Consider a beach that is one mile long and populated by 2,000 people (uniformly distributed). A particular location on this beach is identified by the number x , where 0 \leq x \leq 1 . There are two concession facilities that sell ice cream, Store 1 located at the east end at x = 0, and Store 2 located at the west end at x = 1. Consumers are willing to pay as much as $10 for an ice cream at their location on the beach, but incur a disutility to go to get it at either location. Specifically the travel cost is $4 per mile. The two stores are independently owned and compete with each other by choosing the price they charge to the consumers that show up at their facility. The two stores have a constant unit production cost of ice cream of $2.
Suppose that Store 1 finds a new supplier of ice cream and its constant unit cost of ice cream drops from $2 to $1. Compute the best response function of each seller and explain how they are affected by the change in one of the unit costs.