Consider two firms facing the market demand curve P = 100 - Q, where P is in $/unit, Q is total output, Q = Q1 + Q2, Q1 is the output of firm-1 and Q2 is the output of firm-2. Both firms have identical cost functions. Marginal cost of production is $10.
a. Suppose (as in the Cournot model) that each firm chooses its profit-maximizing level of output on the assumption that its competitor's output is fixed.
I. Find each firm's "reaction function".
III. What will industry output and price be at equilibrium in this model?
b. If firm-1 operates like a Stackelberg leader, what output would it produce in this case?
c. If firm-2 is the Stackelberg follower, how much output will it produce?
d. What will industry output and price be at equilibrium in the case of Stackelberg model?