1. Suppose the demand for pizza in a small isolated town is p = 10 -Q. There areonly two firms, A and B, and each has a cost function TC = 2 + q. Determine the Cournot equilibrium.
2. Two firms compete in a market by selling imperfect substitutes. The demand equations are given by the following equations:
Q1 = 50 - p1 + p2
Q2 = 50 - p2 + p1
For now, assume that each firm has a marginal cost and average cost of 0.
a. From the equations, how can you tell these goods are substitutes. How can you tell they are imperfect substitutes?
b.Suppose the firms compete by simultaneously choosing price. Fine the best response function of each firm as a function of the other firm's price.
c.Compute the equilibrium price and quantity for each firm.
d.Suppose firm 1 (and only firm 1) had a marginal and average cost of $10. How would the equilibrium change? How does this compare to the Bertrand result when the firms sell perfect substitutes?
3. Suppose two firms, A and B, are simultaneously considering entry into a new market. If neither enters, both earn zero. If both enter, they both lose 100. If one firm enters, it gains 50 while the other earns zero.
a.Set up the payoff matrix for this game and determine if any Nash equilibria exist. Can you predict the outcome?
b.What if firm A gets to decide first?