07 Jun Question 1. Two-Part Tariff
Question
1. Two-Part Tariff
Consider a monopoly firm and two consumers 1 and 2. The consumers’ demand functions are P1 = 12 – q1 and P2 = 10 – q2 and the monopoly’s cost function is C(q)=2q. Assume that the monopoly uses a two-part tariff pricing scheme.
A. What is the monopoly’s profit-maximizing quantity if it only faces consumer 1? What is the resulting profit?
B. Assume that the monopoly faces both consumers. What is its profit-maximizing two-part tariff scheme if it needs to ensure participation (i.e. both consumers will buy something)? What is the resulting profit?
C. Assume now that the monopoly faces 5 consumers with the same demand function as consumer 1, and one consumer with the same demand function as consumer 2. Would the monopoly rather exclude the second type of consumer (i.e. set a pricing scheme such that the second type would not buy anything)?
2. Joint Cost Production Suppose a monopoly firm produce two final products with same raw materials, the same as the example showed in Lecture 2. Let’s assume product 1 becomes more popular due to a change of consumers’ taste. Then the demand for product 1 is lager than before, say P1 = 300 – q1. The demand of product 2 does not change, P2 = 100 – q2. Firm has the same cost function: C0 = 30q0, C1 = 10q1, C2 = 4q2.
A. Solve for firms optimal production plan.
B. Find the production plan that maximize the social welfare.
C. Compare the firm’s solution you find in Part A with the solution we have in the slides, try to interpret the difference of these two results, with economic intuition.
3. Vertical Market Separation with Competitive Manufacturer Consider a vertically separated market with the distributor as a monopoly in the retail market, but with the manufacturer as a competitive firm. The demand function of the retail market is P = 20 – q, and the manufacturer’s cost function is C(q)=4q.
A. What is the demand function faced by the manufacturer?
B. What is the wholesale price?
C. How many units would the distributor purchase from the manufacturer?
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