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# Two-parts tariff

A monopolist produces output with constant marginal and average cost of 10 \$. There are two types of consumers (in equal numbers) that are potentially in the market for the good. Consumers of type A have a demand function of QA = 60 - PA , and consumers of type B have a demand function of QB = 60 -2PB.

a. Suppose that the monopolist can identify the type of the consumer, and resales are not possible. Also assume that he can charge a different lump sum entry fee plus a per unit price (i.e., a two-part tariff) for each type of consumer. That is, he charges consumer A an entry fee of LA and a per unit price of P , and consumer B an entry fee of LB and a unit price of P'B . What entry fee and per unit price will each consumer face? What are the profits in this case? [Hint: Here to charge a membership or entry fee, firms must be able to know or calculate the consumers' surplus.]

b. If the firm could adopt a linear two-part tariff under which marginal prices must be equal in the two markets but lump-sum entry fees might vary; that is he charges both consumers the same marginal price; that is the same per unit price P' for both types, but an entry fee of LA for consumers of type A and an entry fee of LB for consumers of type B. What pricing policy should the firm follow? What are the profits in this case?

c. Now assume that the firm should charge each customer the same two-part tariff; that is a per unit price of P and a lump-sum entry fee of L for every type of customer (cannot vary the marginal price and the lump-sum fee among the customers). Find the best two-part tariff assuming that the monopolist serves both types of customers. What are the profits? [Hint: Here to charge a fixed membership fee, firms must adopt the consumers' surplus of only the low demanders.]

#### Solution Summary

The expert examines two-part tariffs for monopolists outputs.

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