Adv. Math. Econ. 7, 113-139 (2005)

The bearing of duality on microeconomics

Jean-Paul Penot

Université de Pau, Faculté des Sciences, Mathématiques, CNRS UMR 5142, BP 1155, 64013 PAU, France

Received: February 20, 2004 Revised: June 30, 2004

JEL classification: D11, D21

Mathematical Subject Classification (2000): 91B16, 91B38, 91B02, 91B08

Abstract. We present some observations about links between some classical theories of microeconomics and dualities which have been used in optimization theory and in the study of first-order Hamilton-Jacobi equations. We introduce a variant of the classical indirect utility function called the wary indirect utility function and a variant of the expenditure function. We focus the attention on the links between these functions, observing that they have better relationships with the direct functions than their classical forms and we give economic interpretations of them.

Key words: conjugacy, cost function, duality, expenditure function, indirect utility function, polarity, price, subdifferential, utility function.