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
b. What are the equilibrium price, combined output, and profits with Bertrand competition?
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)
The solution describes the steps in determining cournot and bertrand equilibrium price and quantity for two firms in an oligopolistic setting.