Question

4. Consider a monopolist that only hires one input, labor, to produce output. The monopolist's demand curve is p 100 q, its production function is q-L5, and the price of labor is w. (The labor market is competitive however.) Derive the firm's labor demand function, which is a function of w. If w 24, how many units of labor will it employ? 0.5

Answer 1

Answer 4

Profit = Total revenue - Total Cost = pq - wL

Total Revenue = Price *quantity = pq = (100 - q)q = (100q - q²)

q = L^0.5 => q² = L

Hence Total Revenue = (100L^0.5 - L)

Total Cost = wL

Now we have to find L that maximizes the profit.

First Order Condition:

Profit = (100L^0.5 - L) - wL

d(Profit)/dL = 0

=> 100/(2L^0.5) - 1 = w

=> L = (50/(1 + w))² -------------------- Labor Demand function

Now If w = 24

Then L = (50/(1 + w))² = (50/(1 + 25))² = 4

Hence If w = 24, Firm will hire 4 units of Labor.