Question

In a coal-mining company town, one employer is the sole buyer of labor services. The labor supply curve is given by W = 7 + 0.01L. The marginal revenue product of labor is MRPL = 19 – 0.02L.

1) What is the firm’s marginal expenditure curve for labor?

2) What quantity of labor does it want to hire, and what wage will it pay?

3) What would the quantity of labor and wage be if the firm’s marginal revenue product curve belonged to a perfectly competitive set of coal-mining companies?

Answer 1

1> The total cost of labor is WL= 7L+0.01L^2

Thus, marginal expenditure of labor is d(Labor Cost)/dL=7+0.02L

2> It will hire the number of labor where MEL meets MRPL. So, it will be

19 – 0.02L. = 7+0.02L

12=0.04L

L=300 (Ans)

The wage will correspond to the labor supply curve, so it will be 7+0.01*300 = $10 (Ans)

3> In that case, the outcome would be where labor supply meets MPRL

So, 19 – 0.02L=7 + 0.01L

L=12/0.03 = 400 (Ans)

The wage will be 7+0.01*400=$11 (Ans)