Mathematical Economics

 

V. L. Makarov, A. M. Rubinov (auth.)-Mathematical Theory of Economic Dynamics and Equilibria-Springer-Verlag New York (1977).pdf

(Got borrowed hardcopy)

@book{book:973518,
title = {Mathematical Theory of Economic Dynamics and Equilibria},
author = {V. L. Makarov, A. M. Rubinov (auth.)},
publisher = {Springer-Verlag New York},
isbn = {978-1-4612-9888-5,978-1-4612-9886-1},
year = {1977},
series = {},
edition = {1},
volume = {},
url = {http://gen.lib.rus.ec/book/index.php?md5=1a7108ebbd1d9e56b03e9fb9b491fc49}
}

This book is devoted to the mathematical analysis of models of economic dynamics and equilibria. These models form an important part of mathemati­ cal economics. Models of economic dynamics describe the motion of an economy through time. The basic concept in the study of these models is that of a trajectory, i.e., a sequence of elements of the phase space that describe admissible (possible) development of the economy. From all trajectories, we select those that are” desirable,” i.e., optimal in terms of a certain criterion. The apparatus of point-set maps is the appropriate tool for the analysis of these models. The topological aspects of these maps (particularly, the Kakutani fixed-point theorem) are used to study equilibrium models as well as n-person games. To study dynamic models we use a special class of maps which, in this book, are called superlinear maps. The theory of superlinear point-set maps is, obviously, of interest in its own right. This theory is described in the first chapter. Chapters 2-4 are devoted to models of economic dynamics and present a detailed study of the properties of optimal trajectories. These properties are described in terms of theorems on characteristics (on the existence of dual prices) and turnpike theorems (theorems on asymptotic trajectories). In Chapter 5, we state and study a model of economic equilibrium. The basic idea is to establish a theorem about the existence of an equilibrium state for the Arrow-Debreu model and a certain generalization of it.
Table of contents :

Front Matter….Pages i-xv

Theory of point-set maps….Pages 1-58

The Neumann-Gale model….Pages 59-92

Optimal trajectories and their characteristics….Pages 93-160

Asymptotes of optimal trajectories….Pages 161-196

Models of economic equilibria….Pages 197-210

Models of economic dynamics with explicit consumption….Pages 211-233

Back Matter….Pages 234-253

 

Angel de la Fuente-Mathematical Methods and Models for Economists-Cambridge University Press (2000).pdf
(Got borrowed hardcopy)

@book{book:931731,

   title =     {Mathematical Methods and Models for Economists},

   author =    {Angel de la Fuente},

   publisher = {Cambridge University Press},

   isbn =      {0521585120,9780521585125},

   year =      {2000},

   series =    {},

   edition =   {},

   volume =    {},

   url =       {http://gen.lib.rus.ec/book/index.php?md5=AE04F15DCB1EA935E104038A0409C65D}}

This book is intended as a textbook for a first-year Ph. D. course in mathematics for economists and as a reference for graduate students in economics. It provides a self-contained, rigorous treatment of most of the concepts and techniques required to follow the standard first-year theory sequence in micro and macroeconomics. The topics covered include an introduction to analysis in metric spaces, differential calculus, comparative statics, convexity, static optimization, dynamical systems and dynamic optimization. The book includes a large number of applications to standard economic models and over two hundred fully worked-out problems.

Table of contents :

Contents……Page 1

Preface……Page 7

1 – Review of Basic Concepts……Page 9

2 – Metric and Normed Spaces……Page 45

3 – Vector Spaces and Linear Transformations……Page 123

4 – Differential Calculus……Page 162

5 – Static Models and Comparative Statics……Page 199

6 – Convex Sets and Concave Functions……Page 233

7 – Static Optimization……Page 278

8 – Some Applications to Microeconomics……Page 329

9 – Dynamical Systems. I Basic Concepts and Scalar Systems……Page 393

10 – Dynamical Systems. II Higher Dimensions……Page 459

11 – Dynamical Systems III Some Applications……Page 496

12 – An Introduction to Dynamic Optimization……Page 551

13 – Some Applications of Dynamic Optimization……Page 584

Appendix. Solutions to the Problems……Page 659

Subject index……Page 827

Author index……Page 834

(Studies in Mathematics and Its Applications 7) Jean-Pierre Aubin (Eds.)-Mathematical Methods of Game and Economic Theory-Elsevier Science Ltd (1979).pdf

(Got borrowed hardcopy)

