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Book Cover
PRINTED BOOKS
Author Silberberg, Eugene.

Title The structure of economics : a mathematical analysis / Eugene Silberberg.

Published New York : McGraw-Hill Pub. Co., [1990]
©1990

Copies

Location Call No. Status
 UniM Bund  330.0151 SILB {Bund81 20190820}    AVAILABLE
Edition 2nd ed.
Physical description xvi, 686 pages : illustrations ; 24 cm
Bibliography Includes bibliographical references and index.
Contents 1 Comparative Statics and the Paradigm of Economics 1 -- 1.2 Marginalist Paradigm 3 -- 1.3 Theories and Refutable Propositions 9 -- 1.4 Theories versus Models; Comparative Statics 14 -- 1.5 Examples of Comparative Statics 16 -- 2 Review of Calculus (One Variable) 26 -- 2.1 Functions, Limits, Continuity 26 -- 2.2 Derivatives 31 -- 2.3 Differentials 34 -- 2.4 Chain Rule 36 -- 2.5 Product and Quotient Rules 38 -- 2.6 Implicit Functions 39 -- 2.7 Elasticity 40 -- 2.8 Maxima and Minima 41 -- 2.9 Two Important Functions: y = ex; y = logex 46 -- 2.10 Mean Value Theorem 53 -- 2.11 Taylor's Series 54 -- 2.12 Integration 58 -- 2.13 Differential Equations 65 -- 3 Functions of Several Variables 68 -- 3.1 Functions of Several Variables 68 -- 3.2 Level Curves: I 69 -- 3.3 Partial Derivatives 70 -- 3.4 Total Differential of a Function of Several Variables 76 -- 3.5 Chain Rule 79 -- 3.6 Level Curves: II 86 -- 3.7 Homogeneous Functions and Euler's Theorem 92 -- 4 Profit Maximization 107 -- 4.1 Unconstrained Maxima and Minima: First-Order Necessary Conditions 107 -- 4.2 Sufficient Conditions for Maxima and Minima: Two Variables 109 -- 4.3 An Extended Footnote 113 -- 4.4 An Application of Maximizing Behavior: The Profit-Maximizing Firm 114 -- 4.5 Homogeneity of the Demand and Supply Functions; Elasticities 122 -- 4.6 Long Run and the Short Run: An Example of the Le Chatelier Principle 124 -- 4.7 Analysis of Finite Changes: A Digression 130 -- 5 Matrices and Determinants 135 -- 5.1 Matrices 135 -- 5.2 Determinants, Cramer's Rule 137 -- 5.3 Implicit Function Theorem 144 -- 6 Comparative Statics: The Traditional Methodology 156 -- 6.1 Introduction; Profit Maximization Once More 156 -- 6.2 Generalizations to n Variables 160 -- 6.3 Theory of Constrained Maxima and Minima: First-Order Necessary Conditions 166 -- 6.4 Constrained Maximization with More than One Constraint: A Digression 171 -- 6.5 Second-Order Conditions 173 -- 6.6 General Methodology 180 -- 7 Envelope Theorem and Duality 190 -- 7.1 History of the Problem 190 -- 7.2 Profit Function 192 -- 7.3 General Comparative Statics Analysis: Unconstrained Models 195 -- 7.4 Models with Constraints 198 -- 7.5 Comparative Statics of Maximization Systems 210 -- 8 Derivation of Cost Functions 223 -- 8.1 Cost Function 223 -- 8.2 Marginal Cost 226 -- 8.3 Average Cost 227 -- 8.4 A General Relationship between Average and Marginal Costs 229 -- 8.5 Cost Minimization Problem 230 -- 8.6 Factor Demand Curves 236 -- 8.7 Comparative Statics Relations: The Traditional Methodology 241 -- 8.8 Comparative Statics Relations Using Duality Theory 249 -- 8.9 Elasticities; Further Properties of the Factor-Demand Curves 258 -- 8.10 Average Cost Curve 263 -- 8.11 Analysis of Firms in Long-Run Competitive Equilibrium 265 -- 9 Cost and Production Functions: Special Topics 272 -- 9.1 Homogeneous and Homothetic Production Functions 272 -- 9.2 Cost Function: Further Properties 275 -- 9.3 Duality of Cost and Production Functions 281 -- 9.4 Elasticity of Substitution; the Constant-Elasticity-of-Substitution (CES) Production Function 285 -- 10 Derivation of Consumer Demand Functions 299 -- 10.1 Introductory Remarks: The Behavioral Postulates 299 -- 10.2 Utility Maximization 308 -- 10.3 Relationship between the Utility Maximization Model and the Cost Minimization Model 319 -- 10.4 Comparative Statics of the Utility Maximization Model; the Traditional Derivation of the Slutsky Equation 323 -- 10.5 Modern Derivation of the