1. Assume that in a certain region there is a single firm producing chocolates, Nestlex. In this region there is a population of N customers whose preferences for chocolate are uniformly distributed over the range (0,1), where this index relates to the chocolate's sweetness. Suppose that chocolate is produced with a constant marginal cost, so small that we take it equal to zero. Each customer is willing to pay up to 4 for a single unit of her preferred chocolate (more units are valueless), but the willingness to pay is reduced by (v - x) 2 when the
consumer in location v buys a chocolate from location x.
a) Suppose that the existing firm can produce a single variety of chocolate only. What variety should it produce, and what price does it charge?
b) A second firm is considering entering this market. What variety should it offer? What prices will the firms charge?