Suppose you have estimated the supply curve for the local labor market as: Qs=W-

Question

Suppose you have estimated the supply curve for the local labor market as: Qs=W-5, where W is the hourly wage and Qs is the quantity of workers willing to work at each wage.  You have estimated the demand curve for the local labor market as: Qd=25-W, where W is the hourly wage and Qd is the quantity of workers demanded by employers at each wage.

a. Using algebra, solve for the equilibrium wage and quantity of labor.

b. If the government imposes a minimum wage of $18, what is the size of the labor force, the number of unemployed workers, and the unemplyment rate?

Explanation / Answer

Supply Curve =  Qs=W-5

Demand Curve = Qd=25-W

For Equilibrium

Supply = Demand

W-5 = 25-W

Hourly wage W = 15

Quantitiy of labor = 25 - 15 or 15 - 5 = 10

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b) minimum wage of $18

quantity of workers willing to work Qs = W - 5 = 18 - 5 = 13

quantity of workers demanded by employers Qd = 25 - W = 25 - 18 = 7

Size of labor force = quantity of workers demanded = 7

Number of Unemployed = 13 - 7 = 6

unemplyment rate = Number of Unemployed / Total Labor Force = 6 / 7 = 85.71%

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