Adv. Math. Econ. 14, 17–38 (2011)

Variational analysis and mathematical economics 2: Nonsmooth regular economies

A.D. Ioffe

Department of Mathematics, Technion, Haifa 32000, Israel (e-mail: alexander.ioffe38@gmail.com)

… In order for the analysis to be useful it must provide information concerning the way in which our equilibrium quantities

will change as a result of change of parameters taken as an independent data

P. Samuelson,

“Foundations of Economic Analysis” 1947

Received: April 19, 2010 Revised: July 26, 2010

JEL classification: D11, C62

Mathematical Subject Classification (2010): 14P10, 49J52, 91B02, 91B42

Abstract. We introduce and study a quantitative concept of regularity (in the spirit of variational analysis) for exchange economies with set-valued demand correspondences and prove that in case the latter are semi-algebraic, every economy with the exception of a set of smaller dimension are regular. We also discuss the determinacy problem for such economies.

Key words: excess demand correspondence, equilibrium price, regular economy, coderivative, critical value of a set-valued map, semi-algebraic mapping