Chiang, Alpha C. 1927- creator Wainwright, Kevin. text bibliography mau Boston, Mass McGraw-Hill/Irwin c2005 2005 4th ed. monographic eng

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xix, 688 p. : ill. ; 24 cm. Part 1. Introduction -- 1. The Nature of Mathematical Economics -- 1.1. Mathematical versus Nonmathematical Economics -- 1.2. Mathematical Economics versus Econometrics -- 2. Economic Models -- 2.1. Ingredients of a Mathematical Model -- 2.2. The Real-Number System -- 2.3. The Concept of Sets -- 2.4. Relations and Functions -- 2.5. Types of Function -- 2.6. Functions of Two or More Independent Variables -- 2.7. Levels of Generality -- Part 2. Static (or Equilibrium) Analysis -- 3. Equilibrium Analysis in Economics -- 3.1. The Meaning of Equilibrium -- 3.2. Partial Market Equilibrium--A Linear Model -- 3.3. Partial Market Equilibrium--A Nonlinear Model -- 3.4. General Market Equilibrium -- 3.5. Equilibrium in National-Income Analysis -- 4. Linear Models and Matrix Algebra -- 4.1. Matrices and Vectors -- 4.2. Matrix Operations -- 4.3. Notes on Vector Operations -- 4.4. Commutative, Associative, and Distributive Laws -- 4.5. Identity Matrices and Null Matrices -- 4.6. Transposes and Inverses -- 5. Linear Models and Matrix Algebra (Continued) -- 5.1. Conditions for Nonsingularity of a Matrix -- 5.2. Test of Nonsingularity by Use of Determinant -- 5.3. Basic Properties of Determinants -- 5.4. Finding the Inverse Matrix -- 5.5. Cramer's Rule -- 5.6. Application to Market and National-Income Models -- 5.7. Leontief Input-Output Models -- 5.8. Limitations of Static Analysis -- Part 3. Comparative-Static Analysis -- 6. Comparative Statics and the Concept of Derivative -- 6.1. The Nature of Comparative Statics -- 6.2. Rate of Change and the Derivative -- 6.3. The Derivative and the Slope of a Curve -- 6.4. The Concept of Limit -- 6.5. Digression on Inequalities and Absolute Values -- 6.6. Limit Theorems -- 6.7. Continuity and Differentiability of a Function -- 7. Rules of Differentiation and Their Use in Comparative Statics -- 7.1. Rules of Differentiation for a Function of One Variable -- 7.2. Rules of Differentiation Involving Two or More Functions of the Same Variable -- 7.3. Rules of Differentiation Involving Functions of Different Variables -- 7.4. Partial Differentiation -- 7.5. Applications to Comparative-Static Analysis -- 7.6. Note on Jacobian Determinants -- 8. Comparative-Static Analysis of General-Function Models -- 8.1. Differentials -- 8.2. Total Differentials -- 8.3. Rules of Differentials -- 8.4. Total Derivatives -- 8.5. Derivatives of Implicit Functions -- 8.6. Comparative Statics of General-Function Models -- 8.7. Limitations of Comparative Statics -- Part 4. Optimization Problems -- 9. Optimization: A Special Variety of Equilibrium Analysis -- 9.1. Optimum Values and Extreme Values -- 9.2. Relative Maximum and Minimum: First-Derivative Test -- 9.3. Second and Higher Derivatives -- 9.4. Second-Derivative Test -- 9.5. Digression on Maclaurin and Taylor Series -- 9.6. Nth-Derivative Test for Relative Extremum of a Function of One Variable -- 10. Exponential and Logarithmic Functions -- 10.1. The Nature of Exponential Functions -- 10.2. Natural Exponential Functions and the Problem of Growth -- 10.3. Logarithms -- 10.4. Logarithmic Functions -- 10.5. Derivatives of Exponential and Logarithmic Functions -- 10.6. Optimal Timing -- 10.7. Further Applications of Exponential and Logarithmic Derivatives -- 11. The Case of More than One Choice Variable -- 11.1. The Differential Version of Optimization Conditions -- 11.2. Extreme Values of a Function of Two Variables -- 11.3. Quadratic Forms--An Excursion -- 11.4. Objective Functions with More than Two Variables -- 11.5. Second-Order Conditions in Relation to Concavity and Convexity -- 11.6. Economic Applications -- 11.7. Comparative-Static Aspects of Optimization -- 12. Optimization with Equality Constraints -- 12.1. Effects of a Constraint -- 