2.- Assume that consumers are uniformly distributed along a one-mile stretch of a beach. N ice...

2.- Assume that consumers are uniformly distributed along a one-mile stretch of a beach. N ice cream vendors are pondering where to position their carts. The price that they are allowed to charge is fixed by the EACAC (Equal Access to Coolness for All Coalition). (Also, each consumer will buy exactly one ice cream.) Consumers incur some transportation cost of t dollars per mile when they move along the beach. (a) Show that there is no equilibrium (in locations) if N=3. That each, for each triple of positions, show that at least one firm will prefer moving to a different location. (b) Suppose N=5 and vendors position their cart each at one of the (mile) points � 1 /6 , 2/ 6 , 3 /6 , 4 /6 , 5/ 6 �. Is that an equilibrium?

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