Suppose the market for labor is perfectly competitive and the demand for labor is $L = 100 - 10 w$ and market supply is $L = - 20 + 10 w$ .If a minimum wage is imposed at w = 8,the deadweight loss of the imposition of the minimum wage is
A)10
B)20
C)30
D)40

Question

Quizplus · Accepted Answer

To determine the deadweight loss (DWL), we need to compare the quantity of labor demanded before and after the minimum wage is imposed at w = 8.

Before the minimum wage, the equilibrium wage and quantity of labor exchanged would be where demand equals supply:

100 - 10w = -20 + 10w

Simplifying this equation, we get:

w* = 6
L* = 80

Therefore, at the equilibrium wage of w* = 6, the quantity of labor demanded and supplied is L* = 80.

After the minimum wage is imposed at w = 8, the new equilibrium is where the demand curve intersects the supply curve at w = 8:

100 - 10w = -20 + 10w = -20 + 10(8) = 60

Simplifying this equation, we get:

w* = 8
L* = 60

Therefore, at the new equilibrium wage of w* = 8, the quantity of labor demanded and supplied is L* = 60.

The deadweight loss (DWL) is the area of the triangle formed by the old equilibrium quantity (Q1), the new equilibrium quantity (Q2), and the minimum wage level (w*):

DWL = 0.5 * (80 - 60) * (8 - 6) = 20

Therefore, the deadweight loss of the minimum wage is 20. The correct answer is D.

Suppose the Market for Labor Is Perfectly Competitive and the Demand