Classical General Equilibrium Theory

by Lionel W. McKenzie

Overview

Although general equilibrium theory originated in the late nineteenth century, modern elaboration and development of the theory began only in the 1930s and 1940s. This book focuses on the version of the theory developed in the second half of the twentieth century, referred to by Lionel McKenzie as the classical general equilibrium theory. McKenzie offers detailed and rigorous treatment of the classical model, giving step-by-step proofs of the basic theorems. In many cases he elaborates on the individual steps to give a fuller understanding of the underlying principles. His goal is to provide readers with a true mastery of the methodology so that they can derive new results that will further enrich their thinking about general equilibrium theory. Special attention is given to the McKenzie model, in which it is not assumed that the number of firms is given but rather that technologies or activities are available to any agents who can supply the resources they require. The McKenzie model is used to establish the turnpike theorems of optimal and competitive capital accumulation.

Product Details

ISBN-13:	9780262633307
Publisher:	MIT Press
Publication date:	08/12/2005
Series:	The MIT Press
Edition description:	Revised ed.
Pages:	332
Product dimensions:	6.00(w) x 9.00(h) x 0.60(d)
Age Range:	18 Years

About the Author

The late Lionel W. McKenzie was Wilson Professor Emeritus of Economics at the University of Rochester.

Table of Contents

	Preface	xi
1	Theory of Demand	1
1.1	A Direct Approach to Demand Theory	1
1.2	Demand Theory without Transitivity	13
1.3	The Classical Theory	15
1.4	The Method of Revealed Preference	22
1.5	Market Demand Functions	25
	Appendixes
A	Continuity of m[subscript x](p)	33
B	Negative Semidefiniteness of [m subscript ij (p)]	34
C	Euler's Theorem for f(p)	35
D	Quasi-linear Preferences	35
E	The Law of Demand and Risk Aversion	36
F	The Strong Axiom of Revealed Preference	38
G	Group Demand Functions	40
2	Tatonnement Stability of Equilibrium	45
2.1	Excess Demand Functions	45
2.2	Market Equilibrium	50
2.3	Matrices with Quasi-dominant Diagonals	50
2.4	The Process of Tatonnement	52
2.5	Local Stability of the Tatonnement	54
2.6	Tatonnement with Expectations	64
2.7	An Economy of Firms	69
2.8	An Economy of Activities	77
2.9	Tatonnment with Trading	82
2.10	Global Stability with Gross Substitutes	89
	Appendixes
A	Individual and Market Excess Demand Functions	96
B	The Gross Substitute Assumption	98
C	The Weak Axiom of Revealed Preference and Local Stability	102
D	Stability in a Temporary Equilibrium Model	104
3	Leontief Models of Production	109
3.1	The Simple Leontief Model	109
3.2	A Simple Leontief Model of Growth	114
3.3	The Simple Model with Variable Coefficients	118
3.4	Nonsubstitution with Capital Stocks	122
3.5	Current Prices and Interest Rates	129
Appendix	Continuity of [mu subscript A](s)	129
4	Comparative Statics	133
4.1	The Local Theory of Comparative Statics	133
4.2	The Morishima Case	140
4.3	Global Comparative Statics	143
4.4	Comparative Statics for the Individual Agent	145
4.5	Comparative Statics and Supermodularity	150
	Appendixes
A	Local Uniqueness of Equilibrium	153
B	Jacobi's Theorem	157
C	Negative Definiteness under Constraint	158
D	Maximization under Constraint	161
E	Matrices Whose Roots Have Negative Real Parts	163
5	Pareto Optimality and the Core	165
5.1	Pareto Optimum and Competitive Equilibrium	165
5.2	Competitive Equilibrium and the Core	171
5.3	Nonemptiness of the Core	181
5.4	The Existence of Competitive Equilibrium	183
6	Existence and Uniqueness of Competitive Equilibrium	189
6.1	Existence in an Economy of Activities	189
6.2	Existence in an Economy of Firms	197
6.3	Interiority and Irreducibility	207
6.4	Existence of Competitive Equilibrium with an Infinite Commodity Space	214
6.5	Uniqueness of Equilibrium	229
Appendix	Existence of a Zero of the Excess Demand Functions	235
7	Competitive Equilibrium over Time	239
7.1	The von Neumann Model	240
7.2	Turnpike Theorems for the von Neumann Model	244
7.3	A Generalized Ramsey Growth Model	248
7.4	Turnpike Theorems over an Infinite Horizon	255
7.5	The Generalized Ramsey Model with Discounting	259
7.6	A Turnpike Theorem for the Quasi-stationary Model	264
7.7	The Turnpike in Competitive Equilibrium	272
Appendix	A Leontief Model with Capital Coefficients as a von Neumann Model	293
	References	301
	Index of Economist Citations	309
	Subject Index	311

What People are Saying About This

Paul A. Samuelson

This book is itself a modern classic. It summarizes deftly, succinctly, and elegantly four decades of vintage frontier findings by two top score academics. McKenzie himself is first among equals in this stellar group.

