Question

A monopsonist faces the following demand curve for their product: P = 20 - 0.005 XQ and the following labor supply curve: W = 10+ 0.05 x L If the firm does not mark-up the price over marginal cost, what is the profit-maximizing wage when average labor productivity is 5?

Answer 1

Answer

Profit(Pr) = TR - TC

where TR = Total Cost = W*L = (10 + 0.05L)L

TR = Total Revenue = P*Q = (20 - 0.005Q)Q

Average Labor productivity = Total Output/Amount of Labor = Q/L

And it is given that Average Labor productivity = 5 => Q/L = 5 => Q = 5L

Thus, Profit(Pr) = TR - TC = (20 - 0.005Q)Q - (10 + 0.05L)L = (20 - 0.005*5L)*5L - (10 + 0.05L)L

=> Profit(Pr) = (20 - 0.005*5L)*5L - (10 + 0.05L)L

Maximize :Pr = (20 - 0.005*5L)*5L - (10 + 0.05L)L

First order condition :

d(Pr)/dL = 0 => 5(20 - 0.05L) - (10 + 0.1L) = 0

=> 100 - 0.25L - 10 - 0.1L = 0

=> 90 = 0.35L

=> L = 90/0.35 = 90/0.35

Hence From labor supply curve we have :

W = 10 + 0.05(90/0.35) = 22.86

Hence, Profit maximizing wage rate = 22.86.