A Proof of the Existence of Competitive Equilibrium in a Generation- Overlapping Exchange Economy with Money

AbstractThis paper attempts to give an overview of the pricing of risks in a pure exchange economy, where trade takes place at time zero and where uncertainty is revealed at time one. An economic equilibrium model under uncertainty is formulated, where conditions characterizing a Pareto optimal exchange equilibrium are derived. We present two sets of sufficient conditions for the existence of an equilibrium, and demonstrate how equilibria can be characterized through several examples. Uniqueness of equilibrium is also discussed. Special attention is given to the principal components that the premiums in a reinsurance market must depend upon. We also apply the general theory to the risk exchange problem between a policyholder and an insurer, and in particular we compute market premiums of the resulting optimal contracts.It is emphasized throughout how the formulation of a competitive equilibrium, rather than merely a general risk exchange formulation, is of particular interest in deriving a well-defined and unique set of equilibrium premiums in an insurance market. The theory is put into a framework which is fruitful for extensions beyond the one-period case.

Download Full-text

The Invisible Hand

10.1093/oso/9780198825142.003.0006 ◽

2018 ◽

Author(s):

Robert Sugden

Keyword(s):

Competitive Equilibrium ◽

Exchange Economy ◽

Invisible Hand ◽

The Core ◽

Pareto Efficient ◽

New Formulation ◽

Over Time ◽

The Invisible

Chapter 6 presents a new formulation of Adam Smith’s ‘invisible hand’ argument. The underlying idea is that markets are valuable because they provide opportunities for voluntary transactions (rather than because they satisfy preferences). I propose a ‘Strong Interactive Opportunity Criterion’ which requires that all opportunities for feasible and non-dominated transactions within groups of individuals are made available to those individuals. I define competitive equilibrium without making assumptions about the rationality of individuals’ choices and show that the Strong Interactive Opportunity Criterion is satisfied in every competitive equilibrium of an exchange economy. This result is analogous with the classic theorems that every competitive equilibrium is Pareto-efficient and is in the ‘core’ of the economy. I extend these results to ‘storage economies’ in which trade and consumption take place over time and in which individuals’ choices may be dynamically inconsistent.

Download Full-text

Existence of a Competitive Equilibrium in a Nonstandard Exchange Economy

Econometrica ◽

10.2307/1913980 ◽

1976 ◽

Vol 44 (3) ◽

pp. 537 ◽

Cited By ~ 11

Author(s):

Donald J. Brown

Keyword(s):

Competitive Equilibrium ◽

Exchange Economy

Download Full-text

Existence of an equilibrium for pure exchange economy with fuzzy preferences

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-191011 ◽

2020 ◽

Vol 39 (3) ◽

pp. 2737-2752

Author(s):

Xia Zhang ◽

Hao Sun ◽

Xuanzhu Jin ◽

Moses Olabhele Esangbedo

Keyword(s):

Cooperative Games ◽

Competitive Equilibrium ◽

Exchange Economy ◽

Fuzzy Preferences ◽

Pure Exchange ◽

Quasi Variational Inequality ◽

Pure Exchange Economy ◽

Set Up ◽

Fuzzy Order ◽

Non Cooperative Games

This paper focuses on a new model to reach the existence of equilibrium in a pure exchange economy with fuzzy preferences (PXE-FP). The proposed model integrates exchange, consumption and the agent’s fuzzy preference in the consumption set. We set up a new fuzzy binary relation on the consumption set to evaluate the fuzzy preferences. Also, we prove that there exists a continuous fuzzy order-preserving function in the consumption set under certain conditions. The existence of a fuzzy competitive equilibrium for the PXE-FP is confirmed through a new result on the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games. The payoffs of all strategy profiles for any agent are fuzzy numbers in fuzzy non-cooperative games. Finally, we show that the fuzzy competitive equilibrium could be characterized as a solution to an associated quasi-variational inequality, giving rise to an equilibrium solution.

Download Full-text

Existence of Equilibria in Incomplete Markets with Non-Ordered Preferences

New Mathematics and Natural Computation ◽

10.1142/s1793005714500112 ◽

2014 ◽

Vol 10 (03) ◽

pp. 203-210

Author(s):

Erkan Yalcin ◽

Duygu Yengin

Keyword(s):

Incomplete Markets ◽

Competitive Equilibrium ◽

Exchange Economy ◽

Compact Set ◽

Consumption Good ◽

Linearly Independent ◽

Finite Set ◽

States Of Nature ◽

Existence Of Equilibria

We consider a two-period exchange economy with a finite set of consumers, states of nature, independent assets and a single consumption good. We prove the existence of competitive equilibrium in incomplete markets, when consumption set is not assumed to be compact, set of assets is linearly independent, and individuals' preferences are not assumed to be complete or transitive. Our study therefore generalizes various results in the existing literature.

Download Full-text

Competitive Equilibrium in an Exchange Economy with Indivisibilities

Journal of Economic Theory ◽

10.1006/jeth.1996.2269 ◽

1997 ◽

Vol 74 (2) ◽

pp. 385-413 ◽

Cited By ~ 139

Author(s):

Sushil Bikhchandani ◽

John W. Mamer

Keyword(s):

Competitive Equilibrium ◽

Exchange Economy

Download Full-text

Assessment criteria for aggregate social welfare

Economic Analysis Theory and Practice ◽

10.24891/ea.19.12.2358 ◽

2020 ◽

Vol 19 (12) ◽

pp. 2358-2371

Author(s):

S.A. Moskal'onov

Keyword(s):

Social Welfare ◽

Mathematical Analysis ◽

Exchange Economy ◽

Assessment Criteria ◽

Impossibility Theorem ◽

New Approaches ◽

History Of Development ◽

Arrow's Impossibility Theorem ◽

History Of

Subject. The article addresses the history of development and provides the criticism of existing criteria for aggregate social welfare (on the simple exchange economy (the Edgeworth box) case). Objectives. The purpose is to develop a unique classification of criteria to assess the aggregate social welfare. Methods. The study draws on methods of logical and mathematical analysis. Results. The paper considers strong, strict and weak versions of the Pareto, Kaldor, Hicks, Scitovsky, and Samuelson criteria, introduces the notion of equivalence and constructs orderings by Pareto, Kaldor, Hicks, Scitovsky, and Samuelson. The Pareto and Samuelson's criteria are transitive, however, not complete. The Kaldor, Hicks, Scitovsky citeria are not transitive in the general case. Conclusions. The lack of an ideal social welfare criterion is the consequence of the Arrow’s Impossibility Theorem, and of the group of impossibility theorems in economics. It is necessary to develop new approaches to the assessment of aggregate welfare.

Download Full-text