The relationship between Mathematical Utility Theory and the Integrability Problem: some arguments in favour
The resort to utility-theoretical issues will permit us to propose a constructive procedure for deriving a homogeneous of degree one, continuous function that gives raise to a primitive demand function under suitably mild conditions. This constitutes the first elementary proof of a necessary and sufficient condition for an integrability problem to have a solution by continuous (subjective utility) functions. Such achievement reinforces the relevance of a technique that was succesfully formalized in Alcantud and Rodríguez-Palmero (2001). The analysis of these two works exposes deep relationships between two apparently separate fields: mathematical utility theory and the revealed preference approach to the integrability problem.
|Date of creation:||28 Aug 2003|
|Note:||Type of Document - Tex; prepared on PC; to print on HP; pages: 25 ; figures: none|
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- Dow, James & da Costa Werlang, Sergio Ribeiro, 1992.
Journal of Mathematical Economics,
Elsevier, vol. 21(4), pages 389-394.
- Dow, James & Werlang, Sérgio Ribeiro da Costa, 1991. "Homothetic preferences," Economics Working Papers (Ensaios Economicos da EPGE) 176, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
- Stephen A. Clark, 1988. "An extension theorem for rational choice functions," Review of Economic Studies, Oxford University Press, vol. 55(3), pages 485-492.
- Shafer, Wayne J, 1977. "Revealed Preference and Aggregation," Econometrica, Econometric Society, vol. 45(5), pages 1173-1182, July.
- Liu, Pak-Wai & Wong, Kam-Chau, 2000. "Revealed homothetic preference and technology," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 287-314, November.
- Gianni Bosi, 2002. "Semicontinuous Representability of Homothetic Interval Orders by Means of Two Homogeneous Functionals," Theory and Decision, Springer, vol. 52(4), pages 303-312, June.
- Bosi, Gianni & Candeal, Juan Carlos & Indurain, Esteban, 2000. "Continuous representability of homothetic preferences by means of homogeneous utility functions," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 291-298, April.
- Fabio Maccheroni, 2001. "Homothetic preferences on star-shaped sets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 24(1), pages 41-47, 05.
- Knoblauch, Vicki, 1993. "Recovering homothetic preferences," Economics Letters, Elsevier, vol. 43(1), pages 41-45.
- Alcantud, J. C. R. & Rodriguez-Palmero, C., 1999. "Characterization of the existence of semicontinuous weak utilities," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 503-509, December.
- Andreu Mas-Colell, 1978. "On Revealed Preference Analysis," Review of Economic Studies, Oxford University Press, vol. 45(1), pages 121-131.
- J.C.R. Alcantud, 1999. "Weak utilities from acyclicity," Theory and Decision, Springer, vol. 47(2), pages 185-196, October.
- Castagnoli, Erio & Maccheroni, Fabio, 2000. "Restricting independence to convex cones," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 215-223, October.
- Candeal, J. C. & Indurain, E., 1995. "Homothetic and weakly homothetic preferences," Journal of Mathematical Economics, Elsevier, vol. 24(2), pages 147-158.
- Sondermann, Dieter, 1982. "Revealed Preference: An Elementary Treatment," Econometrica, Econometric Society, vol. 50(3), pages 777-779, May. Full references (including those not matched with items on IDEAS)
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