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Cournot and Bertrand Equilibrium

Assume that Smith Inc. and Wang, Inc. compete in an oligopolistic setting.

They produce a homogeneous product and face the following industry demand curve:

P = 20 - .01Q
Where Q = Q1 + Q2

a. Each firm faces a marginal cost of $10. Find the equilibrium quantity produced by each firm in the Cournot equilibrium. What is the equilibrium price and profits for each firm?

b. What are the equilibrium price, combined output, and profits with Bertrand competition?

Solution Preview


In Cournot competition firms compete in quantities and tend to maximize their profit.

q1 = output of Smith Inc.
q2 = Output of Wang Inc.

P = equilibrium price

C(1) = cost function for firm Smith Inc.

C(2) = cost function for firm Wang Inc.

P=20-0.01(q1+q2) = 20-0.01q1-0.01q2

Profit for Smith Inc. is given by
Profit-1 = q1*P-C(1)
Profit-1 = q1*(20-0.01q1-0.01q2)-C(1)
=20q1-0.01q1^2-0.01q1*q2 - C(1)

Profit for Wang Inc. is given by
Profit-2 = q2*P-C(2)

Solution Summary

The solution describes the steps in determining cournot and bertrand equilibrium price and quantity for two firms in an oligopolistic setting.