The Edgeworth Cube: An Economic Model for Social Peace

The Edgeworth Cube: An Economic Model for Social Peace

Oliver Kunze (HNU University of Applied Sciences Neu-Ulm, Neu-Ulm, Germany) and Florian Schlatterer (University of Applied Sciences Neu-Ulm, Neu-Ulm, Germany)
Copyright: © 2018 |Pages: 17
DOI: 10.4018/IJABE.2018040103

Abstract

Social peace is an asset to every society. Its absence endangers the well-being and the safety of the population and the stability of states. In order to better understand the interdependencies of poverty, social peace and migration pressure the authors introduce the model of the “Edgeworth-Cube” which is an extension of the classical Edgeworth Box model by one dimension. This new dimension can either be interpreted as “aggression” (which reduces “social peace” for others) or as “migration pressure” (which results from a worldwide heterogeneous distribution of wealth), and this new dimension is modelled as a non-budget-constrained unilateral immaterial good. The “Edgeworth-Cube” also differentiates vital (essential) goods from normal (non-essential) goods. By focusing on extremely imbalanced endowments and by formal mathematical modeling the authors show in their approach that applying behavioral pressure (i.e. aggression or migration pressure) has an existential economic value for the poor on the one hand. On the other hand, the authors show that transfer payments have a systemically limited potential to keep aggression and migration pressure at bay.
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1. Introduction

1.1. Motivation

Social peace is a desirable state of a social community1. In a peaceful environment people can enjoy their lives, societies can prosper, and economies can grow. The absence of peace endangers lives of individuals as well as democratic systems of social co-existence and decision making.

Still different levels of social peace can be observed in different socio-economic environments. Why are some societies able to maintain a desirable level of social peace, whereas in others social peace is less developed? In other words – which mechanisms secure and endanger social peace? Which mechanisms lead to aggressive behavior of parts of a society? And which mechanisms lead to migration pressure and thus actuate aggressive behavior of other parts of a society?

An understanding of these mechanisms is important for solving intra-societal problems (e.g. strikes, riots of the underprivileged, crime level etc.), as well as for inter-societal problems (especially migration issues).

Leaving out all psychological aspects (such as e.g. pleasure in aggression or envy) and sociological aspects (such as e.g. orchestrated manipulation, purposefully misconducted religious beliefs or mass hysteria) the authors want to introduce an extension of the well-known Edgeworth Box model which solely uses economic mechanisms to explain social peace (and aggressive behavior which endangers a peaceful intra societal co-existence). The authors are aware that their model is a significant simplification of the real world, but they also consider that this reduction helps to understand hidden mechanisms more precisely.

1.2. The Problem

The different allocation of goods to different players2 constitutes the basis for economic interactions. If one wants to understand why and to which extend economic transactions happen, the “Edgeworth Box” (see e.g. Pfingsten (1989), pp.120f) is an established basic model for a two-player-two-goods economy. It mathematically explains why “the basis of arbitration between contractors is the greatest possible utility of all concerned” (Edgeworth 1881, p vi). But what happens, if the original endowments of the players are significantly unbalanced and threaten the existence of one player? I.e. what happens, if one player owns almost all the goods and the other player owns almost none?

In other words, the research shall help to understand the nature of the micro-economic mechanisms that lead to aggression by the poor and how aggression-counterbalancing options work from a sheer economic point of view.

1.3. Structure of this Publication

Section two is a brief overview on the state of science with focus on the Edgeworth Box. In section three the authors develop the extension of the Edgeworth Box towards the Edgeworth Cube and discuss the relevant details. Section four translates the mathematical findings into real world observations. In section 5 the authors sum up the results, discuss them critically and show the need for further research.

2. State Of Science

The Edgeworth Box model assumes rationality3 in the choice of goods and competitive behavior of players. Let’s briefly summarize the model of the Edgeworth Box in order to introduce a model notation which we’ll use and expand in section 3.

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