Slutsky Equation 329 -- 10.6 Elasticity Formulas for Money-Income-Held-Constant and Real-Income-Held-Constant Demand Curves 338 -- 10.7 Special Topics 344 -- 11 Special Topics in Consumer Theory 362 -- 11.1 Revealed Preference and Exchange 362 -- 11.2 Strong Axiom of Revealed Preference and Integrability 370 -- 11.3 Composite Commodity Theorem 381 -- 11.4 Household Production Functions 389 -- 11.5 Consumer's Surplus 396 -- 11.6 Empirical Estimation and Functional Forms 405 -- 12 Intertemporal Choice 416 -- 12.1 n-Period Utility Maximization 416 -- 12.2 Determination of the Interest Rate 430 -- 12.3 Stocks and Flows 433 -- 13 Behavior under Uncertainty 440 -- 13.1 Uncertainty and Probability 440 -- 13.2 Specification of Preferences 445 -- 13.3 Risk Aversion 449 -- 13.4 Comparative Statics 455 -- 14 Maximization with Inequality and Nonnegativity Constraints 462 -- 14.1 Nonnegativity 462 -- 14.2 Inequality Constraints 470 -- 14.3 Saddlepoint Theorem 476 -- 14.4 Nonlinear Programming 480 -- 14.5 An "Adding-Up" Theorem 483 -- 15 General Equilibrium I: Linear Models 491 -- 15.1 Introduction: Fixed-Coefficient Technology 491 -- 15.2 Linear Activity Analysis Model: A Specific Example 500 -- 15.3 Rybczynski Theorem 507 -- 15.4 Stolper-Samuelson Theorem 509 -- 15.5 Dual Problem 510 -- 15.6 Simplex Algorithm 520 -- 16 General Equilibrium II: Nonlinear Models 531 -- 16.1 Tangency Conditions 531 -- 16.2 General Comparative Statics Results 539 -- 16.3 Factor Price Equalization and Related Theorems 544 -- 16.4 Applications of the Two-Good, Two-Factor Model 563 -- 17 Welfare Economics 573 -- 17.1 Social Welfare Functions 573 -- 17.2 Pareto Conditions 577 -- 17.3 Classical "Theorems" of Welfare Economics 587 -- 17.4 A "Nontheorem" about Taxation 589 -- 17.5 Theory of the Second Best 591 -- 17.6 Public Goods 593 -- 17.7 Consumer's Surplus as a Measure of Welfare Gains and Losses 596 -- 17.8 Property Rights and Transactions Costs 600 -- 18 Resource Allocation over Time: Optimal Control Theory 613 -- 18.1 Meaning of Dynamics 613 -- 18.2 Solution to the Problem 617 -- 18.3 Solutions to Differential Equations 628 -- 18.4 Interpretations and Solutions 632 -- 19 Equilibrium, Disequilibrium, and the Stability of Markets 647 -- 19.1 Three Sources of Refutable Hypotheses 647 -- 19.2 Equilibrium and Stability 651 -- 19.3 Multimarket Equilibrium and Stability 656 -- 19.4 Game Theory 662 -- Hints and Answers 671.
Summary Addressing the most significant trends in microeconomics today, The Structure of Economics offers a unique blend of mathematical economics and microeconomic theory. Written in a conversational style, it presents and develops the mathematical tools necessary to enable readers to successfully execute economic analyses. The book carefully concentrates on those techniques and methods most widely used by economists, and instructs readers on the proper use of these techniques.
The author presents the theory of comparative statics as the mathematical tool for deriving refutable propositions, and puts constant emphasis on the derivations of the propositions as the goal of empirical economics. In this way, readers will understand the usefulness of mathematics in economic science, not just the mathematical fine points. For a better understanding of the related mathematics, the author has explained every function, formula, and equation in its relation to applied economics. Along with a consistent emphasis on methodology, illuminating examples are found throughout to illustrate the crucial points of the analysis.
The new edition has been thoroughly revised to reflect both the latest theoretical developments in microeconomics as well as state-of-the-art mathematical techniques. The Second Edition now includes such topics as the theory of risk, dynamic optimization, and functional forms.
Subject Economics, Mathematical.
Microeconomics -- Econometric models.
Equilibrium (Economics) -- Econometric models.
ISBN 0070575509