ECON 600 - Microeconomic Theory

PART 4 Please show vour work and fully annotate all graphs. Simplify vour answers onlv to the extent that it will help you answer the problems. Explain ALL vour answers, unless specified otherwise. Feel free to use a calculator. 1. In Country XYZ, a railroad company operates as a monopoly. [t sells its output (12, domestic train trips) to two kinds of customers: type-1 customers (less than 60 vears old) and type-2 customers (over 60 years old). Type-1 customers have an annual demand of: Q, = 200 2P where (J 18 the number of trips and P is the price of a train ticket in dollars. Twpe-2 customers have an annual demand of Q, = 80 2P There are equal numbers of each type of customers. Assume there are no fixed costs and the marginal cost of a trip 1s equal to $10; in other words, the cost function of the railroad company is the following: C(Q) = 10Q. {(a) If the monopolist can separate the two types of customers and price discriminate, what 15 the monopolists optimal pricing policy? What is the total profit made by the firm? (b) If it 1s not possible to discriminate, what price would the monopolist charge to maximize profits? What 1s the firm's total profit in this scenano? (c) Now suppose the monopolist cannot separate customers by type and price discriminate. Instead of charging a uniform price, the firm can impose a two-part tariff on its customers. More precisely, the firm can charge a fixed fee of $T dollars per customer (in form of an annual membership) and a price of $P per trip. What 1s the monopolist's optimal pricing policy? What 1s the firm's total profit in this scenario? (d) Which situation 1s the most profitable for the railroad company? Which situation 1s the least profitable