Fundamental methods of mathematical economics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston, Mass. [u.a.]
McGraw-Hill
2005
|
| Ausgabe: | 4. ed., international ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 688 S. graph. Darst. |
| ISBN: | 0071238239 |
Internformat
MARC
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| 245 | 1 | 0 | |a Fundamental methods of mathematical economics |c Alpha C. Chiang ; Kevin Wainwright |
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Datensatz im Suchindex
| _version_ | 1804133384061976576 |
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| adam_text | CONTENTS PART ONE INTRODUCTION 1 CHAPTER 1 THE NATURE OF MATHEMATICAL
ECONOMICS 2 1.1 MATHEMATICAL VERSUS NONMATHEMATICAL ECONOMICS 2 1.2
MATHEMATICAL ECONOMICS VERSUS ECONOMETRICS 4 CHAPTER 2 ECONOMIC MODELS 5
2.1 INGREDIENTS OF A MATHEMATICAL MODEL 5 VARIABLES, CONSTANTS, AND
PARAMETERS 5 EQUATIONS AND IDENTITIES 6 2.2 THE REAL-NUMBER SYSTEM 7 2.3
THE CONCEPT OF SETS 8 SET NOTATION 9 RELATIONSHIPS BETWEEN SETS 9
OPERATIONS ON SETS 11 LAWS OF SET OPERATIONS 12 EXERCISE 2.3 14 2.4
RELATIONS AND FUNCTIONS 15 ORDERED PAIRS 15 RELATIONS AND FUNCTIONS 16
PART TWO STATIC (OR EQUILIBRIUM) ANALYSIS 29 CHAPTER 3 EQUILIBRIUM
ANALYSIS IN ECONOMICS 30 3.1 THE MEANING OF EQUILIBRIUM 30 3.2 PARTIAL
MARKET EQUILIBRIUM*A LINEAR MODEL 31 CONSTRUCTING THE MODEL 31 SOLUTION
BY ELIMINATION OF VARIABLES 33 EXERCISE 3.2 34 3.3 PARTIAL MARKET
EQUILIBRIUM*A NONLINEAR MODEL 35 QUADRATIC EQUATION VERSUS QUADRATIC
FUNCTION 35 THE QUADRATIC FORMULA 36 ANOTHER GRAPHICAL SOLUTION 37
HIGHER-DEGREE POLYNOMIAL EQUATIONS 3H EXERCISE 3.3 40 3.4 GENERAL MARKET
EQUILIBRIUM 40 TWO-COMMODITY MARKET MODEL 41 NUMERICAL EXAMPLE 42
N-COMMODITY CASE 43 SOLUTION OF A GENERAL-EQUATION SYSTEM 44 EXERCISE
3.4 45 3.5 EQUILIBRIUM IN NATIONAL-INCOME ANALYSIS 46 EXERCISE 3.5 47
EXERCISE 2.4 19 2.5 TYPES OF FUNCTION 20 CONSTANT FUNCTIONS 20
POLYNOMIAL FUNCTIONS 20 RATIONAL FUNCTIONS 21 NONALGEBRAIC FUNCTIONS 23
A DIGRESSION ON EXPONENTS 23 EXERCISE 2.5 24 2.6 FUNCTIONS OF TWO OR
MORE INDEPENDENT VARIABLES 25 2.7 LEVELS OF GENERALITY 27 CHAPTER 4
LINEAR MODELS AND MATRIX ALGEBRA 48 4.1 MATRICES AND VECTORS 49 MATRICES
AS A RRAYS 4 9 VECTORS AS SPECIAL MATRICES 50 EXERCISE 4.1 51 4.2 MATRIX
OPERATIONS 51 ADDITION AND SUBTRACTION OF MATRICES 5! SCALAR
