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Monopoly with Incomplete Information

Monopoly with Incomplete Information. Eric Maskin and John Riley The RAND Journal of Economics, Vol. 15, No. 2 (Summer, 1984), pp. 171-196. Presented by: Ming Lung. Arun Sundararajan , “Nonlinear Pricing of Information Goods,” Management Science, Vol. 50, No. 12 (Dec., 2004), pp. 1660-1673.

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Monopoly with Incomplete Information

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  1. Monopoly with Incomplete Information Eric Maskin and John Riley The RAND Journal of Economics, Vol. 15, No. 2 (Summer, 1984), pp. 171-196 Presented by: Ming Lung ArunSundararajan, “Nonlinear Pricing of Information Goods,” Management Science, Vol. 50, No. 12 (Dec., 2004), pp. 1660-1673

  2. Outline • Introduction • Simple application: nonlinear pricing • Price discrimination • Quantity discount • Monopoly pricing of product quality and optimal bundling

  3. Introduction • Much work has considered incentive schemes (or “principal-agent” relationship) • In political science and economics, the problem of motivating a party to act on behalf of another is known as ‘the principal–agent problem’. – Wikipedia • In this article, parties involved are constrained by asymmetric information

  4. Introduction • We show that a variety of issues can be viewed as members of a single family of principal-agent problems • Price discrimination via quantity discounts • Monopoly pricing of products of differing quality • For each of these problems, the central issue is how to construct a sorting mechanism (?) to extract the greatest possible private gain

  5. Introduction • Our main contribution is to show that, under a separability assumption, we can draw strong conclusions about the nature of optimal incentive schemes • Also shed new light on closely related topics • Optimal income taxation • Monopoly pricing of insurance • Etc.

  6. Simple application: nonlinear pricing • A buyer of type I has preferences represented by • q is the number of units purchased • T is total spending on the units • p(q; v) is the demand price • Assume that higher levels of v are associated with a higher demand

  7. Simple application: nonlinear pricing • Selling procedure • The profit or “return” to the seller • Rewrite the utility function of a buyer of type I • N(q; vi) is the social surplus generated by the sale • Selling procedure is then

  8. Nonlinear pricing: price discrimination • Consider the figure in the next page • First consider only two different buyers • How would the seller change the selling procedure to increase his return • => =>

  9. Nonlinear pricing: price discrimination • Consider more types of the buyers • The selling procedure may look like the following figure

  10. Nonlinear pricing: price discrimination • With ＜q(vi), R(vi)＞ optimal for a buyer with parameter vi, we can write maximized utility as • Combining • Get (?)

  11. Nonlinear pricing: price discrimination • Combining • Obtain • Thus the expected seller revenue from a buyer of type vi would be

  12. Nonlinear pricing: price discrimination • Taking the limiting case of a continuous distribution of types • The expectation of R(v) is • The seller tries to choose q*(v) to maximize expected return

  13. Nonlinear pricing: quantity discount • Quantity discount • “one for a dollar, three for two dollars” • Quantity premium • “one for a dollar, two for three dollars” • Difficult to enforce • Is quantity premium desirable? • Analyze the payment per unit purchased

  14. Nonlinear pricing: quantity discount • The payment per unit purchased • Decreasing in v, and hence in q, iff • And for all x < • Quantity discounts are always optimal for buyers at the upper tail of the distribution

  15. Monopoly pricing of product quality and optimal bundling • Consider the Marshallian utility function • y is spending on other goods • q is the quality level of the single unit purchased • v represents the strength of preference for quality • z is a dichotomous variable equal to unity with purchase and zero otherwise • B is a set of affordable packages (?)

  16. Monopoly pricing of product quality and optimal bundling • If a consumer with income level I pays T for a unit of quality level q, rewrite the indirect utility as • With little loss of generality, we can define units of quality in such a way that the marginal cost of a unit of quality level q is cq • Then the monopolist's problem is identical to the problem considered before

  17. Monopoly pricing of product quality and optimal bundling • The natural generalization of this problem is to incorporate the choice of both quality q and the number of units purchased, z • Then we have

  18. Monopoly pricing of product quality and optimal bundling • Optimal bundling • If z*(v), q*(v) solve • Ρ(v) ≡ F’(v) / (1-F(v)), the hazard rate of F • The expected profit-maximizing selling strategy is • where

  19. Monopoly pricing of product quality and optimal bundling • The optimal selling strategy can be reinterpreted as • Define inverse function x = φ(q) • z**(q) ≡ z*(φ(q)) • T**(q) = T*(φ(q)) • The monopolist announces that quality level q will be sold in bundles of z**(q) units for a total cost of T**(q)

  20. Conclusion & Comments • The seller strategies • Price discrimination • Quantity discount • Quality and bundling • Theoretical work • Hard to find a meaningful story immediately while reading

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