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Fundamental Methods of Mathematical Economics

by ;
Edition:
4th
ISBN13:

9780070109100

ISBN10:
0070109109
Format:
Hardcover
Pub. Date:
2/2/2005
Publisher(s):
McGraw-Hill/Irwin
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Summary

It has been 20 years since the last edition of this classic text. Kevin Wainwright, a long time user of the text (British Columbia University and Simon Fraser University), 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.

Table of Contents

PART ONE INTRODUCTION
1(29)
The Nature of Mathematical Economics
2(3)
Mathematical versus Nonmathematical Economics
2(2)
Mathematical Economics versus Econometrics
4(1)
Economic Models
5(24)
Ingredients of a Mathematical Model
5(2)
Variables, Constants, and Parameters
5(1)
Equations and Identities
6(1)
The Real-Number System
7(1)
The Concept of Sets
8(7)
Set Notation
9(1)
Relationships between Sets
9(2)
Operations on Sets
11(1)
Laws of Set Operations
12(2)
Exercise 2.3
14(1)
Relations and Functions
15(5)
Ordered Pairs
15(1)
Relations and Functions
16(3)
Exercise 2.4
19(1)
Types of Function
20(5)
Constant Functions
20(1)
Polynomial Functions
20(1)
Rational Functions
21(2)
Nonalgebraic Functions
23(1)
A Digression on Exponents
23(1)
Exercise 2.5
24(1)
Functions of Two or More Independent Variables
25(2)
Levels of Generality
27(2)
PART TWO STATIC (OR EQUILIBRIUM) ANALYSIS
29(94)
Equilibrium Analysis in Economics
30(18)
The Meaning of Equilibrium
30(1)
Partial Market Equilibrium---A Linear Model
31(4)
Constructing the Model
31(2)
Solution by Elimination of Variables
33(1)
Exercise 3.2
34(1)
Partial Market Equilibrium---A Nonlinear Model
35(5)
Quadratic Equation versus Quadratic Function
35(1)
The Quadratic Formula
36(1)
Another Graphical Solution
37(1)
Higher-Degree Polynomial Equations
38(2)
Exercise 3.3
40(1)
General Market Equilibrium
40(6)
Two-Commodity Market Model
41(1)
Numerical Example
42(1)
n-Commodity Case
43(1)
Solution of a General-Equation System
44(1)
Exercise 3.4
45(1)
Equilibrium in National-Income Analysis
46(2)
Exercise 3.5
47(1)
Linear Models and Matrix Algebra
48(34)
Matrices and Vectors
49(2)
Matrices as Arrays
49(1)
Vectors as Special Matrices
50(1)
Exercise 4.1
51(1)
Matrix Operations
51(8)
Addition and Subtraction of Matrices
51(1)
Scalar Multiplication
52(1)
Multiplication of Matrices
53(3)
The Question of Division
56(1)
The Σ Notation
56(2)
Exercise 4.2
58(1)
Notes on Vector Operations
59(8)
Multiplication of Vectors
59(1)
Geometric Interpretation of Vector Operations
60(2)
Linear Dependence
62(1)
Vector Space
63(2)
Exercise 4.3
65(2)
Commutative, Associative, and Distributive Laws
67(3)
Matrix Addition
67(1)
Matrix Multiplication
68(1)
Exercise 4.4
69(1)
Identity Matrices and Null Matrices
70(3)
Identity Matrices
70(1)
Null Matrices
71(1)
Idiosyncrasies of Matrix Algebra
72(1)
Exercise 4.5
72(1)
Transposes and Inverses
73(5)
Properties of Transposes
74(1)
Inverses and Their Properties
75(2)
Inverse Matrix and Solution of Linear-Equation System
77(1)
Exercise 4.6
78(1)
Finite Markov Chains
78(4)
Special Case: Absorbing Markov Chains
81(1)
Exercise 4.7
81(1)
Linear Models and Matrix Algebra (Continued)
82(41)
Conditions for Nonsingularity of a Matrix
82(6)
Necessary versus Sufficient Conditions
82(2)
Conditions for Nonsingularity
84(1)
Rank of a Matrix
85(2)
Exercise 5.1
87(1)
Test of Nonsingularity by Use of Determinant
88(6)
Determinants and Nonsingularity
88(1)
Evaluating a Third-Order Determinant
89(2)
Evaluating an nth-Order Determinant by Laplace Expansion
91(2)
Exercise 5.2
93(1)
Basic Properties of Determinants
