Consider the simple Hoteling model we did in class where a unit mass of consumers are uniformly distributed over the [0,1] interval. Each consumer has a valuation V for the good. Firms have a constant marginal cost C. Firms can now not only choose their prices but can also choose their location. This happens in two stages. In the first period, firms choose their locations and in the second period, they choose their prices. The transport cost of the consumer is quadratic and is given by tx2 where x is the distance between the consumer and the firm. Now, we will try and find the Subgame Perfect Equilibrium.

(a) Lets start by looking at period 2. Assume firms have located at locations l1, l2. Find the equilibrium price of each firm. Assume V is large so that every consumer buys a good from atleast one of the two firms.

(b) Using the prices from the second period, write the profit function for the firms in the first period as a function of the choice of location.

(c) Find the equilibrium locations by maximizing the profit functions from part (b) and solving the best response equations. HINT: THIS PART IS LITTLE TRICKY. THE SOLUTIONS TO THE FIRST ORER CONDITION NEED NOT LEAD TO LOCATIONS BETWEEN 0 and 1.

(d) Provide intution for the result. Contrast this result with the case from the situation where the firms could choose location but we3re forced to offer the same price (recall, in equilibrium, both located at 1/2)