Question

3. In this problem you are to find the effects of a legal minimum wage on the labor income of unskilled workers. Assume that the marginal product of labor for unskilled labor is

MPN = 100 - 0.2N.

The supply of unskilled labor is 80 + 2w, where w is the real wage received by unskilled labor.

a. If there is no minimum wage, find the equilibrium values of real wage, employment, and the labor income for unskilled workers.

b. Now suppose that a minimum wage that sets the real wage at 90 is instituted. What are the new levels of employment and total labor income for unskilled workers. c. Repeat parts (a) and (b) for MPN = 100 - 0.9N

Answer 1

Answer 3

(a)

In order to maximize profit a producer hires that amount of labor(N) at which Marginal product of labor = real wage

=> MPN = w

=> 100 - 0.2N = w

=> N = 500 - 5w----------------------Demand of unskilled labor

At equilibrium labor demand = labor supply

=> 500 - 5w = 80 + 2w

=> w = 420/7 = 60. Hence N = 80 + 2*60 = 200

Hence Equilibrium level of :

real wage = 60 , Employment = 200 Total labor income = 60*200 = 12000

(b)

Minimum wage = 90 > equilibrium wage(= 60) . Hence minimum wage is binding as it is greater than equilibrium rel wage.

At w = 90, Labor demand = 500 - 90*5 = 50 and Labor supply = 80 + 2*90 = 260. Hence producer will demand 50 and suppliers are willing to supply 260. Hence Among 260 people who are willing to work only 50 will get the work. Hence Employment = 50 and unemployment = 260 = 50 = 210.

Hence, Employment = 50 and Total Labor income = 50*90 = 4500

(c)

In order to maximize profit a producer hires that amount of labor(N) at which Marginal product of labor = real wage

=> MPN = w

=> 100 - 0.9N = w

=> N = (100 - w)/0.9----------------------Demand of unskilled labor

At equilibrium labor demand = labor supply

=> (100 - w)/0.9 = 80 + 2w

=> w = 28/2.8 = 10. Hence N = 80 + 2*10 = 100

Hence Equilibrium level of :

real wage = 10 , Employment = 100 Total labor income = 10*100 = 1000

Minimum wage = 90 > equilibrium wage(= 10) . Hence minimum wage is binding as it is greater than equilibrium rel wage.

At w = 90, Labor demand = (100 - 90)/0.9 = 100/9 = 11.11 and Labor supply = 80 + 2*90 = 260. Hence producer will demand 11(approx) and suppliers are willing to supply 260. Hence Among 260 people who are willing to work only 11 will get the work. Hence Employment = 10 and unemployment = 260 - 11 = 249.

Hence, Employment = 11 and Total Labor income = 11*90 = 990