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The structure of economics : a mathematical analysis / Eugene Silberberg, Wing Suen

By: Silberberg, Eugene [autor].
Contributor(s): Suen, Wing [autor].
Publisher: New York : Mc Graw Hill, ©2001Edition: 3th ed.Description: xvii, 668 páginas : ilustraciones, tablas ; 24 cm.Content type: texto Media type: no mediado Carrier type: volumenISBN: 0072343524.Subject(s): Economía matemática | Economía matemática | MicroeconomíaDDC classification: 330.0151
Contents:
Comparative statics and the paradigm of econometric. -- Review of calculus (one variable). -- Function of several variables. -- Profit maximization. -- Matrices and determinants. -- Comparative statics: the traditional methodology. -- The envelope theorem and duality. -- the derivation of cost function. -- Cost production functions: special topics. -- The derivation of consumer demand functions. -- Special in consumer theory. -- Intertemporal choice. -- Behavior under uncertainty. -- Maximization with inequality and nonnegativity constraints. -- Contracts and incentives. -- Markets with imperfect information. -- General equilibrium I: linear models. -- General equilibrium II: Nonlinear models. -- Welfare economics. -- Resource allocation over time: optimal control theory.
This text combines mathematical economics with microeconomic theory and can be required or recommended as part of a course in graduate microeconomic theory, advanced undergraduate or graduate-level mathematical economics, or any advanced topics course. It also has reference value for international, library, professional and reference markets. This revision addresses significant new topics--the theory of contracts and markets with imperfect information--that have recently become prominent in the microeconomics literature.
List(s) this item appears in: Economía
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Colección general 330.0151 Si322 (Browse shelf) 3th edition 2001 Ej.1 Available 0000047758
Book Book B. Campus los Cerros
Colección general
Colección general 330.0151 Si322 (Browse shelf) 3th edition 2001 Ej.2 Available 0000047759
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Enhanced descriptions from Syndetics:

This text aims to develop the mathematical tools required when performing economic analyses.

Includes bibliography and index.

Comparative statics and the paradigm of econometric. -- Review of calculus (one variable). -- Function of several variables. -- Profit maximization. -- Matrices and determinants. -- Comparative statics: the traditional methodology. -- The envelope theorem and duality. -- the derivation of cost function. -- Cost production functions: special topics. -- The derivation of consumer demand functions. -- Special in consumer theory. -- Intertemporal choice. -- Behavior under uncertainty. -- Maximization with inequality and nonnegativity constraints. -- Contracts and incentives. -- Markets with imperfect information. -- General equilibrium I: linear models. -- General equilibrium II: Nonlinear models. -- Welfare economics. -- Resource allocation over time: optimal control theory.

This text combines mathematical economics with microeconomic theory and can be required or recommended as part of a course in graduate microeconomic theory, advanced undergraduate or graduate-level mathematical economics, or any advanced topics course. It also has reference value for international, library, professional and reference markets. This revision addresses significant new topics--the theory of contracts and markets with imperfect information--that have recently become prominent in the microeconomics literature.