MULTIPLICATION 52 XI XII CONTENTS MULTIPLICATION OF MATRICES 53 THE
QUESTION OF DIVISION 56 THE NOTATION 56 EXERCISE 4.2 58 4.3 NOTES ON
VECTOR OPERATIONS 59 MULTIPLICATION OF VECTORS 59 GEOMETRIC
INTERPRETATION OF VECTOR OPERATIONS 60 LINEAR DEPENDENCE 62 VECTOR SPACE
63 EXERCISE 4.3 65 4.4 COMMUTATIVE, ASSOCIATIVE, AND DISTRIBUTIVE LAWS
67 MATRIX A DDITION 6 7 MATRIX MULTIPLICATION 68 EXERCISE 4.4 69 4.5
IDENTITY MATRICES AND NULL MATRICES 70 IDENTITY MATRICES 70 NULL
MATRICES 71 IDIOSYNCRASIES OF MATRIX ALGEBRA 72 EXERCISE 4.5 72 4.6
TRANSPOSES AND INVERSES 73 PROPERTIES OFTRANSPOSES 74 INVERSES AND THEIR
PROPERTIES 75 INVERSE MATRIX AND SOLUTION OF LINEAR-EQUATION SYSTEM 77
EXERCISE 4.6 78 4.7 FINITE MARKOV CHAINS 78 SPECIAL CASE: ABSORBING
MARKOV CHAINS 81 EXERCISE 4.7 81 CHAPTER 5 LINEAR MODELS AND MATRIX
ALGEBRA (CONTINUED) 82 5.1 CONDITIONS FOR NONSINGULARITY OF A MATRIX 82
NECESSARY VERSUS SUFFICIENT CONDITIONS 82 CONDITIONS FOR NONSINGULARITY
84 RANK OF A MATRIX 85 EXERCISE 5.1 87 5.2 TEST OF NONSINGULARITY BY USE
OF DETERMINANT 88 DETERMINANTS AND NONSINGULARITY 88 EVALUATING A
THIRD-ORDER DETERMINANT 89 EVALUATING AN NTH-ORDER DETERMINANT BY
LAPLACE EXPANSION 91 EXERCISE 5.2 93 5.3 BASIC PROPERTIES OF
DETERMINANTS 94 DETERMINANTAL CRITERION FOR NONSINGULARITY 96 RANK OF A
MATRIX REDEFINED 97 EXERCISE 5.3 98 5.4 FINDING THE INVERSE MATRIX 99
EXPANSION OF A DETERMINANT BY ALIEN COFACTORS 99 MATRIX INVERSION 100
EXERCISE 5.4 102 5.5 CRAMER S RULE 103 DERIVATION OF THE RULE 103 NOTE
ON HOMOGENEOUS-EQUATION SYSTEMS 105 SOLUTION OUTCOMES FOR A
LINEAR-EQUATION SYSTEM 106 EXERCISE 5.5 107 5.6 APPLICATION TO MARKET
AND NATIONAL-INCOME MODELS 107 MARKET MODEL 107 NATIONAL-INCOME MODEL
108 IS-LM MODEL: CLOSED ECONOMY 109 MATRIX ALGEBRA VERSUS ELIMINATION OF
VARIABLES 111 EXERCISE 5.6 111 5.7 LEONTIEF INPUT-OUTPUT MODELS 112
STRUCTURE OF AN INPUT-OUTPUT MODEL 112 THE OPEN MODEL 113 A NUMERICAL
EXAMPLE 115 THE EXISTENCE OF NONNEGATIVE SOLUTIONS 116 ECONOMIC MEANING
OF THE HAWKINS-SIMON CONDITION 118 THE CLOSED MODEL 119 EXERCISE 5.7 120
5.8 LIMITATIONS OF STATIC ANALYSIS 120 PART THREE COMPARATIVE-STATIC
ANALYSIS 123 CHAPTER 6 COMPARATIVE STATICS AND THE CONCEPT OF DERIVATIVE
124 6.1 THE NATURE OF COMPARATIVE STATICS 124 6.2 RATE OF CHANGE AND THE
DERIVATIVE 125 THE DIFFERENCE QUOTIENT 125 CONTENTS XIII THE DERIVATIVE
126 EXERCISE 6.2 127 6.3 THE DERIVATIVE AND THE SLOPE OF A CURVE 128 6.4