94(5)
Determinantal Criterion for Nonsingularity
96(1)
Rank of a Matrix Redefined
97(1)
Exercise 5.3
98(1)
Finding the Inverse Matrix
99(4)
Expansion of a Determinant by Alien Cofactors
99(1)
Matrix Inversion
100(2)
Exercise 5.4
102(1)
Cramer's Rule
103(4)
Derivation of the Rule
103(2)
Note on Homogeneous-Equation Systems
105(1)
Solution Outcomes for a Linear-Equation System
106(1)
Exercise 5.5
107(1)
Application to Market and National-Income Models
107(5)
Market Model
107(1)
National-Income Model
108(1)
IS-LM Model: Closed Economy
109(2)
Matrix Algebra versus Elimination of Variables
111(1)
Exercise 5.6
111(1)
Leontief Input-Output Models
112(8)
Structure of an Input-Output Model
112(1)
The Open Model
113(2)
A Numerical Example
115(1)
The Existence of Nonnegative Solutions
116(2)
Economic Meaning of the Hawkins-Simon Condition
118(1)
The Closed Model
119(1)
Exercise 5.7
120(1)
Limitations of Static Analysis
120(3)
PART THREE COMPARATIVE-STATIC ANALYSIS
123(96)
Comparative Statics and the Concept of Derivative
124(24)
The Nature of Comparative Statics
124(1)
Rate of Change and the Derivative
125(3)
The Difference Quotient
125(1)
The Derivative
126(1)
Exercise 6.2
127(1)
The Derivative and the Slope of a Curve
128(1)
The Concept of Limit
129(7)
Left-Side Limit and Right-Side Limit
129(1)
Graphical Illustrations
130(1)
Evaluation of a Limit
131(2)
Formal View of the Limit Concept
133(2)
Exercise 6.4
135(1)
Digression on Inequalities and Absolute Values
136(3)
Rules of Inequalities
136(1)
Absolute Values and Inequalities
137(1)
Solution of an Inequality
138(1)
Exercise 6.5
139(1)
Limit Theorems
139(2)
Theorems Involving a Single Function
139(1)
Theorems Involving Two Functions
140(1)
Limit of a Polynomial Function
141(1)
Exercise 6.6
141(1)
Continuity and Differentiability of a Function
141(7)
Continuity of a Function
141(1)
Polynomial and Rational Functions
142(1)
Differentiability of a Function
143(3)
Exercise 6.7
146(2)
Rules of Differentiation and Their Use in Comparative Statics
148(30)
Rules of Differentiation for a Function of One Variable
148(4)
Constant-Function Rule
148(1)
Power-Function Rule
149(2)
Power-Function Rule Generalized
151(1)
Exercise 7.1
152(1)
Rules of Differentiation Involving Two or More Functions of the Same Variable
152(9)
Sum-Difference Rule
152(3)
Product Rule
155(1)
Finding Marginal-Revenue Function from Average-Revenue Function
156(2)
Quotient Rule
158(1)
Relationship Between Marginal-Cost and Average-Cost Functions
159(1)
Exercise 7.2
160(1)
Rules of Differentiation Involving Functions of Different Variables
161(4)
Chain Rule
161(2)
Inverse-Function Rule
163(2)
Exercise 7.3
165(1)
Partial Differentiation
165(5)
Partial Derivatives
165(1)
Techniques of Partial Differentiation
166(1)
Geometric Interpretation of Partial Derivatives
167(1)
Gradient Vector
168(1)
Exercise 7.4
169(1)
Applications to Comparative-Static Analysis
170(5)
Market Model
170(2)
National-Income Model
172(1)
Input-Output Model
173(2)
Exercise 7.5
175(1)
Note on Jacobian Determinants
175(3)
Exercise 7.6
177(1)
Comparative-Static Analysis of General-Function Models
178(41)
Differentials
179(5)
Differentials and Derivatives
179(2)
Differentials and Point Elasticity
181(3)
Exercise 8.1
184(1)
Total Differentials
184(3)
Exercise 8.2
186(1)
Rules of Differentials
187(2)
Exercise 8.3
189(1)
Total Derivatives
189(5)
Finding the Total Derivative
189(2)
A Variation on the Theme
191(1)
Another Variation on the Theme
192(1)
Some General Remarks
193(1)
Exercise 8.4
193(1)
Derivatives of Implicit Functions
194(11)
Implicit Functions
194(2)
Derivatives of Implicit Functions
196(3)
