An industry has three firms each of which produces output at

An industry has three firms each of which produces output at a constant unit cost of $10 per unit. The demand function for the industry is q = 1,000-p.

what is the equilibrium price and output assuming firms compete in a Cournot game?

Solution

PQ = 1000p - p²

MR = 1000 - 2p

MC = 10

In equilibrium, MR = MC

Thus, 1000 - 2p = 10

990 = 2p

p = 495

Thus, q = 1000 - 495

q = 505