Table of contents provided by Syndetics

  • Preface (p. xv)
  • 1 Comparative Statics and the Paradigm of Economics (p. 1)
  • 1.1 Introduction (p. 1)
  • 1.2 The Marginalist Paradigm (p. 3)
  • 1.3 Theories and Refutable Propositions (p. 9)
  • The Structure of Theories (p. 10)
  • Refutable Propositions (p. 12)
  • 1.4 Theories versus Models; Comparative Statics (p. 14)
  • 1.5 Examples of Comparative Statics (p. 16)
  • Problems (p. 23)
  • Bibliography (p. 25)
  • 2 Review of Calculus (One Variable) (p. 26)
  • 2.1 Functions, Limits, Continuity (p. 26)
  • Limits, Continuity (p. 28)
  • Problems (p. 30)
  • 2.2 Derivatives (p. 31)
  • Differentiation of Polynomials (p. 32)
  • Problems (p. 34)
  • 2.3 Differentials (p. 34)
  • Problems (p. 36)
  • 2.4 The Chain Rule (p. 36)
  • 2.5 The Product and Quotient Rules (p. 38)
  • The Product Rule (p. 38)
  • The Quotient Rule (p. 39)
  • 2.6 Implicit Functions (p. 39)
  • 2.7 Elasticity (p. 40)
  • 2.8 Maxima and Minima (p. 41)
  • Problems (p. 45)
  • 2.9 Two Important Functions: y = ex; y = logex (p. 46)
  • 1. The Function y = ex (p. 46)
  • 2. The Function y = logex (p. 50)
  • Problems (p. 52)
  • 2.10 The Mean Value Theorem (p. 53)
  • 2.11 Taylor's Series (p. 54)
  • Applications of Taylor's Series: Derivation of the First- and Second-Order Conditions for a Maximum; Concavity and Convexity (p. 56)
  • 2.12 Integration (p. 58)
  • Indefinite Integrals (p. 58)
  • The Integral as the Area under a Curve (p. 60)
  • Problems (p. 64)
  • 2.13 Differential Equations (p. 65)
  • Problems (p. 67)
  • Selected References (p. 67)
  • 3 Functions of Several Variables (p. 68)
  • 3.1 Functions of Several Variables (p. 68)
  • 3.2 Level Curves: I (p. 69)
  • 3.3 Partial Derivatives (p. 70)
  • 3.4 The Total Differential of a Function of Several Variables (p. 76)
  • Problems (p. 78)
  • 3.5 The Chain Rule (p. 79)
  • Monotonic Transformations (p. 82)
  • Second Derivatives by the Chain Rule (p. 84)
  • 3.6 Level Curves: II (p. 86)
  • Convexity of the Level Curves (p. 89)
  • Problems (p. 91)
  • 3.7 Homogeneous Functions and Euler's Theorem (p. 92)
  • Problems (p. 101)
  • Appendix (p. 101)
  • Selected References (p. 106)
  • 4 Profit Maximization (p. 107)
  • 4.1 Unconstrained Maxima and Minima: First-Order Necessary Conditions (p. 107)
  • 4.2 Sufficient Conditions for Maxima and Minima: Two Variables (p. 109)
  • Problems (p. 112)
  • 4.3 An Extended Footnote (p. 113)
  • 4.4 An Application of Maximizing Behavior: The Profit-Maximizing Firm (p. 114)
  • The Supply Function (p. 121)
  • 4.5 Homogeneity of the Demand and Supply Functions; Elasticities (p. 122)
  • Elasticities (p. 123)
  • 4.6 The Long Run and the Short Run: An Example of the Le Chatelier Principle (p. 124)
  • A More Fundamental Look at the Le Chatelier Principle (p. 126)
  • Problems (p. 128)
  • 4.7 Analysis of Finite Changes: A Digression (p. 130)
  • Appendix (p. 131)
  • Taylor Series for Functions of Several Variables (p. 131)
  • Concavity and the Maximum Conditions (p. 132)
  • Selected References (p. 133)
  • 5 Matrices and Determinants (p. 135)
  • 5.1 Matrices (p. 135)
  • 5.2 Determinants, Cramer's Rule (p. 137)
  • 5.3 The Implicit Function Theorem (p. 144)
  • Problems (p. 149)
  • Appendix (p. 149)
