Non-Separable, Quasiconcave Utilities are Easy -- in a Perfect Price Discrimination Market Model

TL;DR

This paper demonstrates that non-separable, quasiconcave utility functions can be efficiently managed in a market model with perfect price discrimination, supporting unique equilibrium prices and welfare theorems.

Contribution

It introduces a market model that handles complex utility functions efficiently, unlike previous models limited to simpler utility forms.

Findings

Supports unique equilibrium prices in the new model

Satisfies welfare theorems for concave utilities

Handles non-separable, quasiconcave utilities efficiently

Abstract

Recent results, establishing evidence of intractability for such restrictive utility functions as additively separable, piecewise-linear and concave, under both Fisher and Arrow-Debreu market models, have prompted the question of whether we have failed to capture some essential elements of real markets, which seem to do a good job of finding prices that maintain parity between supply and demand. The main point of this paper is to show that even non-separable, quasiconcave utility functions can be handled efficiently in a suitably chosen, though natural, realistic and useful, market model; our model allows for perfect price discrimination. Our model supports unique equilibrium prices and, for the restriction to concave utilities, satisfies both welfare theorems.