Question

The owner of the Martin Marina believes that the relationship between the number of boats serviced and labor inputs is Q = -3 + 8.5L - 2L ^2 . . Her firm receives $40 for each boat serviced and the cost per unit of labor is $20.

a) How many units of labor should she employ in order to maximize profit?

b) What is the firm’s profit?

Answer 1

We have the following information Q = -3 + 8.5L - 2L^2, price P = $40 for each Q and wages w = $20.

a) The optimum rule for hiring labor is MRP = wage rate

MRP is marginal revenue product = marginal product of labor x price of product

MRP = (8.5 - 4L)*40 and wage rate = 20

This implies the optimum L* is

340 - 160L = 20

L* = 2

Optimum labor units is 2.

b) Profit is the difference between Revenue and cost. Output is Q = -3 + 8.5*2 - 2*(2^2) = 6.

Hence Profit = 6*40 - 2*20 = $200.