  • Simple Matrix Operations (p. 149)
  • The Rank of a Matrix (p. 151)
  • The Inverse of a Matrix (p. 153)
  • Orthogonality (p. 154)
  • Problems (p. 155)
  • Selected References (p. 155)
  • 6 Comparative Statics: The Traditional Methodology (p. 156)
  • 6.1 Introduction; Profit Maximization Once More (p. 156)
  • 6.2 Generalizations to n Variables (p. 160)
  • First-Order Necessary Conditions (p. 160)
  • Second-Order Sufficient Conditions (p. 160)
  • Profit Maximization: n Factors (p. 163)
  • 6.3 The Theory of Constrained Maxima and Minima: First-Order Necessary Conditions (p. 166)
  • 6.4 Constrained Maximization with More than One Constraint: A Digression (p. 171)
  • 6.5 Second-Order Conditions (p. 173)
  • The Geometry of Constrained Maximization (p. 176)
  • 6.6 General Methodology (p. 180)
  • Problems (p. 187)
  • Selected References (p. 189)
  • 7 The Envelope Theorem and Duality (p. 190)
  • 7.1 History of the Problem (p. 190)
  • 7.2 The Profit Function (p. 192)
  • 7.3 General Comparative Statics Analysis: Unconstrained Models (p. 195)
  • 7.4 Models with Constraints (p. 198)
  • Comparative Statics: Primal-Dual Analysis (p. 200)
  • An Important Special Case (p. 203)
  • Interpretation of the Lagrange Multiplier (p. 204)
  • Problems (p. 207)
  • 7.5 The Comparative Statics of Maximization Systems (p. 210)
  • Reciprocity Relations (p. 214)
  • Qualitative Results (p. 215)
  • Le Chatelier Effects (p. 216)
  • Bibliography (p. 222)
  • 8 The Derivation of Cost Functions (p. 223)
  • 8.1 The Cost Function (p. 223)
  • 8.2 Marginal Cost (p. 226)
  • 8.3 Average Cost (p. 227)
  • 8.4 A General Relationship between Average and Marginal Costs (p. 229)
  • 8.5 The Cost Minimization Problem (p. 230)
  • 8.6 The Factor Demand Curves (p. 236)
  • Interpretation of the Lagrange Multiplier (p. 237)
  • 8.7 Comparative Statics Relations: The Traditional Methodology (p. 241)
  • 8.8 Comparative Statics Relations Using Duality Theory (p. 249)
  • Reciprocity Conditions (p. 250)
  • Cost Curves in the Short and Long Run (p. 252)
  • Factor Demands in the Short and Long Run (p. 254)
  • Relation to Profit Maximization (p. 256)
  • 8.9 Elasticities; Further Properties of the Factor-Demand Curves (p. 258)
  • Homogeneity (p. 259)
  • Output Elasticities (p. 262)
  • 8.10 The Average Cost Curve (p. 263)
  • 8.11 Analysis of Firms in Long-Run Competitive Equilibrium (p. 265)
  • Analysis of Factor Demands in the Long Run (p. 267)
  • Problems (p. 269)
  • Selected References (p. 271)
  • 9 Cost and Production Functions: Special Topics (p. 272)
  • 9.1 Homogeneous and Homothetic Production Functions (p. 272)
  • 9.2 The Cost Function: Further Properties (p. 275)
  • Homothetic Functions (p. 279)
  • 9.3 The Duality of Cost and Production Functions (p. 281)
  • The Importance of Duality (p. 285)
  • 9.4 Elasticity of Substitution; the Constant-Elasticity-of-Substitution (CES) Production Function (p. 285)
  • Generalization to n Factors (p. 296)
  • The Generalized Leontief Cost Function (p. 297)
  • Problems (p. 297)
  • Bibliography (p. 298)
  • 10 The Derivation of Consumer Demand Functions (p. 299)
  • 10.1 Introductory Remarks: The Behavioral Postulates (p. 299)
  • 10.2 Utility Maximization (p. 308)
  • Interpretation of the Lagrange Multiplier (p. 313)