Extension to the Simultaneous-Equation Case
199(5)
Exercise 8.5
204(1)
Comparative Statics of General-Function Models
205(13)
Market Model
205(2)
Simultaneous-Equation Approach
207(2)
Use of Total Derivatives
209(1)
National-Income Model (IS-LM)
210(3)
Extending the Model: An Open Economy
213(3)
Summary of the Procedure
216(1)
Exercise 8.6
217(1)
Limitations of Comparative Statics
218(1)
PART FOUR OPTIMIZATION PROBLEMS
219(224)
Optimization: A Special Variety of Equilibrium Analysis
220(35)
Optimum Values and Extreme Values
221(1)
Relative Maximum and Minimum: First-Derivative Test
222(5)
Relative versus Absolute Extremum
222(1)
First-Derivative Test
223(3)
Exercise 9.2
226(1)
Second and Higher Derivatives
227(6)
Derivative of a Derivative
227(2)
Interpretation of the Second Derivative
229(2)
An Application
231(1)
Attitudes toward Risk
231(2)
Exercise 9.3
233(1)
Second-Derivative Test
233(9)
Necessary versus Sufficient Conditions
234(1)
Conditions for Profit Maximization
235(3)
Coefficients of a Cubic Total-Cost Function
238(2)
Upward-Sloping Marginal-Revenue Curve
240(1)
Exercise 9.4
241(1)
Maclaurin and Taylor Series
242(8)
Maclaurin Series of a Polynomial Function
242(2)
Taylor Series of a Polynomial Function
244(1)
Expansion of an Arbitrary Function
245(3)
Lagrange Form of the Remainder
248(2)
Exercise 9.5
250(1)
Nth-Derivative Test for Relative Extremum of a Function of One Variable
250(5)
Taylor Expansion and Relative Extremum
250(1)
Some Specific Cases
251(2)
Nth-Derivative Test
253(1)
Exercise 9.6
254(1)
Exponential and Logarithmic Functions
255(36)
The Nature of Exponential Functions
256(4)
Simple Exponential Function
256(1)
Graphical Form
256(1)
Generalized Exponential Function
257(2)
A Preferred Base
259(1)
Exercise 10.1
260(1)
Natural Exponential Functions and the Problem of Growth
260(7)
The Number e
260(2)
An Economic Interpretation of e
262(1)
Interest Compounding and the Function Aert
262(1)
Instantaneous Rate of Growth
263(2)
Continuous versus Discrete Growth
265(1)
Discounting and Negative Growth
266(1)
Exercise 10.2
267(1)
Logarithms
267(5)
The Meaning of Logarithm
267(1)
Common Log and Natural Log
268(1)
Rules of Logarithms
269(2)
An Application
271(1)
Exercise 10.3
272(1)
Logarithmic Functions
272(5)
Log Functions and Exponential Functions
272(1)
The Graphical Form
273(1)
Base Conversion
274(2)
Exercise 10.4
276(1)
Derivatives of Exponential and Logarithmic Functions
277(5)
Log-Function Rule
277(1)
Exponential-Function Rule
278(1)
The Rules Generalized
278(2)
The Case of Base b
280(1)
Higher Derivatives
280(1)
An Application
281(1)
Exercise 10.5
282(1)
Optimal Timing
282(4)
A Problem of Wine Storage
282(1)
Maximization Conditions
283(2)
A Problem of Timber Cutting
285(1)
Exercise 10.6
286(1)
Further Applications of Exponential and Logarithmic Derivatives
286(5)
Finding the Rate of Growth
286(1)
Rate of Growth of a Combination of Functions
287(1)
Finding the Point Elasticity
288(2)
Exercise 10.7
290(1)
The Case of More than One Choice Variable
291(56)
The Differential Version of Optimization Conditions
291(2)
First-Order Condition
291(1)
Second-Order Condition
292(1)
Differential Conditions versus Derivative Conditions
293(1)
Extreme Values of a Function of Two Variables
293(8)
First-Order Condition
294(1)
Second-Order Partial Derivatives
295(2)
Second-Order Total Differential
297(1)
Second-Order Condition
298(2)
Exercise 11.2
300(1)
Quadratic Forms---An Excursion
301(12)
Second-Order Total Differential as a Quadratic Form
301(1)
Positive and Negative Definiteness
302(1)
Determinantal Test for Sign Definiteness
302(3)
Three-Variable Quadratic Forms
