Karl Schmedders, University of Zurich
Abstract:
This paper develops a method to compute the equilibrium
correspondence for exchange economies with semi-algebraic
preferences. Given a class of semi-algebraic exchange economies
parameterized by individual endowments and possibly other exogenous
variables such as preference parameters or asset payoffs, there
exists a semi-algebraic correspondence that maps parameters to
positive numbers such that for generic parameters each competitive
equilibrium can be associated with an element of the correspondence
and each endogenous variable (i.e. prices and consumptions) is a
rational function of that value of the correspondence and the
parameters.
This correspondence can be characterized as zeros of a univariate polynomial equation that satisfy additional polynomial inequalities. This polynomial as well as the rational functions that determine equilibrium can be computed using versions of Buchberger's algorithm which is part of most computer algebra systems. The computation is exact whenever the input data (i.e. preference parameters etc.) are rational. Therefore, the result provides theoretical foundations for a systematic analysis of multiplicity in applied general equilibrium.