THE CONCEPT OF LIMIT 129 LEFT-SIDE LIMIT AND RIGHT-SIDE LIMIT 129
GRAPHICAL ILLUSTRATIONS 130 EVALUATION OF A LIMIT 131 FORMAL VIEW OF THE
LIMIT CONCEPT 133 EXERCISE 6,4 135 6.5 DIGRESSION ON INEQUALITIES AND
ABSOLUTE VALUES 136 RULES OF INEQUALITIES 136 ABSOLUTE VALUES AND
INEQUALITIES 137 SOLUTION OF AN INEQUALITY 138 EXERCISE 6.5 139 6.6
LIMIT THEOREMS 139 THEOREMS INVOLVING A SINGLE FUNCTION 139 THEOREMS
INVOLVING TWO FUNCTIONS 140 LIMIT OF A POLYNOMIAL FUNCTION 141 EXERCISE
6.6 141 6.7 CONTINUITY AND DIFFERENTIABILITY OF A FUNCTION 141
CONTINUITY OF A FUNCTION 141 POLYNOMIAL AND RATIONAL FUNCTIONS 142
DIFFERENTIABILITY OF A FUNCTION 143 EXERCISE 6.7 146 CHAPTER 7 RULES OF
DIFFERENTIATION AND THEIR USE IN COMPARATIVE STATICS 148 7.1 RULES OF
DIFFERENTIATION FOR A FUNCTION OF ONE VARIABLE 148 CONSTANT-FUNCTION
RULE 148 POWER-FUNCTION RULE 149 POWER-FUNCTION RULE GENERALIZED 151
EXERCISE 7.1 152 7.2 RULES OF DIFFERENTIATION INVOLVING TWO OR MORE
FUNCTIONS OF THE SAME VARIABLE 152 SUM-DIFFERENCE RULE 152 PRODUCT RULE
155 FINDING MARGINAL-REVENUE FUNCTION FROM AVERAGE-REVENUE FUNCTION 156
QUOTIENT RULE 158 RELATIONSHIP BETWEEN MARGINAL-COST AND AVERAGE-COST
FUNCTIONS 159 EXERCISE 7.2 160 73 RULES OF DIFFERENTIATION INVOLVING
FUNCTIONS OF DIFFERENT VARIABLES 161 CHAIN RULE 161 INVERSE-FUNCTION
RIDE 163 EXERCISE 7.3 165 7.4 PARTIAL DIFFERENTIATION 165 PARTIAL
DERIVATIVES 165 TECHNIQUES OF PARTIAL DIFFERENTIATION 166 GEOMETRIC
INTERPRETATION OF PARTIAL DERIVATIVES 167 GRADIENT VECTOR 168 EXERCISE
7.4 169 7.5 APPLICATIONS TO COMPARATIVE-STATIC ANALYSIS 170 MARKET MODEL
170 NATIONAL-INCOME MODEL 172 INPUT-OUTPUT MODEL 173 EXERCISE 7.5 175
7.6 NOTE ON JACOBIAN DETERMINANTS 175 EXERCISE 7.6 177 CHAPTER 8
COMPARATIVE-STATIC ANALYSIS OF GENERAL-FUNCTION MODELS 178 8.1
DIFFERENTIALS 179 DIFFERENTIALS AND DERIVATIVES 179 DIFFERENTIALS AND
POINT ELASTICITY 181 EXERCISE 8.1 184 8.2 TOTAL DIFFERENTIALS 184
EXERCISE 8.2 186 8.3 RULES OF DIFFERENTIALS 187 EXERCISE 8.3 189 8.4
TOTAL DERIVATIVES 189 FINDING THE TOTAL DERIVATIVE 189 A VARIATION ON
THE THEME 191 ANOTHER VARIATION ON THE THEME 192 SOME GENERAL REMARKS
193 EXERCISE 8.4 193 8.5 DERIVATIVES OF IMPLICIT FUNCTIONS 194 IMPLICIT
FUNCTIONS 194 DERIVATIVES OF IMPLICIT FUNCTIONS 196 EXTENSION TO THE
SIMULTANEOUS-EQUATION CASE 199 EXERCISE 8.5 204 XIV CONTENTS 8.6
