Q. 1. You are a monopolist. Suppose there are two types of people who buy your product, groups 1 and 2. Their separate demand functions are given by:
D1(p)= A-bp
D2(p)= C-dp
for A,C,b,d>0. Total demand for your product is given by D(p) = D1(p) +D2(p).
a) What is total profit if you set a single price?
b) What is total profit if you use third-degree price discrimination?
c) Under what condition is the optimal p1 under third-degree price discrimination greater than p2? (in terms of the parameters of the model)
2. Suppose that there is a unit mass of consumers who are uniformly distributed on the segment[0,1]. Two firms are located on the line and sell identical products. Consumers obtain K utility from consuming a product; assume that K is large enough that all consumers purchase from at least one of the firms despite the costs of transportation, which are linear in distance with a constant marginal cost of t. For each of the following cases, what is 1) the symmetric demand function, and 2) the symmetric equilibrium price? (in terms of the parameters of the model)
a) maximum differentiation: firms locate at 0 and 1
b) Moderate case: firms locate at 1/4 and 3/4
c) No differentiation: firms both locate at 1/2