Question

Answer both 8 and 9

8.) The supply curve of labor in a competitive industry is given by w = 10 + 5 E; and the demand curve for labor is given by w = 50 - 3E. What is the equilibrium wage and employment? Suppose that the demand for labor increases and the new demand curve is w’ = 70 – 3E. What is the new equilibrium wage and employment level?

9.) Suppose a firm purchases labor in a competitive labor market and sells its product in a competitive product market. The firm’s elasticity of demand for labor is −0.4. Suppose the wage increases by 5 percent. What will happen to the amount of labor hired by the firm? How is the marginal productivity of the last worker hired by the firm different from before the wage increase?

Answer 1

(8)

(i) In equilibrium, labor demand equals labor supply.

50 - 3E = 10 + 5E

8E = 40

E = 5

w = 50 - (3 x 5) = 50 - 15 = 35

(ii) Equating new demand with supply,

70 - 3E = 10 + 5E

8E = 60

E = 7.5

w = 70 - (3 x 7.5) = 70 - 22.5 = 47.5

(9)

Elasticity of labor demand = % Change in quantity of labor demanded (employment) / % Change in wage rate

-0.4 = % Change in quantity of labor demanded (employment) / 5%

% Change in quantity of labor demanded (employment) = -0.4 x 5% = -2% (Decrease)

Since demand for labor is given by VMPL schedule where VMPL = Output price x Marginal productivity of labor (MPL), output price remaining the same, a fall in labor demand (VMPL) will decrease MPL.