Firms 1 and 2 produce identical products and compete by simultaneously setting price in a single period. Firms have constant marginal costs of c=0. 2 and no fixed costs. Firms must set prices no higher than 2.( You may think of $2 as the maximum willingness to pay for the product.)

There is a unit mass of consumers (i.e. the size of the market is 1). Consumers know the distribution of prices, but do not know the specific price set by each firm. Consumers use the following search procedure.

First, each consumer randomly turns up at one of the stores(each store is equally likely). At this point, they learn the price of this store, and because they know the price distribution, they

also learn the price of the other store. Second, each consumer decides whether to purchase at the current store, or to incur a search cost of s to locate and travel to the other store to purchase

(a) Suppose that half of the consumers are shoppers and have no search costs, s=0. The remaining consumers are non-Shoppers with search costs of s= 1

i. Solve for the reaction functions of each firm

ii. Solve for the pure strategy Nash equilibrium, if it exists. Explain

b)Suppose instead that each consumer has a different search cost. In particular, consumer search costs are uniformly distributed between 0 and 1

i. Solve for the reaction functions of each firm

ii. Solve for the pure strategy nash equilibrium, if it exists. explain

(c) Explain the difference between your answers in parts 2a and 2b