305(2)
n-Variable Quadratic Forms
307(1)
Characteristic-Root Test for Sign Definiteness
307(5)
Exercise 11.3
312(1)
Objective Functions with More than Two Variables
313(5)
First-Order Condition for Extremum
313(1)
Second-Order Condition
313(3)
n-Variable Case
316(1)
Exercise 11.4
317(1)
Second-Order Conditions in Relation to Concavity and Convexity
318(13)
Checking Concavity and Convexity
320(4)
Differentiable Functions
324(3)
Convex Functions versus Convex Sets
327(3)
Exercise 11.5
330(1)
Economic Applications
331(11)
Problem of a Multiproduct Firm
331(2)
Price Discrimination
333(3)
Input Decisions of a Firm
336(5)
Exercise 11.6
341(1)
Comparative-Static Aspects of Optimization
342(5)
Reduced-Form Solutions
342(1)
General-Function Models
343(2)
Exercise 11.7
345(2)
Optimization with Equality Constraints
347(55)
Effects of a Constraint
347(2)
Finding the Stationary Values
349(7)
Lagrange-Multiplier Method
350(2)
Total-Differential Approach
352(1)
An Interpretation of the Lagrange Multiplier
353(1)
n-Variable and Multiconstraint Cases
354(1)
Exercise 12.2
355(1)
Second-Order Conditions
356(8)
Second-Order Total Differential
356(1)
Second-Order Conditions
357(1)
The Bordered Hessian
358(3)
n-Variable Case
361(1)
Multiconstraint Case
362(1)
Exercise 12.3
363(1)
Quasiconcavity and Quasiconvexity
364(10)
Geometric Characterization
364(1)
Algebraic Definition
365(3)
Differentiable Functions
368(3)
A Further Look at the Bordered Hessian
371(1)
Absolute versus Relative Extrema
372(2)
Exercise 12.4
374(1)
Utility Maximization and Consumer Demand
374(9)
First-Order Condition
375(1)
Second-Order Condition
376(2)
Comparative-Static Analysis
378(3)
Proportionate Changes in Prices and Income
381(1)
Exercise 12.5
382(1)
Homogeneous Functions
383(7)
Linear Homogeneity
383(3)
Cobb-Douglas Production Function
386(2)
Extensions of the Results
388(1)
Exercise 12.6
389(1)
Least-Cost Combination of Inputs
390(12)
First-Order Condition
390(2)
Second-Order Condition
392(1)
The Expansion Path
392(2)
Homothetic Functions
394(2)
Elasticity of Substitution
396(1)
CES Production Function
397(2)
Cobb-Douglas Function as a Special Case of the CES Function
399(2)
Exercise 12.7
401(1)
Further Topics in Optimization
402(41)
Nonlinear Programming and Kuhn-Tucker Conditions
402(10)
Step 1: Effect of Nonnegativity Restrictions
403(1)
Step 2: Effect of Inequality Constraints
404(4)
Interpretation of the Kuhn-Tucker Conditions
408(1)
The n-Variable, m-Constraint Case
409(2)
Exercise 13.1
411(1)
The Constraint Qualification
412(6)
Irregularities at Boundary Points
412(3)
The Constraint Qualification
415(1)
Linear Constraints
416(2)
Exercise 13.2
418(1)
Economic Applications
418(6)
War-Time Rationing
418(2)
Peak-Load Pricing
420(3)
Exercise 13.3
423(1)
Sufficiency Theorems in Nonlinear Programming
424(4)
The Kuhn-Tucker Sufficiency Theorem: Concave Programming
424(1)
The Arrow-Enthoven Sufficiency Theorem: Quasiconcave Programming
425(1)
A Constraint-Qualification Test
426(1)
Exercise 13.4
427(1)
Maximum-Value Functions and the Envelope Theorem
428(7)
The Envelope Theorem for Unconstrained Optimization
428(1)
The Profit Function
429(1)
Reciprocity Conditions
430(2)
The Envelope Theorem for Constrained Optimization
432(2)
Interpretation of the Lagrange Multiplier
434(1)
Duality and the Envelope Theorem
435(7)
The Primal Problem
435(1)
The Dual Problem
436(1)
Duality
436(1)
Roy's Identity
437(1)
Shephard's Lemma
438(3)
Exercise 13.6
441(1)
Some Concluding Remarks
442(1)
PART FIVE DYNAMIC ANALYSIS
443(212)
Economic Dynamics and Integral Calculus
444(31)
Dynamics and Integration
444(2)
Indefinite Integrals
