Suppose that in a competitive labor market, demand for workers is QD = 10,000 - 100W and the labor supply is QS = 2000 + 1900W, where Q is the quantity of workers employed and W is the hourly wage.
a. Suppose that the government imposes a minimum wage of $5 per hour. How many people will be employed under the new minimum wage law?
b. Suppose that the demand for workers changes to QD = 14,000 – 100W and the labor supply remains the same. The government still imposes a minimum wage of $5 per hour. How many people will be employed?
Equilibrium occurs when demand for labor equals the supply of labor in the factor market.
So,
10000-100W = 2000+1900W
2000W = 10000-2000
W = 8000/2000
W = 4
Quantity of labor Q = 10000-100*4 = 9600
If the wage is set at $5 then
Qs = 2000+1900*5 = 11500
Qd = 10000-100*5 = 9500
There will be surplus labor available in the market. Surplus = Qs - Qd = 11500 - 9500 = 2000
This means that 2000 units of labor will remain unemployed if the minimum wage is set at $5
Now that the Qd changes to Qd = 14000-100W
New Equilibrium,
14000-100W = 2000+1900W
2000W = 12000
W = 6, if the govt still imposes minimum wage of $5 it will not be binding as the market wage is already above the minimum wage.
At W= 6, Q = 14000-100*6 = 13400 labor employed at W=$6
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