Question

1. Suppose that you have been hired to analyze the impact on employment from the imposition of a minimum wage in the labor market. Further suppose that you estimate the demand and supply functions for labor, where L stands for the quantity of labor (measured in thousands of workers) and W stands for the wage rate (measured in dollars per hour):  

Demand: W = 10 – 0.5*Ld;

Supply: W = (1/3)*Ls.  

First, calculate the free market equilibrium wage and quantity of labor. Now suppose the proposed minimum wage is $6. How large will the surplus of labor in this market be?

Answer 1

Equilibrium is where;

Demand = Supply

10 - 0.5L = 1/3 * L

10 = 0.33L + 0.5L

10 = 0.83L

L = 10/0.83 = 12.05

L = 12.05

W = 10 - 0.5(12.05) = 10 - 6.02

W = 3.98

At minimum wage of $ 6, Ls = 3W = 3 x 6 = 18

Ld = (10 - W)/0.5 = (10 - 6)/0.5 = 4/0.5 = 8

Surplus of labor = Ls - Ld = 18 - 8 = 10