Consider a beach of length 1. Consumers are evenly (uniformly) distributed along the

beach and dislike walking in the hot sand. There are two ice cream stands.

(a) What is the location of the stands in equilibrium if prices are fixed exogenously (and

cover the expenses)?

(b) Now suppose that the first stand is fixed at point zero. Prices are still fixed exogenously. What location will the second stand choose?

(c) Consider the full game, where stands first choose a location and then a price. How

would you solve this game (a sketch of the steps needed)?

(d) Now solve the full game (that is, find prices and locations), assuming that the first

stand is fixed at point zero, production costs are zero and walking cost is quadratic,

meaning that when a consumer walks the distance x, the cost is x2. You are allowed

to use the fact that with quadratic costs the strategic effect of a change in location

towards the competitor dominates the demand effect (i.e. profits fall when you move

closer to your competitor). Are the locations you get the same as in part (b)? Why?

What would profits be if locations were the same as in part (b)?

(e) Does the full game have an equilibrium if prices and locations are endogenous

and walking costs are linear?