The following expressions describe a perfectly competitive labor marke

The following expressions describe a perfectly competitive labor market. The labor supply curve is:

SL = AE = $3.00 + $0.000375L.
The marginal revenue product of labor curve is:
MRPL = $13.00 – 0.000433L.

a. Find the equilibrium wage in this labor market. Also, find the optimal number of labor hours worked per week. Let L represent the number of labor hours worked per week, and let W represent the hourly wage of workers.
b. Determine the economic rent earned by labor in this situation.

ANSWER

a.
The equilibrium wage and number of labor hours worked per week are determined at the intersection of the supply and demand for labor curves. These curves are represented by AE and MRP. Equate these two curves to get L first.
3.00 + 0.000375L = 13 – 0.000433L
L = 12,376.24
Insert L into the MRP curve to get equilibrium wage rate.
W = MPL = 13.00 – 0.000433(12,376.24 )
W = $7.64

b.
The economic rent is the area of the triangle between W ($7.64 ) and AE bounded by L = 0 and L = 12,376.24.
The area is (1/2)(base)(height)
b = 12,376.24 – 0 = 12,376.24
h’ = 7.64 – 3 = 4.64
economic rent = (1/2 )(12,376.24 )(4.64 ) = $28,712.88