Assume 2 firms on a street of length 1, with zero costs of production. Consumers are uniformly distributed on this street, desire only one unit of the good, and value the good at V = 100. To get to the firms and purchase the good, consumers need to pay a transportation cost TC = x2.
a) Assume the firms are both located in the middle of the street. What are the optimal prices that the firms should set. What are their profits?
b) Assume that one firm decides to move at one end of the street, while the other firm remains in the middle. What are the optimal prices and profits now?
c) Was it a good decision for the firm that moved to do so? Should the other firm also move to the other end?