution effect (since the real wage isn’t changed). An increase in the lump-sum tax reduces a worker’s wealth, so labor supply increases.  This is a very micro type of question and we did not emphasize it.  It belongs in Dr. Bolduc intermediate micro.

b)      Suppose that T=30. What are the equilibrium values of employment and the real wage?

(b)  If T = 30, then NS = 22 + 12w + (2 ´ 30) = 82 + 12 w

 Labor demand is given by  w = MPN = 284 - 2N.

 To solve you can either substitute one equation into the other of solve for N and setting labor supply equal to labor demand.

 
With w = 120/25 or 4.8 , N = 139.6.

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?

 Oops!  That should have been T = 30.  I graded with both 30 and 35.  You can plug w=7 back into the two equations to determine the quantities.

2. Suppose that the production function is Y=5K^0.5N^0.5. With the production function, the marginal product of labor is MPN=4.5K^0.5N^-0.5. The capital stock is K=30. The labor supply curve is NS=100[(1-t)w]², where wis the real wage rate, t is the tax rate on labor income, and hence (1-t)w is the after-tax real wage rate.

a)      Assume that the tax rate on labor income, t, equals zero. Find the equation of the labor demand curve. Calculate the equilibrium levels of the real wage and employment, the level of full-employment output, and the total after-tax wage income of workers.

(a)  If t = 0.0, then NS = 100w². Setting labor demand equal to labor supply gives 506.25/w² = 100w², so w⁴ = 5.0625, or w = 1.5. Then NS = 100 (1.5)² = 225. [Check: N = 506.25/1.5² = 225.] Y = 45N^0.5 = 45(225)^0.5 = 675. The total after-tax wage income of workers is (1 - t) w NS = 1.5 ´ 225 = 337.5.

b)      Repeat part (a) under the assumption that the tax rate on labor income, t, equals 0.6.

(b)  If t = 0.6, then NS = 100 [(1 - 0.6) w]² = 16w². The marginal product of labor is MPN = 22.5/N^0.5, so N = 100 [(1 - 0.6) ´ 22.5/N^0.5]², so N² = 8100, so N = 90. Then Y = 45N^0.5 = 45(90)^0.5 = 426.91. Then w = 22.5/90^0.5 = 2.37. The total after-tax wage income of workers is (1 - t) w NS = 0.4 ´ 2.37 ´ 90 = 85.38. Note that there’s a big decline in output and income, although the wage is higher.

c)       Suppose that a minimum wage of w=2 is imposed. If the tax rate of labor income, t, equals zero, what are the resulting values of employment and the real wage? Does the introduction of the minimum wage increase the total income of workers, taken as a group?

(c)  A minimum wage of 2 is binding if the tax rate is zero. Then N = 506.25/2² = 126.6, NS = 100 ´ 2² = 400. Unemployment is 273.4. Income of workers is wN = 2 ´ 126.6 = 253.2, which is lower than without a minimum wage, because employment has declined so much.

3. How would each of the following affect the current level of full-employment output? Explain and illustrate your answer with a graph.

a)      A large number of immigrants enter the country.

(a)   An increase in the number of immigrants increases the labor force, increasing employment and increasing full-employment output.

b)      Energy supplies become depleted.

(b)  If energy supplies become depleted, this is likely to reduce productivity, because energy is a factor of production. So the reduction in energy supplies reduces full-employment output.

c)       New teaching techniques improve the educational performance of high school seniors.

(c)  Better education raises future productivity and output, but has no effect on current full-employment output.

d)      A new law mandates the shutdown of some unsafe forms of capital.

(d)  This reduction in the capital stock reduces full-employment output (although it may very well increase welfare).

4. How would each of the following affect Joe Economist's supply of labor?

a)      The value of Joe's home triples in an unexpectedly hot real estate market.

(a)   The increased value of Joe’s home increases his wealth. The rise in wealth leads to an income effect that leads Helena to reduce her labor supply.

b)      Originally an unskilled worker, Joe acquires skills that give him access to a higher-paying job. Assume that his preferences about leisure are not affected by the change in jobs.

(b)  Another great micro question, but probably not one I should have asked in macro.  I did not grade this part.  The permanent rise in Joe’s real wage gives rise to offsetting income and substitution effects. The income effect of the higher wage reduces Joe’s labor supply, but the substitution effect increases it. So the result is theoretically ambiguous.

c)       A temporary income tax surcharge raises the percentage of his income that he must pay in taxes, for the current year only. (Taxes are proportional to income in Joe's country.)

(c)  The temporary income tax surcharge is equivalent to a temporary reduction in the real wage, which reduces current labor supply, assuming that the income effect is smaller than the substitution effect.  Another good micro question.  Do not expect questions like this on the test.  Basic labor supply and demand is enough.