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Connected Substitutes and Invertibility of Demand

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Abstract

We consider the invertibility (injectivity) of a nonparametric nonseparable demand system. Invertibility of demand is important in several contexts, including identification of demand, estimation of demand, testing of revealed preference, and economic theory exploiting existence of an inverse demand function or (in an exchange economy) uniqueness of Walrasian equilibrium prices. We introduce the notion of "connected substitutes" and show that this structure is sufficient for invertibility. The connected substitutes conditions require weak substitution between all goods and sufficient strict substitution to necessitate treating them in a single demand system. The connected substitutes conditions have transparent economic interpretation, are easily checked, and are satisfied in many standard models. They need only hold under some transformation of demand and can accommodate many models in which goods are complements. They allow one to show invertibility without strict gross substitutes, functional form restrictions, smoothness assumptions, or strong domain restrictions. When the restriction to weak substitutes is maintained, our sufficient conditions are also "nearly necessary" for even local invertibility.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1806R.

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Length: 33 pages
Date of creation: Jun 2011
Date of revision: Jul 2012
Publication status: Published in Econometrica (September 2013), 81(5): 2087-2111
Handle: RePEc:cwl:cwldpp:1806r

Note: CFP 1391
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Keywords: Univalence; Injectivity; Weak substitutes; Complements;

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References

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  1. Cheng, Leonard, 1985. "Inverting systems of demand functions," Journal of Economic Theory, Elsevier, vol. 37(1), pages 202-210, October.
  2. Kelvin J. Lancaster, 1966. "A New Approach to Consumer Theory," Journal of Political Economy, University of Chicago Press, vol. 74, pages 132.
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  12. Aviv Nevo, 2000. "Mergers with Differentiated Products: The Case of the Ready-to-Eat Cereal Industry," RAND Journal of Economics, The RAND Corporation, vol. 31(3), pages 395-421, Autumn.
  13. Deneckere, Raymond J & Rothschild, Michael, 1992. "Monopolistic Competition and Preference Diversity," Review of Economic Studies, Wiley Blackwell, vol. 59(2), pages 361-73, April.
  14. Dick, Astrid A., 2008. "Demand estimation and consumer welfare in the banking industry," Journal of Banking & Finance, Elsevier, vol. 32(8), pages 1661-1676, August.
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Cited by:
  1. Reynaert, Mathias & Verboven, Frank, 2012. "Improving the Performance of Random Coefficients Demand Models: the Role of Optimal Instruments," CEPR Discussion Papers 9026, C.E.P.R. Discussion Papers.

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