Consider the horizontal quality model on the unit interval from 0 to 1. There are N consumers located uniformly along the interval. There are two firms, with zero marginal costs, initially located at 0 and 1. Consumers will buy one unit of the good from the lowest- cost retailer as long as the effective price is below V . They have transportation costs of t getting from their location to the store and back.

please help me solve this problem

A) Solve for the equilibrium price if both firms only sell to a part of the market.

B) Suppose that firm 1 is located at a and firm 2 is located at b (without loss of generality, let 0 ≤ a < b ≤ 1). Show the profit function for each firm as a function of their prices and the location of both firms.

C) What are the two first-order conditions for firm 1 with respect to a and its price? What does the FOC with respect to a imply?