446(8)
The Nature of Integrals
446(1)
Basic Rules of Integration
447(1)
Rules of Operation
448(3)
Rules Involving Substitution
451(2)
Exercise 14.2
453(1)
Definite Integrals
454(7)
Meaning of Definite Integrals
454(1)
A Definite Integral as an Area under a Curve
455(3)
Some Properties of Definite Integrals
458(2)
Another Look at the Indefinite Integral
460(1)
Exercise 14.3
460(1)
Improper Integrals
461(3)
Infinite Limits of Integration
461(2)
Infinite Integrand
463(1)
Exercise 14.4
464(1)
Some Economic Applications of Integrals
464(7)
From a Marginal Function to a Total Function
464(1)
Investment and Capital Formation
465(3)
Present Value of a Cash Flow
468(2)
Present Value of a Perpetual Flow
470(1)
Exercise 14.5
470(1)
Domar Growth Model
471(4)
The Framework
471(1)
Finding the Solution
472(1)
The Razor's Edge
473(1)
Exercise 14.6
474(1)
Continuous Time: First-Order Differential Equations
475(28)
First-Order Linear Differential Equations with Constant Coefficient and Constant Term
475(4)
The Homogeneous Case
476(1)
The Nonhomogeneous Case
476(2)
Verification of the Solution
478(1)
Exercise 15.1
479(1)
Dynamics of Market Price
479(4)
The Framework
480(1)
The Time Path
480(1)
The Dynamic Stability of Equilibrium
481(1)
An Alternative Use of the Model
482(1)
Exercise 15.2
483(1)
Variable Coefficient and Variable Term
483(3)
The Homogeneous Case
484(1)
The Nonhomogeneous Case
485(1)
Exercise 15.3
486(1)
Exact Differential Equations
486(6)
Exact Differential Equations
486(1)
Method of Solution
487(2)
Integrating Factor
489(1)
Solution of First-Order Linear Differential Equations
490(1)
Exercise 15.4
491(1)
Nonlinear Differential Equations of the First Order and First Degree
492(3)
Exact Differential Equations
492(1)
Separable Variables
492(1)
Equations Reducible to the Linear Form
493(2)
Exercise 15.5
495(1)
The Qualitative-Graphic Approach
495(3)
The Phase Diagram
495(1)
Types of Time Path
496(2)
Exercise 15.6
498(1)
Solow Growth Model
498(5)
The Framework
498(2)
A Qualitative-Graphic Analysis
500(1)
A Quantitative Illustration
501(1)
Exercise 15.7
502(1)
Higher-Order Differential Equations
503(41)
Second-Order Linear Differential Equations with Constant Coefficients and Constant Term
504(7)
The Particular Integral
504(1)
The Complementary Function
505(5)
The Dynamic Stability of Equilibrium
510(1)
Exercise 16.1
511(1)
Complex Numbers and Circular Functions
511(11)
Imaginary and Complex Numbers
511(1)
Complex Roots
512(1)
Circular Functions
513(2)
Properties of the Sine and Cosine Functions
515(2)
Euler Relations
517(2)
Alternative Representations of Complex Numbers
519(2)
Exercise 16.2
521(1)
Analysis of the Complex-Root Case
522(5)
The Complementary Function
522(2)
An Example of Solution
524(1)
The Time Path
525(2)
The Dynamic Stability of Equilibrium
527(1)
Exercise 16.3
527(1)
A Market Model with Price Expectations
527(5)
Price Trend and Price Expectations
527(1)
A Simplified Model
528(1)
The Time Path of Price
529(3)
Exercise 16.4
532(1)
The Interaction of Inflation and Unemployment
532(6)
The Phillips Relation
532(1)
The Expectations-Augmented Phillips Relation
533(1)
The Feedback from Inflation to Unemployment
534(1)
The Time Path of π
534(3)
Exercise 16.5
537(1)
Differential Equations with a Variable Term
538(2)
Method of Undetermined Coefficients
538(1)
A Modification
539(1)
Exercise 16.6
540(1)
Higher-Order Linear Differential Equations
540(4)
Finding the Solution
540(2)
Convergence and the Routh Theorem
542(1)
Exercise 16.7
543(1)
Discrete Time: First-Order Difference Equations
544(24)
Discrete Time, Differences, and Difference Equations
544(2)