COMPARATIVE STATICS OF GENERAL-FUNCTION MODELS 205 MARKET MODEL 205
SIMULTANEOUS-EQUATION APPROACH 207 USE OF TOTAL DERIVATIVES 209
NATIONAL-INCOME MODEL (IS-LM) 210 EXTENDING THE MODEL: AN OPEN ECONOMY
213 SUMMARY OF THE PROCEDURE 216 EXERCISE 8.6 217 8.7 LIMITATIONS OF
COMPARATIVE STATICS 218 PART FOUR OPTIMIZATION PROBLEMS 219 CHAPTER 9
OPTIMIZATION: A SPECIAL VARIETY OF EQUILIBRIUM ANALYSIS 220 9.1 OPTIMUM
VALUES AND EXTREME VALUES 221 9.2 RELATIVE MAXIMUM AND MINIMUM:
FIRST-DERIVATIVE TEST 222 RELATIVE VERSUS ABSOLUTE EXTREMUM 222
FIRST-DERIVATIVE TEST 223 EXERCISE 9.2 226 9.3 SECOND AND HIGHER
DERIVATIVES 227 DERIVATIVE OF A DERIVATIVE 227 INTERPRETATION OF THE
SECOND DERIVATIVE 229 AN APPLICATION 231 ATTITUDES TOWARD RISK 231
EXERCISE 9.3 233 9.4 SECOND-DERIVATIVE TEST 233 NECESSARY VERSUS
SUFFICIENT CONDITIONS 234 CONDITIONS FOR PROFIT MAXIMIZATION 235
COEFFICIENTS OF A CUBIC TOTAL-COST FUNCTION 238 UPWARD-SLOPING
MARGINAL-REVENUE CURVE 240 EXERCISE 9.4 241 9.5 MACLAURIN AND TAYLOR
SERIES 242 MACLAURIN SERIES OF A POLYNOMIAL FUNCTION 242 TAYLOR SERIES
OF A POLYNOMIAL FUNCTION 244 EXPANSION OF AN ARBITRARY FUNCTION 245
LAGRANGE FORM OF THE REMAINDER 248 EXERCISE 9.5 250 9.6 MH-DERIVATIVE
TEST FOR RELATIVE EXTREMUM OF A FUNCTION OF ONE VARIABLE 250 TAYLOR
EXPANSION AND RELATIVE EXTREMUM 250 SOME SPECIFIC CASES 251
NTH-DERIVATIVE TEST 253 EXERCISE 9.6 254 CHAPTER 10 EXPONENTIAL AND
LOGARITHMIC FUNCTIONS 255 10.1 THE NATURE OF EXPONENTIAL FUNCTIONS 256
SIMPLE EXPONENTIAL FUNCTION 256 GRAPHICAL FORM 256 GENERALIZED
EXPONENTIAL FUNCTION 25 7 A PREFERRED BASE 259 EXERCISE 10.1 260 10.2
NATURAL EXPONENTIAL FUNCTIONS AND THE PROBLEM OF GROWTH 260 THE NUMBER E
260 AN ECONOMIC INTERPRETATION OFE 262 INTEREST COMPOUNDING AND THE
FUNCTION AE RT 262 INSTANTANEOUS RATE OF GROWTH 263 CONTINUOUS VERSUS
DISCRETE GROWTH 265 DISCOUNTING AND NEGATIVE GROWTH 266 EXERCISE 10.2
267 10.3 LOGARITHMS 267 THE MEANING OF LOGARITHM 267 COMMON LOG AND
NATURAL LOG 268 RULES OF LOGARITHMS 269 AN APPLICATION 271 EXERCISE 10.3
272 10.4 LOGARITHMIC FUNCTIONS 272 LOG FUNCTIONS AND EXPONENTIAL
FUNCTIONS 272 THE GRAPHICAL FORM 2 73 BASE CONVERSION 274 EXERCISE 10.4
276 10.5 DERIVATIVES OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS 277
LOG-FUNCTION RULE 277 EXPONENTIAL-FUNCTION RULE 278 THE RULES
GENERALIZED 278 THE CASE OF BASE B 280 HIGHER DERIVATIVES 280 AN
