Question

A product is produced by two profit-maximizing firms in a Stackelberg duopoly: firm 1 chooses a quantity q1 ? 0, then firm 2 observes q1 and chooses a quantity q2 ? 0. The market price is determined by the following formula: P ( Q ) = 4 ? Q , where Q = q(1) +q(2) . The cost to firm i of producing q i is Ci( qi ) = q^2)i . (Note: the only difference between this problem and the usual problem is that instead of Ci(qi ) = cq i we have Ci(qi ) = q^2i ).

a.) Calculate the best-response function for firm 2 as a function of firm 1’s quantity q(1) .

b.) What are the equilibrium quantities of the subgame-perfect Nash equilibrium?

c.) How does the total quantity, Q = q(1) + q(2) , produced in this Stackelberg model of duopoly compare with the total quantity produced in the Cournot model of duopoly? Which type of market competition is more beneficial for consumers? (In the Nash equilibrium of the Cournot model, each firm produces 4/5)

Answer 1