Twenty-five different stores sell the same product in a given area to a population of 2,000 consumers. Consumers are equally likely to first visit any of the 25 stores. half of the consumers have no search costs and purchase at the lowest price so long as it is lower than $45. The other half is willing to buy one unit of the product up to a maximum of $70 and must incur a cost of $44 in order to find out about the prices charged by other stores. Each store can sell up to 90 units and has a unit cost of $25.

a. Show that. in equilibrium, there exists at most two different prices

b. Show that, if there exist two different equilibrium prices, then the higher price must be 70.

c. Show tat the following is an equilibrium: five firms set a price of 70 and the remaining 20 firms set a price of 45.