Question

Two firms compete with quantities as in Cournot. Each firm has a marginal cost of $12. The industry demand is P=48-2Q. How much output will each firm produce individually?

Answer 1

In Cournot competition, both firm maximize profits at a point where MR = MC

Firm 1:

TR = (48 - 2Q1 - 2Q2)*Q1

=> MR = 48 - 4Q1 - 2Q2

MC = 12

Thus, at profit max we have: 48 - 4Q1 - 2Q2 = 12 .............................(1)

By symmetry of revenue and cost we have,

Firm 2 maximized profit according to the condition:

48 - 4Q2 - 2Q1 = 12 .............................(2)

from (1) and (2) we get, Q1 = Q2

Putting this in (1) we get

6Q1 = 48-12 = 36

=> Q1 = 6 = Q2