Question

Consider a market served by duopolists. The market’s demand function is given
by D(p) = 3600 − 40p. The marginal cost for firms in this market is constant
at MC = 30, and firms have zero fixed costs. Here, we restrict our attention to
”one-shot” games.
(a) What price and quantity, p
m and Qm, would a monopolist set in
this market? What is its corresponding profit level, Πm?

Answer 1

D(p) = 3600 − 40p, p = 90 - Q/40, MC = AVC = ATC = 30, FC = 0.
(a) The price and quantity, pm and Qm, that a monopolist would set in this market are:
MR = MC,
MR = TR' = (p*Q)' = 90 - Q/20,
90 - Q/20 = 30,
Q/20 = 60,
Qm = 1,200 units,
pm = 90 - 1,200/40 = $60.
Its corresponding profit level is Πm = (p - ATC)*Q = (60 - 30)*1,200 = $36,000.