  • Roy's Identity (p. 315)
  • 10.3 The Relationship between the Utility Maximization Model and the Cost Minimization Model (p. 319)
  • 10.4 The Comparative Statics of the Utility Maximization Model; the Traditional Derivation of the Slutsky Equation (p. 323)
  • 10.5 The Modern Derivation of the Slutsky Equation (p. 329)
  • Conditional Demands (p. 333)
  • The Addition of a New Commodity (p. 335)
  • 10.6 Elasticity Formulas for Money-Income-Held-Constant and Real-Income-Held-Constant Demand Curves (p. 338)
  • The Slutsky Equation in Elasticity Form (p. 338)
  • Compensated Demand Curves (p. 341)
  • 10.7 Special Topics (p. 344)
  • Separable Utility Functions (p. 344)
  • The Labor-Leisure Choice (p. 346)
  • Slutsky versus Hicks Compensations (p. 351)
  • The Division of Labor Is Limited by the Extent of the Market (p. 353)
  • Problems (p. 357)
  • Selected References (p. 360)
  • 11 Special Topics in Consumer Theory (p. 362)
  • 11.1 Revealed Preference and Exchange (p. 362)
  • 11.2 The Strong Axiom of Revealed Preference and Integrability (p. 370)
  • Integrability (p. 373)
  • 11.3 The Composite Commodity Theorem (p. 381)
  • Shipping the Good Apples Out (p. 384)
  • 11.4 Household Production Functions (p. 389)
  • Comparative Statics (p. 393)
  • 11.5 Consumer's Surplus (p. 396)
  • Example (p. 402)
  • Empirical Approximation (p. 403)
  • 11.6 Empirical Estimation and Functional Forms (p. 405)
  • Linear Expenditure System (p. 406)
  • CES Utility Function (p. 407)
  • Indirect Addilog Utility Function (p. 408)
  • Translog Specifications (p. 409)
  • Almost Ideal Demand System (p. 411)
  • Problems (p. 412)
  • References on Theory (p. 414)
  • References on Functional Forms (p. 415)
  • 12 Intertemporal Choice (p. 416)
  • 12.1 n-Period Utility Maximization (p. 416)
  • Time Preference (p. 419)
  • The Fisher Separation Theorem (p. 426)
  • Real versus Nominal Interest Rates (p. 428)
  • 12.2 The Determination of the Interest Rate (p. 430)
  • 12.3 Stocks and Flows (p. 433)
  • Problems (p. 437)
  • Selected References (p. 438)
  • 13 Behavior under Uncertainty (p. 440)
  • 13.1 Uncertainty and Probability (p. 440)
  • Random Variables and Probability Distributions (p. 441)
  • Mean and Variance (p. 442)
  • 13.2 Specification of Preferences (p. 445)
  • State Preference Approach (p. 445)
  • The Expected Utility Hypothesis (p. 446)
  • Cardinal and Ordinal Utility (p. 447)
  • 13.3 Risk Aversion (p. 449)
  • Measures of Risk Aversion (p. 451)
  • Gambling, Insurance and Diversification (p. 452)
  • Problems (p. 454)
  • 13.4 Comparative Statics (p. 455)
  • Allocation of Wealth to Risky Assets (p. 455)
  • Problems (p. 456)
  • Output Decisions under Price Uncertainty (p. 456)
  • Increases in Riskiness (p. 458)
  • References (p. 460)
  • 14 Maximization with Inequality and Nonnegativity Constraints (p. 462)
  • 14.1 Nonnegativity (p. 462)
  • Functions of Two or More Variables (p. 467)
  • 14.2 Inequality Constraints (p. 470)
  • 14.3 The Saddlepoint Theorem (p. 476)
  • 14.4 Nonlinear Programming (p. 480)
  • 14.5 An "Adding-Up" Theorem (p. 483)
  • Problems (p. 485)
  • Appendix (p. 487)
  • Bibliography (p. 490)
  • 15 General Equilibrium I: Linear Models (p. 491)
