By David Kreps
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Extra info for Notes On The Theory Of Choice
It might seem natural to say that the welfare of a consumer is given by his indirect utility, as 1. This is the case even if, strictly speaking, only the company’s shareholders have a welfare, and so on. 38 Collective Choice Ïmax U (x) Ô V (p , R) = Ìx Œ X Ôp ◊ x £ R Ó However, such a gauge of welfare depends on the choice of the utility function U and so is not satisfactory. For our purposes a more stable measure must be found that can be expressed, for example, in terms of equivalent income. To this end, in the 1940s, Hicks introduced two measures:2 The equivalent variation of income E, which is the sum that must be given to the consumer in the initial state in order for him or her to have the same utility in the final state; that is, • V (p ¢ , R) = V (p , R + E) The compensating variation of income C, which is the sum that must be deducted from the consumer in the final state in order for him or her to have the same utility as in the initial state; that is, • V (p ¢ , R - C) = V (p , R) First we note that these two measures are quite independent of the choice of the utility function U.
7. One trial (a Formula One Grand Prix) results in a ranking just like a voting poll. So formally a sports event could correspond to an election, and the competitors to candidates. The Aggregation of Preferences 17 a and of b. Technically Borda’s method violates an axiom which we will later call independence of irrelevant alternatives. ) possess their own inconveniences. This is a consequence of Arrow’s famous theorem, which is at the heart of the next section. 1 Arrow’s Theorem Consider the following very general problem.
Willig, R. 1976. Consumer’s surplus without apology. American Economic Review 66: 589–97. 4 Implementation The results obtained in chapter 2, though negative, still allow for the possibility that at least in certain cases, one can effectively aggregate preferences in a satisfactory manner. As Arrow (1951) wrote,1 it nonetheless remains to collect the necessary information: Even when it is possible to aggregate individual preferences into a coherent model of collective ones, one still must define the rules such that individuals actually express their preferences, even when they are reacting rationally.
Notes On The Theory Of Choice by David Kreps