On the minimal simplex economy

TL;DR

This paper introduces the concept of minimal simplex economies, a specific class of affine economies, and demonstrates that a competitive equilibrium can be intrinsically computed within them, extending previous theoretical results.

Contribution

It defines minimal simplex economies and proves that a competitive equilibrium can be intrinsically computed in these economies, advancing the theoretical understanding of equilibrium computation.

Findings

Competitive equilibrium can be intrinsically computed in minimal simplex economies.

Minimal simplex economies are a specific class of affine economies with stochastic allocations.

The paper extends previous results on affine economies to this new class.

Abstract

In our previous paper we proved that every affine economy has a competitive equilibrium. We define a simplex economy as an affine economy consisting of a stochastic allocation (defining the initial endowments) and a variation with repetition of the number of commodities taking the number of consumers (representing the preferences). We show that a competitive equilibrium can be intrinsically computed in any minimal simplex economy.