@book{book:831928,

   title =     {Mathematical Methods of Game and Economic Theory},

   author =    {Jean-Pierre Aubin (Eds.)},

   publisher = {Elsevier Science Ltd},

   isbn =      {0444851844,9780444851840},

   year =      {1979},

   series =    {Studies in Mathematics and Its Applications 7},

   edition =   {Revised},

   volume =    {},

   url =       {http://gen.lib.rus.ec/book/index.php?md5=6990DF3709F8F760A6FBC2DBE64A7C37}}

This book presents a unified treatment of optimization theory, game theory and a general equilibrium theory in economics in the framework of nonlinear functional analysis. It not only provides powerful and versatile tools for solving specific problems in economics and the social sciences but also serves as a unifying theme in the mathematical theory of these subjects as well as in pure mathematics itself.

Preface Pages vii-ix

Summary of Results: A Guideline for the Reader Pages xxi-xxvi

Contents of Other Possible Courses Pages xxvii-xxviii

Notations Pages xxix-xxxii

Chapter 1 Minimization Problems and Convexity Pages 3-41

Chapter 2 Existence, Uniqueness and Stability of Optimal Solutions Pages 42-74

Chapter 3 Compactness and Continuity Properties Pages 75-102

Chapter 4 Differentiability and Subdifferentiability: Characterization of Optimal Solutions Pages 103-132

Chapter 5 Introduction to Duality Theory Pages 133-161

Chapter 6 Two-Person Games: An Introduction Pages 165-203

Chapter 7 Two-Person Zero-Sum Games: Existence Theorems Pages 204-240

Chapter 8 The Fundamental Economic Model: Walras Equilibria Pages 241-262

Chapter 9 Non-Cooperative n-Person Games Pages 263-292

Chapter 10 Main Solution Concepts of Cooperative Games Pages 293-335

Chapter 11 Games with Side-Payments Pages 336-371

Chapter 12 Games without Side-Payments Pages 372-392

Chapter 13 Minimax Type Inequalities, Monotone Correspondences and γ-Convex Functions Pages 395-440

Chapter 14 Introduction to Calculus of Variations and Optimal Control Pages 441-520

Chapter 15 Fixed Point Theorems, Quasi-Variational Inequalities and Correspondences Pages 521-560

Appendix A Summary of Linear Functional Analysis Pages 561-568

Appendix B The Knaster-Kuratowski-Mazurkiewicz Lemma Pages 569-579

Appendix C Lyapunov’s Theorem on the Range of a Vector Valued Measure Pages 580-581

Comments Pages 582-589

References Pages 590-616

Subject Index Pages 614-616

George Hadley, Murray C. Kemp-Variational Methods in Economics-Elsevier Science Publishing Co Inc.,U.S (1971).pdf

(Got hardcopy)

@book{book:1375454,

   title =     {Variational Methods in Economics},

   author =    {George Hadley, Murray C. Kemp},

   publisher = {Elsevier Science Publishing Co Inc.,U.S},

   isbn =      {072043601X,9780720436013},

   year =      {1971},

   series =    {},

   edition =   {First Edition},

   volume =    {},

   url =       {http://gen.lib.rus.ec/book/index.php?md5=75BE01856A23930395AC11E4BDD8CA7A}}

Advanced Textbooks in Economics, Volume 1: Variational Methods in Economics focuses on the application of variational methods in economics, including autonomous system, dynamic programming, and phase spaces and diagrams.
The manuscript first elaborates on growth models in economics and calculus of variations. Discussions focus on connection with dynamic programming, variable end points-free boundaries, transversality at infinity, sensitivity analysis-end point changes, Weierstrass and Legendre necessary conditions, and phase diagrams and phase spaces. The text then ponders on the constraints of classical theory, including unbounded intervals of integration, free boundary conditions, comparison functions, normality, and the problem of Bolza.
The publication explains two-sector models of optimal economic growth, optimal control theory, and connections with the classical theory. Topics include capital good immobile between industries, constrained state variables, linear control problems, conversion of a control problem into a problem of Lagrange, and the conversion of a nonautonomous system into an autonomous system.
The book is a valuable source of information for economists and researchers interested in the variational methods in economics.

