In the market:
P=150-Q,
where Q=q1+q2.
The firms cost functions are given by the following functional form: C(qi)=ciqi, where i=1,2. Under this functional form, the firms marginal cost equals its average cost. This functional form is chosen for its mathematical convenience, it is not an assumption of the model. The same can be said about the use of the linear demand function.
Consider the case where c1=$30 and c2=$30.
a) Discuss each firm’s best-response function when the firms compete by choosing prices.
b) What is the Bertrand equilibrium in this market?
c) Discuss the conditions under which the equilibrium in part b will not hold.