Consider a standard Hotelling Model. There are two firms, firm A and firm B, located on opposite ends of unit line with consumers located evenly across. For simplicity suppose both firms have marginal costs of zero. Consumers face a travel t=1 and their demand for the product is high enough that consumers always buy from one or the other endpoint firm.

a) Find equilibrium prices and profits for both firms.

b) Suppose antitrust officials find it very difficult to detect and prosecute cartels in this particular market. A new a law is passed that makes collusion legal in this market, but there is now a price ceiling of 3. What would be each firm's profits if they collude perfectly?

c) What is the threshold discount factor for such a collusive equilibrium to exist?

d) Suppose a firm could engage in advertising that leads to greater product differentiation. Suppose this is modeled as an increase in travel costs experienced by consumers. Would the firm want to increase travel costs to t= 3/2 in such a manner if it was in a non-collusive equilibrium? Now considering collusion, how would such a change in travel costs effect the threshold discount factor? Explain clearly why this occurs