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Unformatted text preview: Lecture 11: Consumer Surplus c & 2008 Je/rey A. Miron Outline 1. Introduction 2. Consumer Welfare from a Discrete Good under Quasilinear Preferences 3. Consumer Surplus 4. Compensating and Equivalent Variation 5. Cost-Bene&t Analysis 1 Introduction Our analysis in the &rst eight lectures aimed at understanding what choices a con- sumer would make when faced with a given set of prices and income. That is one question of interest in many contexts. In particular, it provides a positive analysis, meaning one that describes what actions the consumer will take. This is exactly what individuals, or &rms, or policymakers might want to know in some circum- stances. An additional question, however, concerns to what degree di/erent prices or poli- cies make a consumer better or worse o/. We have already examined whether changes in the economic environment raise or lower consumer welfare ¡whether the consumer ends up on a higher or lower indi/erence curve ¡but we have not dis- cussed any way to quantify these changes. In many circumstnaces, it is important to provide a magnitude, not just a direction, for the welfare implications. This lecture discusses several approaches to quantifying consumer welfare. Each is related to the others, and in practice they do not di/er radically. They do di/er conceptually, however, and it is useful to understand each approach and its limitations. 1 2 Consumer Welfare from a Discrete Good with Quasilinear Preferences Consider &rst the case where one good is discrete, meaning it can only be purchased in ¡lumpy¢increments. For example, one can buy one car, or two cars, and so on, but not 30% of a car. Assume also that preferences are quasilinear. In particular, they are linear in some composite good that we can think of as money spent on all other goods. Thus, the utility function is u ( x;y ) = v ( x ) + y where x is the number of units of the discrete good and y is spending on all other goods. The price of the discrete good is p and the price of the composite good is 1 : It is useful to describe the consumer£s demand for the discrete good in terms of reservation prices. A reservatino price is de&ned as the price at which the consumer is just indi/erent between consuming or not consuming the good. Thus, the reservation price this consumer would assign to consuming one unit of the discrete good is r 1 = v (1) & v (0) ; the reservation price this consumer would assign to consuming a second unit of the good is r 2 = v (2) & v (1) ; and so on. The relation between these reservation prices and the quantity of the discrete good demanded is as follows. If n units are demanded, then it must be that r n ¡ p ¡ r n +1 That is, the actual price of the good must be less than or equal to the reservation price for purchasing an nth unit of the good and greater than or equal to the reservation price for purchasing an ( n + 1) st unit of the good....
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- Fall '09
- Consumer Surplus