Hugo Sonnenschein

Over a period of fifty years McKenzie has pioneered, organized, and taught general equilibrium. This volume, by a master of the subject, serves as an indispensable guide to rigorous general equilibrium. The serious reader will be amply rewarded.

Kenneth J. Arrow

McKenzie is one of the great innovators in the field of general equilibrium theory; his was the first paper published establishing the existence of general equilibrium. His new book is a tour de force of synthesis, presenting with admirable clarity and rigor the important results in the field. Indeed, he goes beyond the field to discuss such issues as turnpike theorems and optimal capital accumulation, to whose development he has contributed so much.

Robert E. Lucas

Lionel McKenzie's new monograph is a pleasure to read. Only a major contributor to economic theory could teach general equilibrium theory with such clarity and authority. The book is gracefully written and rigorous, and does an elegant job of situating competitive equilibrium theory in the economic and mathematical traditions from which it evolved.

Jerry Green

A beautifully written, integrated treatment of the main topics in microeconomics, this book takes the reader from first principles to the cutting edge of theory today. It is, and will remain, a classic work.

Endorsement

Over a period of fifty years McKenzie has pioneered, organized, and taught general equilibrium. This volume, by a master of the subject, serves as an indispensable guide to rigorous general equilibrium. The serious reader will be amply rewarded.

—Hugo Sonnenschein, Charles L. Hutchinson Distinguished Service Professor and President Emeritus, University of Chicago

From the Publisher

A beautifully written, integrated treatment of the main topics in microeconomics, this book takes the reader from first principles to the cutting edge of theory today. It is, and will remain, a classic work.

—Jerry Green, John Leverett Professor in the University and David A. Wells Professor of Political Economy, Harvard University

McKenzie is one of the great innovators in the field of general equilibrium theory; his was the first paper published establishing the existence of general equilibrium. His new book is a tour de force of synthesis, presenting with admirable clarity and rigor the important results in the field. Indeed, he goes beyond the field to discuss such issues as turnpike theorems and optimal capital accumulation, to whose development he has contributed so much.

—Kenneth J. Arrow, Professor of Economics Emeritus, Stanford University

This book is a masterwork by one of the three founders of the modern field of general equilibrium theory. All economists will want to own this volume. It covers not only classical theory but also the research frontier. It is written with the beauty and clarity that one would expect of a founding father.

—William A. Brock, Vilas Research Professor of Economics, The University of Wisconsin, Madison

Lionel McKenzie's new monograph is a pleasure to read. Only a major contributor to economic theory could teach general equilibrium theory with such clarity and authority. The book is gracefully written and rigorous, and does an elegant job of situating competitive equilibrium theory in the economic and mathematical traditions from which it evolved.

—Robert E. Lucas, Jr., John Dewey Distinguished Service Professor, University of Chicago

This book is itself a modern classic. It summarizes deftly, succinctly, and elegantly four decades of vintage frontier findings by two top score academics. McKenzie himself is first among equals in this stellar group.

—Paul A. Samuelson, Institute Professor Emeritus, MIT, and Nobel Laureate in Economics (1970)

Over a period of fifty years McKenzie has pioneered, organized, and taught general equilibrium. This volume, by a master of the subject, serves as an indispensable guide to rigorous general equilibrium. The serious reader will be amply rewarded.

—Hugo Sonnenschein, Charles L. Hutchinson Distinguished Service Professor and President Emeritus, University of Chicago

William A. Brock

This book is a masterwork by one of the three founders of the modern field of general equilibrium theory. All economists will want to own this volume. It covers not only classical theory but also the research frontier. It is written with the beauty and clarity that one would expect of a founding father.

Editorial Reviews

"A beautifully written, integrated treatment of the main topics in microeconomics, this book takes the reader from first principles to the cutting edge of theory today. It is, and will remain, a classic work."--Jerry Green, John Leverett Professor in the University and David A. Wells Professor of Political Economy, Harvard University

"Lionel McKenzie's new monograph is a pleasure to read. Only a major contributor to economic theory could teach general equilibrium theory with such clarity and authority. The book is gracefully written and rigorous, and does an elegant job of situating competitive equilibrium theory in the economic and mathematical traditions from which it evolved."--Robert E. Lucas, Jr., John Dewey Distinguished Service Professor, University of Chicago

"McKenzie is one of the great innovators in the field of general equilibrium theory; his was the first paper published establishing the existence of general equilibrium. His new book is a tour de force of synthesis, presenting with admirable clarity and rigor the important results in the field. Indeed, he goes beyond the field to discuss such issues as turnpike theorems and optimal capital accumulation, to whose development he has contributed so much."--Kenneth J. Arrow, Professor of Economics Emeritus, Stanford University

