《General Equilibrium Theory-An Introduction.pdf》由会员分享，可在线阅读，更多相关《General Equilibrium Theory-An Introduction.pdf（379页珍藏版）》请在三一文库上搜索。
1、 GENERAL EQUILIBRIUM THEORY Second Edition General Equilibrium Theory: An Introduction presents the mathematical economic theory of price determination and resource allocation from elementary to advanced levels, suitable for advanced undergraduates and graduate students of economics. This Arrow-Debr
2、eu model (known for two of its most prominent founders, both Nobel Laureates) is the basis of modern price theory and of a wide range of appli- cations. The text starts with elementary models: Robinson Crusoe, the Edgeworth Box, and a two-commodity two-household two-fi rm model. It gives a brief int
3、ro- duction to the mathematics used in the fi eld (continuity, convexity, separation theo- rems, Brouwer fi xed-point theorem, point-to-set mappings, and Shapley-Folkman theorem). It then presents the mathematical general equilibrium model in progres- sively more general settings, including point-va
4、lued, set-valued, and nonconvex set-valued demand and supply. Existence of general equilibrium, fundamental the- orems of welfare economics, core convergence, and futures markets with time and uncertainty are treated fully. This new edition updates the discussion throughout and expands the number an
5、d variety of exercises. It offers a revised and extended treatment of core convergence, including the case of nonconvex preferences, and introduces the investigation of approximate equilibrium with U-shaped cost curves and nonconvex preferences. RossM.StarrisProfessorofEconomicsattheUniversityofCali
6、fornia,SanDiego, where he has taught since 1980. He has also served on the faculties of Yale Uni- versity, the London School of Economics, and the University of California, Davis, and he held a Guggenheim Fellowship at the University of California, Berkeley. Professor Starrs research focuses on gene
7、ral equilibrium theory, mathematical economics, and monetary theory. He is the editor of General Equilibrium Models of Monetary Economies (1989) and coeditor of the three-volume Essays in Honor of Kenneth Arrow (Cambridge University Press, 1986). His articles have appeared in journals such as Econom
8、etrica; Economic Theory; Journal of Economic The- ory; Journal of Money, Credit, and Banking; Quarterly Journal of Economics; and Review of Economic Studies. Cambridge University Press published the fi rst edition of General Equilibrium Theory: An Introduction in 1997. GENERAL EQUILIBRIUM THEORY An
9、Introduction Second Edition ross m. starr University of California, San Diego cambridgeuniversitypress Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S ao Paulo, Delhi, Tokyo, Mexico City Cambridge University Press 32 Avenue of the Americas, New York, NY 10013-2473, USA www.cambridge.
10、org Information on this title: www.cambridge.org/9780521533867 Ross M. Starr 2011 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge
11、 University Press. First published 2011 Printed in the United States of America A catalog record for this publication is available from the British Library. Library of Congress Cataloging in Publication data Starr, Ross M. General equilibrium theory : an introduction / Ross M. Starr. 2nd ed. p.cm. I
12、ncludes bibliographical references and index. ISBN 978-0-521-82645-7 (hardback) 1. Equilibrium (Economics)2. Economics, Mathematical.I. Title. HB145.S82011 330.01?51dc222010054600 ISBN 978-0-521-82645-7 Hardback ISBN 978-0-521-53386-7 Paperback Cambridge University Press has no responsibility for th
13、e persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate. For Susan Contents List of illustrationspage xiii Introduction to the second edition
14、xv Preface to the second editionxxi Preface to the fi rst editionxxiii Table of notationxxv Table of assumptionsxxix AGeneral equilibrium theory: Getting acquainted1 1Concept and history of general equilibrium theory3 1.1 Partial and general equilibrium: Development of the fi eld3 1.2The role of mat
15、hematics7 1.3History of general equilibrium theory8 1.4Bibliographic note10 2An elementary general equilibrium model: The Robinson Crusoe economy12 2.1Centralized allocation14 2.2Decentralized allocation16 2.3 Pareto effi ciency of the competitive equilibrium allocation: First fundamental Theorem of
16、 Welfare Economics23 2.4Bibliographic note24 Exercises24 3The Edgeworth box31 3.1Geometry of the Edgeworth box32 3.2 Calculating an effi cient allocation35 3.3A competitive market solution in the Edgeworth box37 3.4Bibliographic note40 Exercises40 vii viiiContents 4Integrating production and multipl
17、e consumption decisions: A 2 2 2 model44 4.1A 2 2 2 model46 4.2 Technical effi ciency46 4.3 Pareto effi ciency48 4.4First Fundamental Theorem of Welfare Economics: Competitive equilibrium is Pareto effi cient50 Exercises52 5Existence of general equilibrium in an economy with an excess demand functio
