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Expected Consumer's Surplus as an Approximate Welfare Measure

Willig (1976) argues that the change in consumer's surplus is often a good approximation to the willingness to pay for a price change: if the income elasticity of demand is small, or the price change is small, then the percentage error from using consumer's surplus is small. If the price of a good is random, then the change in expected consumer's surplus (ECS) equals a consumer's willingness to pay for a change in its distribution if and only if its demand is independent of income and the consumer is risk neutral. We ask how well the change in ECS approximates the willingness to pay if these conditions fail. We show that the difference between the change in ECS and willingness to pay is of higher order than the L_1 distance between the price distributions if and only if the indirect utility function is additively separable in the price and income. If additively separability fails, then the percentage error from using ECS is unbounded for small distribution changes, and is always nonzero in the limit except for knife-edge cases. If, however, the distribution change is smooth on the space of random variables, and either the initial price is nonrandom or state-contingent payments are possible, then the change in ECS might approximate the willingness to pay well. Unfortunately, this smoothness condition necessarily fails in some important applications of ECS.

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Paper provided by Department of Economics, W. P. Carey School of Business, Arizona State University in its series Working Papers with number 2144340.

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Handle: RePEc:asu:wpaper:2144340
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  1. Deneckere, Raymond & Marvel, Howard P & Peck, James, 1997. "Demand Uncertainty and Price Maintenance: Markdowns as Destructive Competition," American Economic Review, American Economic Association, vol. 87(4), pages 619-641, September.
  2. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
  3. Rey, Patrick & Tirole, Jean, 1986. "The Logic of Vertical Restraints," American Economic Review, American Economic Association, vol. 76(5), pages 921-939, December.
  4. Raith, Michael, 1996. "A General Model of Information Sharing in Oligopoly," Journal of Economic Theory, Elsevier, vol. 71(1), pages 260-288, October.
  5. William Novshek & Hugo Sonnenschein, 1982. "Fulfilled Expectations Cournot Duopoly with Information Acquisition and Release," Bell Journal of Economics, The RAND Corporation, vol. 13(1), pages 214-218, Spring.
  6. Raymond Deneckere & Howard P. Marvel & James Peck, 1996. "Demand Uncertainty, Inventories, and Resale Price Maintenance," The Quarterly Journal of Economics, Oxford University Press, vol. 111(3), pages 885-913.
  7. Rogerson, William P, 1980. "Aggregate Expected Consumer Surplus as a Welfare Index with an Application to Price Stabilization," Econometrica, Econometric Society, vol. 48(2), pages 423-436, March.
  8. Blundell, Richard & Pashardes, Panos & Weber, Guglielmo, 1993. "What Do We Learn About Consumer Demand Patterns from Micro Data?," American Economic Review, American Economic Association, vol. 83(3), pages 570-597, June.
  9. Xavier Vives, 1987. "Small Income Effects: A Marshallian Theory of Consumer Surplus and Downward Sloping Demand," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 87-103.
  10. Hausman, Jerry A, 1981. "Exact Consumer's Surplus and Deadweight Loss," American Economic Review, American Economic Association, vol. 71(4), pages 662-676, September.
  11. Chade, Hector & Schlee, Edward, 2002. "Another Look at the Radner-Stiglitz Nonconcavity in the Value of Information," Journal of Economic Theory, Elsevier, vol. 107(2), pages 421-452, December.
  12. Graham, Daniel A, 1981. "Cost-Benefit Analysis under Uncertainty," American Economic Review, American Economic Association, vol. 71(4), pages 715-725, September.
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