Table of contents :

Content:

ADVANCED TEXTBOOKS IN ECONOMICS, Page ii

Front Matter, Page iii

Copyright, Page iv

Preface, Pages v-vi

1 – Growth models in economics, Pages 1-5

2 – Calculus of variations — classical theory, Pages 6-174

3 – Classical theory — constraints, Pages 175-237

4 – Optimal control theory, Pages 238-281

5 – Connections with the classical theory, Pages 282-325

6 – Two-sector models of optimal economic growth, Pages 326-363

Appendix I – Uniqueness of the utility functional and the utility function, Pages 364-366

Appendix II – Implicit function theorems, Pages 367-369

Appendix III – Existence theorems for systems of ordinary differential equations, Pages 370-373

References, Pages 374-376

Index, Pages 377-378

Akira Takayama-Mathematical economics-Dryden Press (1974).pdf
(Got borrowed hardcopy 2nd edition, 1985, xxiii + 737p)

@book{book:833822,

   title =     {Mathematical economics},

   author =    {Akira Takayama},

   publisher = {Dryden Press},

   isbn =      {0030866537,9780030866531},

   year =      {1974},

   series =    {},

   edition =   {},

   volume =    {},

   url =       {http://gen.lib.rus.ec/book/index.php?md5=7BFAE05B931B9E653B9E57688A78A9B3}}

Table of contents :

Title Page……Page 1

Copyright and Dedication……Page 2

Preface……Page 3

Contents……Page 7

Some Frequently Used Notations……Page 12

A. Scope of the Book……Page 15

B. Outline of the Book……Page 18

a. Some Basic Concepts and Notations……Page 25

b. Rn and Linear Space……Page 29

c. Basis and Linear Functions……Page 34

d. Convex Sets……Page 40

e. A Little Topology……Page 43

B. Separation Theorems……Page 59

C. Activity Analysis and the General Production Set……Page 69

A. Introduction……Page 79

B. Concave Programming-Saddle-Point Characterization……Page 86

a. Differentiation……Page 99

b. Unconstrained Maximum……Page 106

D. The Quasi-Saddle-Point Characterization……Page 110

Appendix to Section D: A Further Note on the Arrow-Hurwicz-Uzawa Theorem……Page 126

E. Some Extensions……Page 132

a. Quasi-Concave Programming……Page 133

b. The Vector Maximum Problem……Page 136

c. Quadratic Forms, Hessians, and Second-Order Conditions”……Page 141

F. Some Applications……Page 153

a. Linear Programming……Page 154

b. Consumption Theory……Page 157

c. Production Theory……Page 160

d. Activity Analysis……Page 164

e. Ricardo’s Theory of Comparative Advantage and Mill’s Problem……Page 166

a. The Classical Theory of Optimization……Page 175

b. Comparative Statics……Page 178

c. The Second-Order Conditions and Comparative Statics……Page 179

d. An Example: Hicks-Slutsky Equation……Page 180

e. The Envelope Theorem……Page 184

A. Introduction……Page 193

a. Consumption Set……Page 199

b. Quasi-Ordering and Preference Ordering……Page 200

c. Utility Function……Page 203

d. The Convexity of Preference Ordering……Page 205

C. The Two Classical Propositions of Welfare Economics……Page 209

a. Introduction……Page 228

b. Some Basic Concepts……Page 231

c. Theorems of Debreu and Scarf……Page 237

d. Some Illustrations……Page 242

e. Some Remarks……Page 248

D. Demand Theory……Page 258

a. Various Concepts of Semi continuity……Page 273

b. The Maximum Theorem……Page 277

a. Historical Background……Page 279

b. McKenzie’s Proof……Page 289

Appendix to Section E: On the Uniqueness of Competitive Equilibrium……Page 304

F. Programming, Pareto Optimum, and the Existence of Competitive Equilibria”……Page 309

A. Introduction……Page 319

B. Elements of the Theory of Differential Equations……Page 326

C. The Stability of Competitive Equilibrium-The Historical Background……Page 337

D. A Proof of Global Stability for the Three-Commodity Case (with Gross Substitutability)-An Illustration of the Phase Diagram Technique……Page 345

