# First-order risk aversion and non-differentiability (*)

## Author

Listed:
• Uzi Segal

(Department of Economics, University of Western Ontario, London, CANADA N6A 5C2)

• Avia Spivak

(Department of Economics, Ben Gurion University, Beer Sheva 84105, ISRAEL)

## Abstract

First-order risk aversion happens when the risk premium a decision maker is willing to pay to avoid the lottery $t\cdot {\tilde \epsilon }, E[{\tilde \epsilon }]=0,$ is proportional, for small t, to t. Equivalently, $\partial \pi /\partial t\mid_{t=0^{+}}> 0.$ We show that first-order risk aversion is equivalent to a certain non-differentiability of some of the local utility functions (Machina [7]).

## Suggested Citation

• Uzi Segal & Avia Spivak, 1996. "First-order risk aversion and non-differentiability (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 179-183.
• Handle: RePEc:spr:joecth:v:9:y:1996:i:1:p:179-183 Note: Received: June 26, 1995; revised version November 20, 1995
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## References listed on IDEAS

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1. Neary, J Peter, 2002. "Foreign Competition and Wage Inequality," Review of International Economics, Wiley Blackwell, vol. 10(4), pages 680-693, November.
2. Fridolfsson, Sven-Olof & Stennek, Johan, 2005. "Hold-up of anti-competitive mergers," International Journal of Industrial Organization, Elsevier, vol. 23(9-10), pages 753-775, December.
3. Persson, Lars, 2004. "Predation and mergers: Is merger law counterproductive?," European Economic Review, Elsevier, vol. 48(2), pages 239-258, April.
4. Blonigen, Bruce A, 1997. "Firm-Specific Assets and the Link between Exchange Rates and Foreign Direct Investment," American Economic Review, American Economic Association, vol. 87(3), pages 447-465, June.
5. Kamal Saggi & Halis Murat Yildiz, 2006. "On the International Linkages between Trade and Merger Policies," Review of International Economics, Wiley Blackwell, vol. 14(2), pages 212-225, May.
6. Kjell Erik Lommerud & Odd Rune Straume & Lars Sørgard, 2006. "National versus international mergers in unionized oligopoly," RAND Journal of Economics, RAND Corporation, vol. 37(1), pages 212-233, March.
7. Nocke, Volker & Yeaple, Stephen, 2007. "Cross-border mergers and acquisitions vs. greenfield foreign direct investment: The role of firm heterogeneity," Journal of International Economics, Elsevier, vol. 72(2), pages 336-365, July.
8. Keith Head & John Ries, 1997. "International Mergers and Welfare under Decentralized Competition Policy," Canadian Journal of Economics, Canadian Economics Association, vol. 30(4), pages 1104-1123, November.
9. Straume, Odd Rune, 2003. "International mergers and trade liberalisation: implications for unionised labour," International Journal of Industrial Organization, Elsevier, vol. 21(5), pages 717-735, May.
10. Mattoo, Aaditya & Olarreaga, Marcelo & Saggi, Kamal, 2004. "Mode of foreign entry, technology transfer, and FDI policy," Journal of Development Economics, Elsevier, vol. 75(1), pages 95-111, October.
11. Morton I. Kamien & Israel Zang, 1990. "The Limits of Monopolization Through Acquisition," The Quarterly Journal of Economics, Oxford University Press, vol. 105(2), pages 465-499.
Full references (including those not matched with items on IDEAS)

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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Cited by:

1. Zvi Safra & Uzi Segal, 2008. "Calibration Results for Non-Expected Utility Theories," Econometrica, Econometric Society, vol. 76(5), pages 1143-1166, September.
2. repec:kap:iaecre:v:17:y:2011:i:2:p:169-180 is not listed on IDEAS
3. 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.
4. Matthias Lang, 2015. "First-Order and Second-Order Ambiguity Aversion," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_13, Max Planck Institute for Research on Collective Goods.
5. Dionne, Georges & Li, Jingyuan, 2014. "When can expected utility handle first-order risk aversion?," Journal of Economic Theory, Elsevier, vol. 154(C), pages 403-422.

### JEL classification:

• D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
• D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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