Independence, Trade-Offs, and Transformations in Bivariate Utility Functions

Peter C. Fishburn
Additional contact information
Peter C. Fishburn: Research Analysis Corporation

Management Science, 1965, vol. 11, issue 9, 792-801

Abstract: This paper explores several important notions relevant to modern utility theory. Restricting the discussion to the consideration of bivariate utility functions, the paper defines and examines the interrelationships between (1) independence in the utility sense, (2) trade-off or indifference curves, and (3) transformation curves (as defined herein). Following the form in which a set of basic axioms of utility are stated, independence is defined in terms of indifference between 50-50 gambles, and it is shown that, if the condition of the definition holds, then \varphi (x, y), the bivariate utility function, can be written as a function of x plus a function of y. The concepts of trade-off curve (indifference curve) and transformation curve are also defined on the basis of the indifference relation but are not concerned with gambles. After exploring relationships among the three notions it is shown how the utility curves for the two variables under independence can be constructed on the basis of two trade-off curves.

Date: 1965
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://dx.doi.org/10.1287/mnsc.11.9.792 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:11:y:1965:i:9:p:792-801

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().