On the Economic Meaning of Machina's Frâ„chet Differentiability Assumption
AbstractThis note shows that Machina's (1982) assumption that preferences over lotteries are smooth has some economic implications. We show that Frâ„chet differentiability implies that preferences represent second order risk aversion (as well as conditional second order risk aversion). This implies, among other things, that decision makers buy full insurance only at the absence of marginal loading. We also show that with constant absolute and relative risk aversion, expected value maximization, second order risk aversion, and Frâ„chet differentiability are equivalent.
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Bibliographic InfoPaper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 511.
Length: 14 pages
Date of creation: 01 Oct 2001
Date of revision:
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Other versions of this item:
- Safra, Zvi & Segal, Uzi, 2002. "On the Economic Meaning of Machina's Frechet Differentiability Assumption," Journal of Economic Theory, Elsevier, vol. 104(2), pages 450-461, June.
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
This paper has been announced in the following NEP Reports:
- NEP-ALL-2001-10-16 (All new papers)
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