Multivariable Utility Functions

Abstract. Utility functions of several variables are ubiquitous in economics. Their maximization requires inversion of the gradient map. Using convex analysis tools, we provide a representation of an extension of this inverse that accounts for possible constraints. To solve economic equilibrium problems, the utility functions of the agents are frequently aggregated into a representative (agent's) utility function. We establish regularity and inversion properties of such representative utility functions. Key words: multivariable utility functions, representative agent utility function, convex analysis. AMS subject classification: 91B16 This work was supported by the Natural Sciences and Engineering Research Council of Canada under Grant 88051, and by the Program for Cultural and Scientific Cooperation between Universit`a di Roma "La Sapienza" and the University of British Columbia. Dipartimento di Matematica per le Dec. Econ. Finanz. e Assic., Facolt`a di Economia, Univ...

• Type: Journal
• Year: 2008
• Where: SIAMJO
• Authors: Maria B. Chiarolla, Ulrich G. Haussmann
• Keywords: Convex Analysis, Representative Utility Functions, SIAMJO 2008, Utility Function