Academic Book on Finance and Economics

General Equilibrium: Theory and Evidencehttp://www.worldscientific.com/worldscibooks/10.1142/6875
By W D A Bryant (Macquarie University, Australia)ISBN: 978-981-281-834-8 (hardcover)Category: Economics & FinanceCopyright 2010
481 pages 
£ 94.00; $ 125.00Zentralblatt MATH Database 1931 – 2013©2013 European Mathematical Society, FIZ Karlsruhe & Springer-Verlag


Reviewed by Krzysztof Cichy (Poznań) originally for  ZentralblattMATH:

General equilibrium theory (GET) is one of the most classic branches of mathematical economics, dating back to the work of Leon Walras in the 19th century. After so many years it is still an area of broad research and many questions have remained unanswered. Its main aim is to thoroughly analyze the properties of market economies. It focuses on four main areas, dealing with the conditions that ensure the existence of equilibrium,the optimality of the equilibrium state, the stability of equilibrium and the relation between model equilibria and real economic data.

 

The book by W. D. A. Bryant deals with theoretical and empirical aspects of general equilibrium. The principal aim of the author is “to achieve an understanding of what general equilibrium theory has to say about the circumstances in which deregulated market economies function well, along with circumstances where this is not the case”. The book begins with an overview of GET (Chapter 1). The basic Walrasian conjecture that the deregulated market mechanism leads to optimal outcomes is stated and it leads to the basic questions of GET about the existence, uniqueness, stability, optimality of equilibrium states, the role of parameter values for the properties of these states and the empirical congruence of GET models. Next, some applications of GET are discussed, i.e., branches of economics that rely on general equilibrium assumptions, such as international trade, new-classical economics and economies in transition.

 

Chapter 2 deals with the fundamental issue of sufficient conditions for the existence of equilibrium. Basic notions are carefully defined, such as commodity, consumption sets and preference orderings. They serve to define Walrasian equilibrium and freedisposal equilibrium. A non-mathematical discussion about the possibility of having such equilibria is provided. Next, sufficient conditions for the existence of equilibrium are thoroughly analyzed (the theorems by Arrow and Debreu (1954), Debreu (1962), Arrow and Hahn (1971), Moore (1975), McKenzie (1981) and others).

 

In Chapter 3, the author moves on to necessary conditions for the existence of equilibria, showing that the common belief that Walrasian equilibria exist under weak and general conditions might not be justified. He argues that the “conditions necessary for existence require potentially restrictive relationship conditions to hold across the primitives which define the economy”.

 

Chapter 4 deals with the issue of irreducibility, i.e., the assumption that each agent in the economy is the owner of something which other people are interested in purchasing. In particular, the notion of McKenzie-irreducibility is analyzed from the point of view of its empirical justification. This notion is very important in establishing the existence of a Walrasian equilibrium. Different views emerging from empirical data are thoroughly reviewed and commented on.

 

In Chapter 5 some alternative approaches to establishing the existence of a Walrasian equilibrium are analyzed, with a focus on the ones that avoid strong relationship conditions, such as assumptions of irreducibility. It is explored how such important properties as the individual agents’ survival can appear without such assumptions. In particular, policy induced existence results, as well as ones related to voluntary transfers and altruism are discussed.

 

Chapter 6 deals with the existence of a Walrasian equilibrium in non-Arrow-Debreu environments. This includes the existence of equilibrium in a temporary equilibrium setup of Hicks, in the presence of money and in a Keynesian setup.

 

In Chapter 7 the uniqueness of equilibrium is discussed. This is one of the most fundamental and interesting questions in GET and a subject of intense debate. The conditions that need to be fulfilled in order that uniqueness is guaranteed are carefully elucidated. The author shows that they are rather restrictive. Next, the much less-restrictive case of finitely many isolated equilibria is analyzed.

 

Chapter 8 addresses the question of the stability of equilibrium. The discovery of a universal and globally stable adjustment process is believed by many to be the Holy Grail of GET. A variety of adjustment processes are analyzed, such as classical tâtonnement, global Newton process, discrete time adjustment processes and random adjustment processes. The author argues that all of them yield interesting, but not fully-satisfactory results, therefore implying the need for further research.

 

In Chapter 9, the author moves to the issue of optimality of equilibrium. The fundamental theorems of welfare economics are discussed. It is shown that there exist conditions under which equilibria are optimal, but no universal connection between equilibria and optima can be established, thus leading to the necessity of considering this connection in particular economic environments.

 

Chapter 10 deals with comparative statics of equilibrium states, i.e., the role of parameter values for the properties of equilibria and the response to shocks. This is especially important from the point of view of policy implications of GET models. A special attention is paid to welfare comparative statics.

 

In Chapter 11, the link between the theory and empirics is analyzed. In other words, it is investigated whether GET captures the essential features of real world economies and under which circumstances. Various tests of GET are discussed, in particular ones using microeconomic data (consumer and producer side, market clearing). It is shown that GET can indeed produce meaningful and testable results, but it can not provide fully satisfactory results in all cases - it can not be regarded as the universal theory valid anytime and anywhere. Still, it is argued that there is compelling empirical evidence that under certain conditions and in some economies it yields interesting results and provides a good description of the analyzed real world economies.

Chapter 12 offers a general outlook on the successes and failures of GET. The most important results of the book are discussed and summarized.

 

One of the most important virtues of this book is the abundance of references (over 40 pages) and the thorough discussions of historical achievements of GET, making it a good starting point for an exploration of many subtle details that had to be omitted from the book if it was to remain reasonable in length. Therefore, it will be invaluable to any researcher interested in GET.

 

Krzysztof Cichy (Poznań)

Keywords : general equilibrium theory; existence of equilibrium; uniqueness of equilibrium; stability of equilibrium; optimality of equilibrium; empirical tests of general

equilibrium theory

 

Classification :

*91-02 Research exposition (Social and behavioral sciences)

 91B50 Equilibrium in economics

 91B02 Fundamental topics on applicability to economics

 91B26 Market models

 

 

 

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