  • 15.1 Introduction: Fixed-Coefficient Technology (p. 491)
  • 15.2 The Linear Activity Analysis Model: A Specific Example (p. 500)
  • 15.3 The Rybczynski Theorem (p. 507)
  • 15.4 The Stolper-Samuelson Theorem (p. 509)
  • 15.5 The Dual Problem (p. 510)
  • 15.6 The Simplex Algorithm (p. 520)
  • Mathematical Prerequisites (p. 520)
  • The Simplex Algorithm: Example (p. 524)
  • Problems (p. 528)
  • Bibliography (p. 530)
  • 16 General Equilibrium II: Nonlinear Models (p. 531)
  • 16.1 Tangency Conditions (p. 531)
  • 16.2 General Comparative Statics Results (p. 539)
  • 16.3 The Factor Price Equalization and Related Theorems (p. 544)
  • The Four-Equation Model (p. 550)
  • The Factor Price Equalization Theorem (p. 553)
  • The Stolper-Samuelson Theorems (p. 554)
  • The Rybczynski Theorem (p. 561)
  • 16.4 Applications of the Two-Good, Two-Factor Model (p. 563)
  • Summary and Conclusions (p. 567)
  • Problems (p. 570)
  • Bibliography (p. 571)
  • 17 Welfare Economics (p. 573)
  • 17.1 Social Welfare Functions (p. 573)
  • 17.2 The Pareto Conditions (p. 577)
  • Pure Exchange (p. 578)
  • Production (p. 581)
  • 17.3 The Classical "Theorems" of Welfare Economics (p. 587)
  • 17.4 A "Nontheorem" about Taxation (p. 589)
  • 17.5 The Theory of the Second Best (p. 591)
  • 17.6 Public Goods (p. 593)
  • 17.7 Consumer's Surplus as a Measure of Welfare Gains and Losses (p. 596)
  • 17.8 Property Rights and Transactions Costs (p. 600)
  • Private Property (p. 602)
  • Common Property (p. 603)
  • The Coase Theorem (p. 604)
  • The Theory of Share Tenancy: An Application of the Coase Theorem (p. 607)
  • Problems (p. 611)
  • Bibliography (p. 612)
  • 18 Resource Allocation over Time: Optimal Control Theory (p. 613)
  • 18.1 The Meaning of Dynamics (p. 613)
  • Brief History (p. 617)
  • 18.2 Solution to the Problem (p. 617)
  • The Calculus of Variations (p. 622)
  • Endpoint (Transversality) Conditions (p. 624)
  • Autonomous Problems (p. 625)
  • Sufficient Conditions (p. 627)
  • 18.3 Solutions to Differential Equations (p. 628)
  • Simultaneous Differential Equations (p. 631)
  • 18.4 Interpretations and Solutions (p. 632)
  • Intertemporal Choice (p. 632)
  • Harvesting a Renewable Resource (p. 635)
  • Capital Utilization (p. 639)
  • Problems (p. 644)
  • Selected References (p. 645)
  • 19 Equilibrium, Disequilibrium, and the Stability of Markets (p. 647)
  • 19.1 Three Sources of Refutable Hypotheses (p. 647)
  • 19.2 Equilibrium and Stability (p. 651)
  • Walrasian Stability (p. 652)
  • Marshallian Stability (p. 655)
  • 19.3 Multimarket Equilibrium and Stability (p. 656)
  • Open Systems: Stability (p. 657)
  • Closed Economics (p. 661)
  • 19.4 Game Theory (p. 662)
  • 19.5 Overview and Conclusions (p. 666)
  • Problems (p. 669)
  • Bibliography (p. 669)
  • Hints and Answers (p. 671)
  • Index (p. 681)

Author notes provided by Syndetics

Eugene Silberberg is Professor of Economics at the University of Washington in Seattle. He received his B.S. from the City College of New York and his Ph.D. from Purdue. His publications contributed to the development of modern duality theory in economics. He has specialized in teaching the application of these techniques to important economic models.

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