Question

A monopolist faces the demand curve q = 90 - p/2, where q is the number of units sold and p is the price in dollars. She has quasi-fixed costs, C, and constant marginal costs of $20 per unit of output. Therefore, her total costs are C + 20q if q > 0 and 0 if q = 0. What is the largest value of C for which she would be willing to produce positive output?

a. $20

b. $2,560

c. $3,200

d. $4,800

e. $3,840

Answer 1

Option (c).

q = 90 - (p/2)

p/2 = 90 - q

p = 180 - 2q

TC = C + 20q

Marginal cost (MC) = dTC/dq = 20

Profit is maximized when Marginal revenue (MR) equals Marginal cost (MC).

Total revenue (TR) = p x q = 180q - 2q²

MR = dTR/dq = 180 - 4q

Equating with MC,

180 - 4q = 20

4q = 160

q = 40

p = 180 - (2 x 40) = 180 - 80 = $100

Monopolist will produce output as long as ATC < Price, where

ATC = TC/q = (C/q) + 20

When q = 40,

ATC = (C/40) + 20

When ATC < Price,

(C/40) + 20 < 100

C/40 < 80

C < $3,200.

Maximum allowable value of fixed cost = $3,200