12.2. Finding the Stationary Values -- 12.3. Second-Order Conditions -- 12.4. Quasiconcavity and Quasiconvexity -- 12.5. Utility Maximization and Consumer Demand -- 12.6. Homogeneous Functions -- 12.7. Least-Cost Combination of Inputs -- 12.8. Some Concluding Remarks -- Part 5. Dynamic Analysis -- 13. Economic Dynamics and Integral Calculus -- 13.1. Dynamics and Integration -- 13.2. Indefinite Integrals -- 13.3. Definite Integrals -- 13.4. Improper Integrals -- 13.5. Some Economic Applications of Integrals -- 13.6. Domar Growth Model -- 14. Continuous Time: First-Order Differential Equations -- 14.1. First-Order Linear Differential Equations with Constant Coefficient and Constant Term -- 14.2. Dynamics of Market Price -- 14.3. Variable Coefficient and Variable Term -- 14.4. Exact Differential Equations -- 14.5. Nonlinear Differential Equations of the First Order and First Degree -- 14.6. The Qualitative-Graphic Approach -- 14.7. Solow Growth Model -- 15. Higher-Order Differential Equations -- 15.1. Second-Order Linear Differential Equations with Constant Coefficients and Constant Term -- 15.2. Complex Numbers and Circular Functions -- 15.3. Analysis of the Complex-Root Case -- 15.4. A Market Model with Price Expectations -- 15.5. The Interaction of Inflation and Unemployment -- 15.6. Differential Equations with a Variable Term -- 15.7. Higher-Order Linear Differential Equations -- 16. Discrete Time: First-Order Difference Equations -- 16.1. Discrete Time, Differences, and Difference Equations -- 16.2. Solving a First-Order Difference Equation -- 16.3. The Dynamic Stability of Equilibrium -- 16.4. The Cobweb Model -- 16.5. A Market Model with Inventory -- 16.6. Nonlinear Difference Equations--The Qualitative-Graphic Approach -- 17. Higher-Order Difference Equations -- 17.1. Second-Order Linear Difference Equations with Constant Coefficients and Constant Term -- 17.2. Samuelson Multiplier-Acceleration Interaction Model -- 17.3. Inflation and Unemployment in Discrete Time -- 17.4. Generalizations to Variable-Term and Higher-Order Equations -- 18. Simultaneous Differential Equations and Difference Equations -- 18.1. The Genesis of Dynamic Systems -- 18.2. Solving Simultaneous Dynamic Equations -- 18.3. Dynamic Input-Output Models -- 18.4. The Inflation-Unemployment Model Once More -- 18.5. Two-Variable Phase Diagrams -- 18.6. Linearization of a Nonlinear Differential-Equation System -- 18.7. Limitations of Dynamic Analysis -- Part 6. Mathematical Programming -- 19. Linear Programming -- 19.1. Simple Examples of Linear Programming -- 19.2. General Formulation of Linear Programs -- 19.3. Convex Sets and Linear Programming -- 19.4. Simplex Method: Finding the Extreme Points -- 19.5. Simplex Method: Finding the Optimal Extreme Point -- 19.6. Further Notes on the Simplex Method -- 20. Linear Programming (Continued) -- 20.1. Duality -- 20.2. Economic Interpretation of a Dual -- 20.3. Activity Analysis: Micro Level -- 20.4. Activity Analysis: Macro Level -- 21. Nonlinear Programming -- 21.1. The Nature of Nonlinear Programming -- 21.2. Kuhn-Tucker Conditions -- 21.3. The Constraint Qualification -- 21.4. Kuhn-Tucker Sufficiency Theorem: Concave Programming -- 21.5. Arrow-Enthoven Sufficiency Theorem: Quasiconcave Programming -- 21.6. Economic Applications -- 21.7. Limitations of Mathematical Programming -- The Greek Alphabet -- Mathematical Symbols -- A Short Reading List -- Answers to Selected Exercise Problems. Alpha C. Chiang, Kevin Wainwright. Includes bibliographical references p. 659-661 and index. Economics, Mathematical Mathématiques économiques Wiskundige economie HB135 .C47 2005 330.0151 CHF 83.03 0070109109 (alk. paper) 2004059546 http://www.loc.gov/catdir/enhancements/fy0618/2004059546-t.html http://www.loc.gov/catdir/enhancements/fy0632/2004059546-d.html http://www.loc.gov/catdir/enhancements/fy0618/2004059546-t.html http://www.loc.gov/catdir/enhancements/fy0632/2004059546-d.html DLC 040910 20160508142210.0 5833829