经典综合平衡理论Classical General Equilibrium Theory
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☆☆☆☆☆
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【下载次数】 |
23 次 |
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【作者】 |
Lionel W. McKenzie
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【出版社】 |
The MIT Press,Cambridge, Massachusetts
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【文件格式】 |
PDF
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【ISBN】 |
0-262-13413-6
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【资料语言】 |
英文
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【文件大小】 |
1.47MB
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【上传时间】 |
2008-06-29
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【共享者】 |
gj05245515
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资料说明：
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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 mxepT 33
B. Negative Semidefiniteness of ?mijepT 34
C. Euler’s Theorem for f epT 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 Ta?tonnement 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 Ta?tonnement 52
2.5 Local Stability of the Ta?tonnement 54
2.6 Ta?tonnement with Expectations 64
2.7 An Economy of Firms 69
2.8 An Economy of Activities 77
2.9 Ta?tonnment 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 Coe‰cients 118
3.4 Nonsubstitution with Capital Stocks 122
3.5 Current Prices and Interest Rates 129
Appendix
Continuity of mAesT 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
viii Contents
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 Coe‰cients as a von
Neumann Model 293
References 301
Index of Economist Citations 309
Subject Index 311
Contents ix
Preface
General equilibrium theory in the modern sense was first developed in the
second half of the nineteenth century by Francis Edgeworth, Alfred Marshall,
and Le′on Walras, most systematically by Walras. In the first half of
the century some earlier moves in the direction of formal analysis of competitive
markets using mathematics had been made by Augustin Cournot
and Jules Dupuit. Then in the early twentieth century Vilfredo Pareto and
Gustav Cassel added some additional formulations to this theory. However,
the modern elaboration and rigorous development of general equilibrium
theory from these foundations was begun in the 1930s and 1940s
by John Hicks and Paul Samuelson, in the tradition of academic economics
but with liberal appeal to mathematics, and by Abraham Wald
and John von Neumann, from a rigorous mathematical viewpoint. Frank
Ramsey in the late 1920s and von Neumann in the 1930s had laid the
ground for optimal growth theory, which I relate to general equilibrium
over time. However, the general equilibrium theory that this book is concerned
to present was developed in the second half of the twentieth century
primarily by Kenneth Arrow, Gerard Debreu, and me but with many
contributions from others. In particular, Tjalling Koopmans should be
mentioned for his activity analysis and optimal growth theory. Morgenstern,
Samuelson, Hicks, and Koopmans were my teachers. Of the authors
whose work is cited here Hiroshi Atsumi, Robert Becker, Sho-Ichiro
Kusumoto, Leonard Mirman, Tapan Mitra, Anjan Mukherji, Kazuo
Nishimura, Jose′ Scheinkman, and Makoto Yano were my students. I
apologize to my many students whose valuable contributions to economics
happened not to be relevant to this book. However, I must mention Jerry
Green (1977) and Charles Wilson (1976) who were pioneers in the study of
markets with asymmetric information. General equilibrium is far from the
whole of economics.
I characterize the general equilibrium theory that I will discuss as classical
to indicate that it is the theory developed in the 1950s and 1960s
along with continuations in the period after that. It was then that theorists
began to derive theorems in a more satisfactory way from the same
basic assumptions and to provide natural extensions of the original
results. The assumptions that I refer to, in the case of the existence, optimality,
and turnpike theorems, are perfect foresight for each future state
of the world, or equivalently one initial market in which all transactions
are made for the whole future and for all states of the world. The traders
in both models are assumed to continue to live throughout the period,
finite or infinite, to which the market refers. On the other hand, for the
stability theory which is the Walrasian ta?tonnement, it is assumed that
equilibrium is reached before transactions are made final. This theory
received much attention in the 1930s, 1940s, and 1950s While not realistic,
it gives an indication of the conditions for stability in the very short
run. It may also be relevant to later theories of temporary equilibrium
where the question of how expectations are formed is important.
In the literature after 1970 these assumptions were generalized in some
fundamental ways. In the existence theory the case was treated of repeated
markets in which assets including stocks, bonds, and money are
traded. However, perfect foresight of future prices in each state of the
world is still assumed. Thus what is achieved is the description of the
relations between asset prices and other prices. These relations depend on
asset payo¤s for di¤erent states of the world whose objective probabilities
are unknown and will be estimated di¤erently by di¤erent traders (see
Magill and Quinzii 1996). This elaboration of the model may be compared
with the elaboration in optimal growth theory that retains the
assumption of perfect foresight but examines the progress of capital accumulation
in these circumstances leading to turnpike theorems. (See
Becker and Boyd 1997 for many extensions of this theory beyond the
scope of this book.) Perfect foresight means that the future state of the
world is known. Thus the assumption is actually stronger than that used
in the classical existence theory where trading takes place for goods that
include a specification of the state in which they are to be delivered but
perfect foresight of the future state is not assumed. In another direction
the assumption that traders live through the whole future that is covered
by the market is replaced by the assumption of an infinite sequence of
overlapping generations. (See Balasko, Cass, and Shell 1980 for an existence
proof.) In macro models of optimal capital accumulation uncertainty
was introduced by Brock and Mirman (1972; see also Stokey and
Lucas 1989). Finally in recent years much attention has been given in one
sector models to chaotic paths of capital accumulation (see, for example,
Majumdar and Mitra 1994; Nishimura and Sorger 1999).
This book does not attempt to cover these many amendments of the
classical theory. It is aimed rather at presenting a detailed and rigorous
treatment of the classical model itself in which proofs of the basic theorems
are given step by step. This does not mean that the argument is easy.
Every step of the proofs is given, but in many cases the individual steps
xii Preface
require some elaboration by the reader to achieve a full understanding. I
believe this is the only way to obtain a mastery of the method that will
allow the student to go beyond what has been done already and derive
new results. The class notes that are the original form of the material of
the book owe a great deal to the suggestions of my students over the
years. Also I am grateful to many of my former students for their assistance
in removing errors and misprints from earlier versions of my
manuscript. These are too numerous to list, but I owe a special debt to
Kazuo Nishimura and Makoto Yano who used some of the chapters in
their own general equilibrium seminars and to Hajime Kubota who came
to Rochester during several summers to give my chapters their most
careful reading. Of course, I know from experience that not all errors
have been removed or ever will be removed, but I think that unfortunate
circumstance should be laid at my door.
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