Question

Question 1 (Dixit model, capacity expansion as a credible entry deterring commitment) In the Dixit model market demand is given by P=100-2(q1+q2). Production or each unit of the good requires a cost r=20 per unit of capacity and w=20 for labor. Each firm also has a fixed cost F1=100 and F2>0. [Advice before you start the problem: as preliminary work, you may find it helpful to start with deriving the best response function of a firm in a quantity competition when market demand is as above and the firm’s marginal cost is a general constant c. You can then use this for several of the parts below, replacing with the relevant marginal cost and quantity as needed for each time.]

a) If the firms compete according to a symmetric Cournot game when each firm has a marginal cost c=w+r=40, what are the best response functions? What is the equilibrium?

b) If the incumbent were a monopolist in the market, with a constant marginal cost c=40, what would his price, quantity and profit be?

c) If the two firms compete according to an asymmetric Cournot game where the incumbent had a marginal cost c1=w=20 and the entrant had a marginal cost c2=w+r=40, what would the asymmetric Cournot equilibrium be?

d) If both firm have a marginal cost c=w+r=40, but they compete according to the Stackelberg game, (incumbent moves first and then the entrant) what quantity would each firm produce? What would the market price be? What would the profit or each firm be?

e) For what value of the fixed cost F2 is entry blockaded?

f) If F2=98 is entry deterred or accommodated?

Answer 1