18、n58 5.1Bibliographic note64 Exercises64 BMathematics67 6Logic and set theory69 6.1Quasi-orderings71 6.2Functions73 6.3Bibliographic note73 Exercises73 7RN: Real N-dimensional Euclidean space75 7.1Continuous functions82 7.2Bibliographic note85 Exercises85 8Convex sets, separation theorems, and noncon
19、vex sets in RN91 8.1Separation theorems92 8.2The Shapley-Folkman Theorem95 8.3Bibliographic note97 Exercises98 9The Brouwer Fixed-Point Theorem99 9.1Bibliographic note106 Exercises106 CAn economy with bounded production technology and supply and demand functions109 10Markets, prices, commodities, an
20、d mathematical economic theory112 10.1Commodities and prices112 10.2The formal structure of pure economic theory112 10.3Markets, commodities, and prices113 10.4Bibliographic note114 Exercise114 Contentsix 11 Production with bounded-fi rm technology115 11.1Firms and production technology115 11.2The f
21、orm of production technology116 11.3Strictly convex production technology117 11.4Aggregate supply120 11.5Attainable production plans120 11.6Bibliographic note121 Exercises121 12Households124 12.1The structure of household consumption sets and preferences124 12.2Consumption sets124 12.3Representation
22、 of ?i: Existence of a continuous utility function129 12.4Choice and boundedness of budget sets, Bi(p)131 12.5Demand behavior under strict convexity134 12.6Bibliographic note137 Exercises137 13A market economy142 13.1 Firms, profi ts, and household income142 13.2Excess demand and Walrass Law143 13.3
23、Bibliographic note145 Exercises145 14General equilibrium of the market economy with an excess demand function147 14.1Existence of equilibrium147 14.2Bibliographic note152 Exercises152 DAn economy with unbounded production technology and supply and demand functions161 15Theory of production: The unbo
24、unded technology case164 15.1Unbounded production technology164 15.2Boundedness of the attainable set165 15.3 An artifi cially bounded supply function169 15.4Bibliographic note172 Exercises172 16Households: The unbounded technology case174 16.1Households174 16.2Choice in an unbounded budget set174 1
25、6.3Demand behavior under strict convexity177 16.4Bibliographic note179 Exercise179 xContents 17A market economy: The unbounded technology case180 17.1Firms and households180 17.2 Profi ts180 17.3Household income181 17.4Excess demand and Walrass Law181 17.5Bibliographic note184 Exercises184 18General
26、 equilibrium of the market economy: The unbounded technology case185 18.1General equilibrium185 18.2 An artifi cially restricted economy186 18.3General equilibrium of the unrestricted economy187 18.4The Uzawa Equivalence Theorem190 18.5Bibliographic note193 Exercises193 EWelfare economics and the sc
27、ope of markets203 19 Pareto effi ciency and competitive equilibrium205 19.1 Pareto effi ciency205 19.2First Fundamental Theorem of Welfare Economics206 19.3Second Fundamental Theorem of Welfare Economics209 19.4Corner solutions214 19.5Bibliographic note214 Exercises214 20Time and uncertainty: Future
28、s markets225 20.1Introduction225 20.2Time: Futures markets227 20.3Uncertainty: Arrow-Debreu contingent commodity markets233 20.4Uncertainty: Arrow securities markets238 20.5Conclusion: The missing markets241 20.6Bibliographic note242 Exercises243 FBargaining and equilibrium: The core249 21The core o
29、f a market economy251 21.1Bargaining and competition251 21.2The core of a pure exchange economy252 21.3The competitive equilibrium allocation is in the core254 21.4Bibliographic note255 Exercise255 Contentsxi 22Convergence of the core of a large economy256 22.1Replication: A large economy256 22.2Equ
30、al treatment257 22.3Core convergence in a large economy259 22.4A large economy without replication263 22.5Interpreting the core convergence result267 22.6Bibliographic note268 Exercises269 GAn economy with supply and demand correspondences275 23Mathematics: Analysis of point-to-set mappings279 23.1C
31、orrespondences279 23.2Upper hemicontinuity (also known as upper semicontinuity)279 23.3Lower hemicontinuity (also known as lower semicontinuity)282 23.4Continuous correspondence284 23.5Cartesian product of correspondences285 23.6Optimization subject to constraint: Composition of correspondences; the
32、 Maximum Theorem285 23.7Kakutani Fixed-Point Theorem287 23.8Bibliographic note291 Exercises291 24General equilibrium of the market economy with an excess demand correspondence293 24.1General equilibrium with set-valued supply and demand293 24.2Production with a (weakly) convex production technology2
33、94 24.3Households298 24.4The market economy304 24.5 The artifi cially restricted economy307 24.6Existence of competitive equilibrium308 24.7Bibliographic note310 Exercises310 25U-shaped cost curves and concentrated preferences312 25.1U-shaped cost curves and concentrated preferences312 25.2The nonco
