Consider a quadratic Hotelling model with two firms located on l1, l2 [0, 1]. The representative consumer x's transportation cost is (x li)2 if she chooses to purchase from firm i. The representative consumer gets utility v for her purchase at both firms, so that her net utility if she purchases from firm i (with price pi) is v pi (x li)2. The mass of the consumers are uniformly distributed over the unit interval [0,1]. Suppose the production cost for firm i is ci.

(a) Find the indifference consumer x.

(b) Assume without loss of generality that l1 l2. Derive firm 1 and firm 2's profit functions.

(c) Given the location choice (l1,l2), find the equilibrium price.

(d) Discuss how the markup changes with l2 l1.

(e) Suppose now every firm advertises their goods, so that the utility each consumer x gets from purchasing the good becomes v w, and the cost of advertising is A for both firms. How does the firms' profit change in equilibrium?