Question

2. Suppose that the production function is Y=20K^0.3N^0.7. With the production function, the marginal product of labor is MPN=14K^0.3N^-0.3. The capital stock is K=214. The labor supply curve is NS=100[(1-t)w]², where w is 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.

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

c)Suppose that a minimum wage $2 over the equilibrium wage 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?

Part c is needed.

Answer 1

q.2

in eqm

mpn = w(1-t)

a) t = 0

mpn = w

14K^0.3N^-0.3 = w

putting value of k

14 * 5 *n^-0.3 = w

now putting value of n

14*5*(100(w)²)^-0.3 = w

70* 1/3.98 *1/w^0.6 = w

17.5 = w^1.6

w = 6 (approx)

ns = 100 * (1-0)w² = 100* 6² = 3600

nd = Y = 20* 5* 309 = 30900

b)

mpn = w(1-t)

14K^0.3N^-0.3 = w*0.4

putting value of k

14 * 5 *n^-0.3 = 0.4w

now putting value of n

70*100(0.4w)² =  0.4w

7000 = 1/w

w = 0.00014

ns = 100 *(0.4*0.00014)²

c) w = 2

14K^0.3N^-0.3 = 2

5*n^-0.3 = 2

n^-0.3 = 0.4

1/n^{0.3 =0.4}

2.5 = n^0.3

ns = 21

minimum wage will increase the supply of labor , given that it is above the eqm wage . but there will be unemployment due to excess supply and hence it is uncertain that total income will increase.