Question

5. Suppose we have the following information about the market for labor: Demand for labor: w = 9 - 3L Supply of labor: w = 3 + 5L L = hundreds of thousands of hours per week w = real wage in dollars per hour, base year dollars. Find the equilibrium wage and quantity of labor employed. After a wage increase of 25%, how many people are unemployed?

Answer 1

Answer : 5) At equilibrium, labor demand = labor supply.

=> 9 - 3L = 3 + 5L

=> 9 - 3 = 5L + 3L

=> 6 = 8L

=>> L = 6 / 8

=> L = 0.75

From demand function we get,

W = 9 - 3L = 9 - (3 * 0.75)

=> W = 6.75

Therefore, the equilibrium wage is $6.75 per hour and quantity of employed labor is 0.75 hundreds of thousands of hours per week.

After increase in wage rate by 25% the wage rate becomes,

W = 6.75 + (6.75 * 25%) = 6.75 + 1.69

=> W = 8.44

Now, labor demand : w = 9 - 3L

=>8.44 = 9 - 3L

=> 3L = 9 - 8.44

=> 3L = 0.56

=> L = 0.56 / 3

=> L = 0.19

Labor supply :  w = 3 + 5L

=> 8.44 = 3 + 5L

=> 8.44 - 3 = 5L

=> 5.44 = 5L

=> L = 5.44 / 5

=> L = 1.09

Unemployed people = Labor supply - Labor demand = 1.09 - 0.19 = 0.9

Therefore, after increasing wage rate by 25% the quantity of unemployed people is 0.9 hundreds of thousands of hours per week.