Question

4. Suppose that in the short run a firm has a production function relating workers to output per hour: Q = 10L Where L is hours of labor. Suppose also that the firm sells its product in a perfectly competitive output market, at a price of $8 per unit produced

a. Suppose that the firm is a monopsonist in the labor market, facing a labor supply curve that can be written as: L = 2W (for W = wage per hour). Derive the marginal value product of labor as a function of L (from the production function and price), and derive the marginal expenditure on labor as a function of L from the labor supply curve. (It might help to figure out total expenditure on labor as a function of L, and then take the derivative with respect to L.) How many hours of labor will the firm want to hire in this case? What will the wage be?

b. Continuing with the monopsony case, suppose the firm faced a more inelastic labor supply curve: L = W Econ 4010 Fall 2019, Problem Set 3, p. 3 Now, given the same production function and the same perfectly competitive price in the output market, how many hours of labor will the firm employ, and at what wage?

Answer 1

a)

Given Q=10L

Marginal Product of labor=MPL=dQ/dL=10

Marginal Revenue product of labor=MRPL=MP*Price=10*8=$80

Given

L=2W or W=L/2

Total expenditure on labor=TCL=L*W=L*L/2=L²/2

Marginal labor Cost=MLC=TCL/dL=2L/2=L

Set MRPL=MLC for profit maximization

L=80

W=L/2=80/2=$40

So, the firm should employ 80 hours of labor at a wage rate of $40.to maximize profit.

b)

Given

L=W

Total expenditure on labor=TCL=L*W=L*L=L²

Marginal labor Cost=MLC=TCL/dL=2L=2L

Set MRPL=MLC for profit maximization

2L=80

L=40

W=L=$40

So, the firm should employ 40 hours of labor at a wage rate of $40 to maximize profit.