Solving a First-Order Difference Equation
546(5)
Iterative Method
546(2)
General Method
548(3)
Exercise 17.2
551(1)
The Dynamic Stability of Equilibrium
551(4)
The Significance of b
551(2)
The Role of A
553(1)
Convergence to Equilibrium
554(1)
Exercise 17.3
554(1)
The Cobweb Model
555(4)
The Model
555(1)
The Cobwebs
556(2)
Exercise 17.4
558(1)
A Market Model with Inventory
559(3)
The Model
559(1)
The Time Path
560(1)
Graphical Summary of the Results
561(1)
Exercise 17.5
562(1)
Nonlinear Difference Equations---The Qualitative-Graphic Approach
562(6)
Phase Diagram
562(2)
Types of Time Path
564(1)
A Market with a Price Ceiling
565(2)
Exercise 17.6
567(1)
Higher-Order Difference Equations
568(24)
Second-Order Linear Difference Equations with Constant Coefficients and Constant Term
569(7)
Particular Solution
569(1)
Complementary Function
570(3)
The Convergence of the Time Path
573(2)
Exercise 18.1
575(1)
Samuelson Multiplier-Acceleration Interaction Model
576(5)
The Framework
576(1)
The Solution
577(1)
Convergence versus Divergence
578(2)
A Graphical Summary
580(1)
Exercise 18.2
581(1)
Inflation and Unemployment in Discrete Time
581(5)
The Model
581(1)
The Difference Equation in p
582(1)
The Time Path of p
583(1)
The Analysis of U
584(1)
The Long-Run Phillips Relation
585(1)
Exercise 18.3
585(1)
Generalizations to Variable-Term and Higher-Order Equations
586(6)
Variable Term in the Form of cmt
586(1)
Variable Term in the Form ctn
587(1)
Higher-Order Linear Difference Equations
588(1)
Convergence and the Schur Theorem
589(2)
Exercise 18.4
591(1)
Simultaneous Differential Equations and Difference Equations
592(39)
The Genesis of Dynamic Systems
592(2)
Interacting Patterns of Change
592(1)
The Transformation of a High-Order Dynamic Equation
593(1)
Solving Simultaneous Dynamic Equations
594(9)
Simultaneous Difference Equations
594(2)
Matrix Notation
596(3)
Simultaneous Differential Equations
599(2)
Further Comments on the Characteristic Equation
601(1)
Exercise 19.2
602(1)
Dynamic Input-Output Models
603(6)
Time Lag in Production
603(2)
Excess Demand and Output Adjustment
605(2)
Capital Formation
607(1)
Exercise 19.3
608(1)
The Inflation-Unemployment Model Once More
609(5)
Simultaneous Differential Equations
610(1)
Solution Paths
610(2)
Simultaneous Difference Equations
612(1)
Solution Paths
613(1)
Exercise 19.4
614(1)
Two-Variable Phase Diagrams
614(9)
The Phase Space
615(1)
The Demarcation Curves
615(2)
Streamlines
617(1)
Types of Equilibrium
618(2)
Inflation and Monetary Rule a la Obst
620(3)
Exercise 19.5
623(1)
Linearization of a Nonlinear Differential-Equation System
623(8)
Taylor Expansion and Linearization
624(1)
The Reduced Linearization
625(1)
Local Stability Analysis
625(4)
Exercise 19.6
629(2)
Optimal Control Theory
631(24)
The Nature of Optimal Control
631(8)
Illustration: A Simple Macroeconomic Model
632(1)
Pontryagin's Maximum Principle
633(6)
Alternative Terminal Conditions
639(5)
Fixed Terminal Point
639(1)
Horizontal Terminal Line
639(1)
Truncated Vertical Terminal Line
639(1)
Truncated Horizontal Terminal Line
640(3)
Exercise 20.2
643(1)
Autonomous Problems
644(1)
Economic Applications
645(4)
Lifetime Utility Maximization
645(2)
Exhaustible Resource
647(2)
Exercise 20.4
649(1)
Infinite Time Horizon
649(5)
Neoclassical Optimal Growth Model
649(2)
The Current-Value Hamiltonian
651(1)
Constructing a Phase Diagram
652(1)
Analyzing the Phase Diagram
653(1)
Limitations of Dynamic Analysis
654(1)
The Greek Alphabet 655(1)
Mathematical Symbols 656(3)
A Short Reading List 659(3)
Answers to Selected Exercises 662(15)
Index 677


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