"This book is a masterwork by one of the three founders of the modern field of general equilibrium theory. All economists will want to own this volume. It covers not only classical theory but also the research frontier. It is written with the beauty and clarity that one would expect of a founding father."--William A. Brock, Vilas Research Professor of Economics, The University of Wisconsin, Madison

"This book is itself a modern classic. It summarizes deftly, succinctly, and elegantly four decades of vintage frontier findings by two score top academics. McKenzie himself is first among equals in this stellar group."--Paul A. Samuelson, Institute Professor Emeritus, Massachusetts Institute of Technology, and Nobel Laureate in Economics (1970)

& quot; A beautifully written, integrated treatment of the main topics in microeconomics, this book takes the reader from first principles to the cutting edge of theory today. It is, and will remain, a classic work.& quot; -- Jerry Green, John Leverett Professor in the University and David A. Wells Professor of Political Economy, Harvard University

& quot; Lionel McKenzie's new monograph is a pleasure to read. Only a major contributor to economic theory could teach general equilibrium theory with such clarity and authority. The book is gracefully written and rigorous, and does an elegant job of situating competitive equilibrium theory in the economic and mathematical traditions from which it evolved.& quot; -- Robert E. Lucas, Jr., John Dewey Distinguished Service Professor, University of Chicago

& quot; McKenzie is one of the great innovators in the field of general equilibrium theory; his was the first paper published establishing the existence of general equilibrium. His new book is a tour de force of synthesis, presenting with admirable clarity and rigor the important results in the field. Indeed, he goes beyond the field to discuss such issues as turnpike theorems and optimal capital accumulation, to whose development he has contributed so much.& quot; -- Kenneth J. Arrow, Professor of Economics Emeritus, Stanford University

& quot; This book is a masterwork by one of the three founders of the modern field of general equilibrium theory. All economists will want to own this volume. It covers not only classical theory but also the research frontier. It is written with the beauty and clarity that one would expect of a founding father.& quot; -- William A. Brock, Vilas Research Professor of Economics, The University of Wisconsin, Madison

& quot; This book is itself a modern classic. It summarizes deftly, succinctly, and elegantly four decades of vintage frontier findings by two score top academics. McKenzie himself is first among equals in this stellar group.& quot; -- Paul A. Samuelson, Institute Professor Emeritus, Massachusetts Institute of Technology, and Nobel Laureate in Economics (1970)

" A beautifully written, integrated treatment of the main topics in microeconomics, this book takes the reader from first principles to the cutting edge of theory today. It is, and will remain, a classic work." -- Jerry Green, John Leverett Professor in the University and David A. Wells Professor of Political Economy, Harvard University

" Lionel McKenzie's new monograph is a pleasure to read. Only a major contributor to economic theory could teach general equilibrium theory with such clarity and authority. The book is gracefully written and rigorous, and does an elegant job of situating competitive equilibrium theory in the economic and mathematical traditions from which it evolved." -- Robert E. Lucas, Jr., John Dewey Distinguished Service Professor, University of Chicago

" McKenzie is one of the great innovators in the field of general equilibrium theory; his was the first paper published establishing the existence of general equilibrium. His new book is a tour de force of synthesis, presenting with admirable clarity and rigor the important results in the field. Indeed, he goes beyond the field to discuss such issues as turnpike theorems and optimal capital accumulation, to whose development he has contributed so much." -- Kenneth J. Arrow, Professor of Economics Emeritus, Stanford University

" This book is a masterwork by one of the three founders of the modern field of general equilibrium theory. All economists will want to own this volume. It covers not only classical theory but also the research frontier. It is written with the beauty and clarity that one would expect of a founding father." -- William A. Brock, Vilas Research Professor of Economics, The University of Wisconsin, Madison

" This book is itself a modern classic. It summarizes deftly, succinctly, and elegantly four decades of vintage frontier findings by two score top academics. McKenzie himself is first among equals in this stellar group." -- Paul A. Samuelson, Institute Professor Emeritus, Massachusetts Institute of Technology, and Nobel Laureate in Economics (1970)

-- Jerry Green, John Leverett Professor in the University and David A. Wells Professor of Political Economy, Harvard University

-- Kenneth J. Arrow, Professor of Economics Emeritus, Stanford University

-- Paul A. Samuelson, Institute Professor Emeritus, Massachusetts Institute of Technology, and Nobel Laureate in Economics (1970)

-- Robert E. Lucas, Jr., John Dewey Distinguished Service Professor, University of Chicago

-- William A. Brock, Vilas Research Professor of Economics, The University of Wisconsin, Madison

From the Publisher