A Model Distinguishing Production and Consumption Bundles

In contrast to the neo-classical theory of Arrow and Debreu, a model of a private ownership economy is presented in which production and consumption bundles are treated separately. Each of the two types of bundles is assumed to establish a convex cone. The main part in the modelling is the introduction of production technologies which can be thought of as replacing the notion of production sets in Arrow and Debreu’s model. It is a point of further investigationwhether the notion of production technology is also generating the notion of production setmathematical models;production;consumption

A Model Distinguishing Production and Consumption Bundles

In contrast with the classical theory of Arrow and Debreu, a model of a private ownership economy is presented in which production and consumption bundles are treated separately.Each of the two types of bundles is assumed to establish a convex cone.This also offers a point of contrast in comparison with the classical theory.The main part in the modelling is the introduction of production technologies which can be thought of as replacing the notion of production sets in Arrow and Debreu s model.It is shown that under mild economically interpretable conditions, a Walrasian equilibrium exists.

General Equilibrium Model with a Convex Cone as the Set of Commodity Bundles

In this paper, we present a model for an exchange economy which is an extension of the classical model as introduced by Arrow and Debreu.In the classical model, there is a nite number of commodi- ties and a nite number of consumers.The commodities are treated separately, and so a commodity bundle is an element of the positive orthant of the Euclidean space IR l , wherelis the number of com- modities.A closer look at Arrow and Debreu's model shows that this Euclidean structure is used only indirectly.Instead of using the Euclidean structure, we allow for just the exis- tence of commodity bundles, and do not take into consideration indi- vidual commodities.More speci cally, we model the set of all possible commodity bundles in the exchange economy under consideration, by a pointed convex cone in a nite-dimensional vector space.This vec- tor space is used only to de ne the suitable topological concepts in the cone, and therefore is not part of the model.Since we do not consider separate commodities, we do not intro- duce prices of individual commodities.Instead, we consider price systems, which attach a positive value to every commodity bundle. These price systems are modelled by the linear functionals on the vec- tor space that are positive on the cone of commodity bundles.The set of price systems is a cone with similar properties as the commodity cone.More precisely, the price cone is the polar cone of the commodity cone.The commodity cone introduces a partial ordering on the commod- ity bundles and the price systems are compatible with this ordering.If we take the positive orthant of the Euclidean space IR l as the pointed convex cone then the partial ordering coincides with the Euclidean order relation on IR l taken in the classical approach.In this setting, given a nite number of consumers each with an ini- tial endowment and a preference relation on the commodity cone, we prove existence of a Walrasian equilibrium under assumptions which are essentially the same as the ones in Arrow and Debreu's model.We introduce the new concept of equilibrium function on the price system cone; zeroes of an equilibrium function correspond with equilibrium price systems.So proving existence of a Walrasian equilibrium comes down to constructing an equilibrium function with zeroes.

Restriction of Preferences to the Set of Consumption Bundles, In a Model with Production and Consumption Bundles

In contrast to the neo-classical theory of Arrow and Debreu, a model of a private ownership economy is presented, in which production and consumption bundles are treated separately. Each of the two types of bundles is assumed to establish a con- vex cone. Production technologies can convert production bundles into consumption bundles, and the preferences of the consumers are assumed to lie only on the set of consumption bundles. The main theorem of this paper states the existence of a Walrasian equilibrium in this setting.

Equilibrium Theory: A Salient Approach.

Abstract: Whereas the neoclassical models in General Equilibrium Theory focus on the existence of separate commodities, this thesis regards 'bundles of trade' as the unit objects of exchange. Apart from commodities and commodity bundles in the neoclassical sense, the term `bundle of trade' includes, for example, fixed pre-packed commodity bundles and exchangeable objects which are solely defined and valued by their characteristics. In the first part of the thesis, the new mathematical concept of salient space is formalised and thoroughly investigated. In the second part, several models of exchange economies are stated, each constructed around the set consisting of all bundles of trade. This set is represented in a natural way by a salient space. Finally, for each model one or more equilibrium existence theorems are presented and proven.

10252 Executive Summary -- Game Semantics and Program Verification

The seminar took place from 20th until 25th June 2010. Its primary aim was to foster interaction between researchers working on modelling programs/proofs using games and the verification community. The meeting brought together 28 researchers from eight different countries, both junior and senior, for a systematic assessment of what the two areas have to offer to one another, critical evaluation of what has been achieved so far, with a view to establishing common research goals for the future