34、nvex economy313 25.3 Artifi cial convex counterpart to the nonconvex economy314 25.4Approximate equilibrium317 25.5Bibliographic note319 Exercises320 xiiContents HStanding on the shoulders of giants323 26Next steps325 26.1Large economies325 26.2Anything goes!327 26.3Regular economies and the determi
35、nacy of equilibrium328 26.4General equilibrium with incomplete markets329 26.5Computing general equilibrium330 26.6Bibliographic note331 27Summary and conclusion332 27.1Overview and summary332 27.2Bibliographic note333 Exercises334 Bibliography335 Index341 List of illustrations 2.1 The Robinson Crus
36、oe economy: Effi cient allocation.page 14 2.2The Robinson Crusoe economy: Equilibrium and disequilibrium.17 3.1The Edgeworth box.32 3.2The Edgeworth box: Bargaining and allocation.33 3.3 The Edgeworth box: Effi cient allocation and the contract curve.37 3.4The Edgeworth box: Disequilibrium.39 3.5The
37、 Edgeworth box: General equilibrium.39 4.1A two-good economy: General equilibrium in production and distribution.45 7.1A vector in R2.76 7.2Vector addition.77 8.1Convex and nonconvex sets.92 8.2Bounding and separating hyperplanes for convex sets.94 9.1The Brouwer Fixed-Point Theorem in R.100 9.2An a
38、dmissibly labeled simplicial subdivision of a simplex.101 9.3Sperners Lemma for N = 1.102 11.1Yj : Technology set of fi rm j.116 11.2Convex and nonconvex technology sets.118 12.1Lexicographic preferences.128 14.1Mapping from P into P.149 15.1 Bounding fi rm js production technology.169 16.1Household
39、 is budget sets and demand functions.178 18.1The Uzawa Equivalence Theorem.192 19.1 Supporting an effi cient allocation (Theorem 19.2).210 20.1Uncertain states of the world: An event tree.234 22.1Core convergence (Theorem 22.2).261 22.2Nonconvex preferences (Exercise 22.6).272 G.1Linear production t
40、echnology and its supply correspondence.276 G.2Preferences for perfect substitutes and the demand correspondence.277 G.3Equilibrium in a market with supply and demand correspondences.278 23.1A typical correspondence, (x) = y|x 1 y x + 1.280 23.2Example 23.1 An upper hemicontinuous correspondence.281
41、 xiii xivList of illustrations 23.3Example 23.2 A correspondence that is not upper hemicontinuous at 0.282 23.4Example 23.3 A lower hemicontinuous correspondence.283 23.5Example 23.5 A continuous correspondence.284 23.6The maximum problem.286 23.7An upper hemicontinuous mapping from an interval (1-s
42、implex) into itself without a fi xed point.288 23.8An upper hemicontinuous convex-valued mapping from an interval (1-simplex) into itself with a fi xed point.288 23.9Lemma 23.2 Approximating an upper hemicontinuous convex-valued correspondence by a continuous function.289 23.10 Example 23.7 Applying
43、 the Kakutani Fixed-Point Theorem.290 24.1Example 24.1 An upper hemicontinuous, convex-valued supply correspondence.295 24.2Example 23.2 An upper hemicontinuous supply correspondence that is not convex valued.296 24.3Theorem 23.2 Continuity of the budget set showing the construction of y.301 26.1 An
44、 economy with an infi nite number of equilibria.328 Introduction to the second edition The foundations of modern economic general equilibrium theory are contained in a surprisingly short list of references. For primary sources, it is suffi cient to master Arrow and Debreu (1954), Arrow (1951), Arrow
45、 (1953), and Debreu and Scarf (1963). An even shorter list is comprehensive; Debreu (1959) and Debreu and Scarf (1963) cover the topic admirably. Why should anyone write (or read!) a secondary source, a textbook? Because, unfortunately, this body of material is extremely diffi cult for most students
46、 to read and comprehend. Professor Hahn described Debreus (1959) book as “very short, but it may well take as long to read as many works three times as long. This is not due to faulty exposition but to the demands rigorous analysis makes on the reader. It is to be hoped that no one will be put off b
47、y this, for the.return.is very high indeed” (Hahn 1961). Unfortunately, in teaching economic theory we fi nd that many capable students are indeed put off by the mathematical abstraction of the above works. What theorists regard as elegantly terse expression, students may fi nd inaccessible formalit
48、y. The focus of this textbook is to overcome this barrier and to make this body of work accessible to a wider audience of advanced undergraduate and graduate students in economics. This book presents the theory of general economic equilibrium incrementally, from elementary to more sophisticated trea
49、tments. Part A (Chapters 1 through 5) presents an elementary introduction. Chapters 2 and 3 present a nontechnical introduction to the Robinson Crusoe and Edgeworth box models of general equi- librium and Pareto effi ciency using differential calculus. Chapter 4 goes over the 2 2 2(twocommodities,twohouseholds,twofactors)modelusingdifferential calculus, including the marginal equivalence results typical of the classical welfare economics. Chapter 5 briefl y presents an introduction to the use of the Brouwer Fixed-Point Theorem to prove t