Reference no: EM133081805

Consider a horizontally differentiated product market in which two firms are located at any points l1 and l2 on the real line, respectively, with the notation l1 ≤ l2. Firms produce at marginal costs c. There is a continuum of consumers of mass 1 who are uniformly distributed on the unit interval. They have unit demand and have an outside utility of -∞. A consumer located at x ∈ [0; 1] obtains indirect utility v = max (v1; v2) with v1 = r - τ(x - l1) 2 - p1 if she buys one unit from firm 1 and v2 = r - τ(l2 - x) 2 - p2 if she buys from firm 2. Firms have marginal costs equal to c.

a. Suppose that prices are regulated at pi = 2c. In the game in which firms simultaneously decide where to locate their product, characterize the Nash equilibrium.

b. Determine the demand function for each firm for each admissible price pair (p1; p2) given locations l1 and l2.

c. Suppose that the two firms simultaneously set prices. Determine the market equilibrium for all possible combinations of (l1; l2).

d. Suppose that the social planner chooses first-best optimal prices. Which price pairs would be socially optimal for the pair of locations l1 = 0 and l2 = 1/2?

e. Compare your results obtained in (c) and (d) for locations l1 = 0 and l2 = 1/2. Is the equilibrium socially efficient? Depending on your answer elaborate on the sources of the inefficiency or give the reason for efficiency.