E. A Proof of Global Stability with Gross Substitutability-The n-commodity Case……Page 349

a. An Example of Gross Substitutability……Page 355

b. Scarfs Counterexample……Page 357

c. Consistency of Various Assumptions……Page 359

d. Nonnegative Prices……Page 360

G. The Tatonnement and the Non-Tatonnement Processes……Page 363

a. The Behavioral Background and the Tiltonnement Process……Page 364

b. The Tiltonnement and the Non-Tatonnement Processes……Page 365

H. Liapunov’s Second Method……Page 371

A. Introduction……Page 383

B. Frobenius Theorems……Page 391

C. Dominant Diagonal Matrices……Page 404

a. Summary of Results……Page 415

b. Input-Output Analysis……Page 418

c. The Expenditure Lag Input-Output Analysis……Page 420

d. Multicountry Income Flows……Page 421

e. A Simple Dynamic Leontief Model……Page 422

f. Stability of Competitive Equilibrium……Page 423

g. Comparative Statics……Page 427

a. Statement of the Problem……Page 434

b. Euler’s Equation……Page 437

c. Solutions of Illustrative Problems……Page 439

a. Introduction……Page 443

b. Spaces of Functions and Optimization……Page 445

c. Euler’s Condition and a Sufficiency Theorem……Page 450

C. A Digression: The Neo-Classical Aggregate Growth Model……Page 456

a. Introduction……Page 468

b. The Case of a Constant Capital: Output Ratio……Page 474

c. Nonlinear Production Function with Infinite Time Horizon……Page 483

a. Introduction……Page 492

b. Model……Page 494

c. The Optimal Attainable Paths……Page 498

d. Sensitivity Analysis: Brock’s Theorem……Page 504

a. Introduction……Page 510

b. Major Theorems……Page 515

c. Two Remarks……Page 521

a. Introduction……Page 527

b. The Output System……Page 531

c. The Price System……Page 541

d. Inequalities and Optimization Model (Solow)……Page 546

e. Morishima’s Model of the Dynamic Leontief System……Page 551

Appendix to Section B: Some Problems in the Dynamic Leontief Model-The One-Industry Illustration……Page 565

a. Introduction……Page 583

b. The Basic Model and Optimality……Page 80

c. Free Disposability and the Condition for Optimality……Page 587

d. The Radner Turnpike Theorem……Page 591

a. Introduction……Page 599

b. The Model……Page 601

c. Finite Horizon: Optimality and Competitiveness……Page 604

d. Optimal Stationary Program……Page 607

e. O.S.P. and Eligibility……Page 611

f. Optimal Program for an Infinite Horizon Problem……Page 618

a. Optimal Control: A Simple Problem and the Maximum Principle……Page 624

b. The Proof of a Simple Case……Page 630

c. Various Cases……Page 633

d. An Illustrative Problem: The Optimal Growth Problem……Page 641

a. Regional Allocation of Investment……Page 651

b. Optimal Growth with a Linear Objective Function……Page 662

a. Constraint: g[x(t), u(t), t] ;:;; 0″……Page 670

b. Hestenes’ Theorem……Page 675

c. A Sufficiency Theorem……Page 684

a. Optimal Growth Once Again……Page 691

b. Two Peak-Load Problems……Page 695

a. Introduction……Page 709

b. The Case of No Adjustment Costs……Page 712

c. The Case with Adjustment Costs……Page 721

d. Some Remarks……Page 727

Name Index……Page 745

Subject Index……Page 751

Alpha C. Chiang, Kevin Wainwright-Fundamental Methods of Mathematical Economics, 4th Edition-McGraw-Hill (2005).pdf
(Got hardcopy 3rd edition, 1984, xii + 788pp)

@book{book:828179,

   title =     {Fundamental Methods of Mathematical Economics, 4th Edition},

   author =    {Alpha C. Chiang, Kevin Wainwright},

   publisher = {McGraw-Hill},

   isbn =      {9780071238236,0071238239,9780070109100,0070109109},

   year =      {2005},

   series =    {},

   edition =   {4},

   volume =    {},

   url =       {http://gen.lib.rus.ec/book/index.php?md5=9F065A54E99296ABB3397A4A0FAD1BA8}}

3rd edition:

The best-selling, best known text in Mathematical Economics course, Chiang teaches the basic mathematical methods indispensable for understanding current economic literature. the book’s patient explanations are written in an informal, non-intimidating style. To underscore the relevance of mathematics to economics, the author allows the economist’s analytical needs to motivate the study of related mathematical techniques; he then illustrates these techniques with appropriate economics models. Graphic illustrations often visually reinforce algebraic results. Many exercise problems serve as drills and help bolster student confidence. These major types of economic analysis are covered: statics, comparative statics, optimization problems, dynamics, and mathematical programming. These mathematical methods are introduced: matrix algebra, differential and integral calculus, differential equations, difference equations, and convex sets.
4th edition

It has been twenty years since the last edition of this classic book. Kevin Wainwright (British Columbia University and Simon Fraser University), a long time user of the text, has executed the perfect revision: he has updated examples, applications and theory without changing the elegant, precise presentation style of Alpha Chiang. Readers will find the wait was worthwhile.

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