There are 100 consumers that are uniformly distributed on one kilometer long linear beach.Each consumer's willingness to pay for ice cream is$5. Each consumer would buy only one ice cream per week. It cost a consumer $1 per kilometer to travel. Assume ice cream stores are considering opening shops on opposite ends of the street. After opening, each store would have a marginal cost of $3 per

ice cream, an there is no fixed cost for opening a store.

(a) What are the equilibrium prices each store will charge for ice cream? What would their profits be?

(b) Suppose the firms decide to merge (i.e., they become a monopolist). What would the firms incentive to merge be (assume that the firms would serve the entire market after the merger?