APPLICATION 281 EXERCISE 10.5 282 CONTENTS XV 10.6 OPTIMAL TIMING 282 A
PROBLEM OF WINE STORAGE 282 MAXIMIZATION CONDITIONS 283 A PROBLEM OF
TIMBER CUTTING 285 EXERCISE 10.6 286 10.7 FURTHER APPLICATIONS OF
EXPONENTIAL AND LOGARITHMIC DERIVATIVES 286 FINDING THE RATE OF GROWTH
286 RATE OF GROWTH OF A COMBINATION OF FUNCTIONS 287 FINDING THE POINT
ELASTICITY 288 EXERCISE 10.7 290 CHAPTER 11 THE CASE OF MORE THAN ONE
CHOICE VARIABLE 291 11.1 THE DIFFERENTIAL VERSION OF OPTIMIZATION
CONDITIONS 291 FIRST-ORDER CONDITION 291 SECOND-ORDER CONDITION 292
DIFFERENTIAL CONDITIONS VERSUS DERIVATIVE CONDITIONS 293 11.2 EXTREME
VALUES OF A FUNCTION OF TWO VARIABLES 293 FIRST-ORDER CONDITION 294
SECOND-ORDER PARTIAL DERIVATIVES 295 SECOND-ORDER TOTAL DIFFERENTIAL 297
SECOND-ORDER CONDITION 298 EXERCISE 11.2 300 11.3 QUADRATIC FORMS*AN
EXCURSION 301 SECOND-ORDER TOTAL DIFFERENTIAL AS A QUADRATIC FORM 301
POSITIVE AND NEGATIVE DEFINITENESS 302 DETERMINANTAL TEST FOR SIGN
DEFINITENESS 302 THREE- VARIABLE QUADRATIC FORMS 305 N-VARIABLE
QUADRATIC FORMS 307 CHARACTERISTIC-ROOT TEST FOR SIGN DEFINITENESS 307
EXERCISE 11.3 312 11.4 OBJECTIVE FUNCTIONS WITH MORE THAN TWO VARIABLES
313 FIRST-ORDER CONDITION FOR EXTREMUM 313 SECOND-ORDER CONDITION 313 N-
VARIABLE CASE 316 EXERCISE ! 1.4 317 11.5 SECOND-ORDER CONDITIONS IN
RELATION TO CONCAVITY AND CONVEXITY 318 CHECKING CONCAVITY AND CONVEXITY
320 DIFFERENTIABLE FUNCTIONS 324 CONVEX FUNCTIONS VERSUS CONVEX SETS 327
EXERCISE 11.5 330 11.6 ECONOMIC APPLICATIONS 331 PROBLEM OF A
MULTIPRODUCT FIRM 33 / PRICE DISCRIMINATION 333 INPUT DECISIONS OF A
FIRM 336 EXERCISE 11.6 341 11.7 COMPARATIVE-STATIC ASPECTS OF
OPTIMIZATION 342 REDUCED-FORM SOLUTIONS 342 GENERAL-FUNCTION MODELS 343
EXERCISE 11.7 345 CHAPTER 12 OPTIMIZATION WITH EQUALITY CONSTRAINTS 347
12.1 EFFECTS OF A CONSTRAINT 347 1 2.2 FINDING THE STATIONARY VALUES 349
LAGRANGE-MULTIPLIER METHOD 350 TOTAL-DIFFERENTIAL APPROACH 352 AN
INTERPRETATION OF THE LAGRANGE MULTIPLIER 353 N- VARIABLE AND
MULTICONSTRAINT CASES 354 EXERCISE 12.2 355 12.3 SECOND-ORDER CONDITIONS
356 SECOND-ORDER TOTAL DIFFERENTIAL 356 SECOND-ORDER CONDITIONS 357 THE
BORDERED HESSIAN 358 N- VARIABLE CASE 361 MULTICONSTRAINT CASE 362
EXERCISE 12.3 363 1 2.4 QUASICONCAVITY AND QUASICONVEXITY 364 GEOMETRIC
CHARACTERIZATION 364 ALGEBRAIC DEFINITION 365 DIFFERENTIABLE FUNCTIONS
368 A FURTHER LOOK AT THE BORDERED HESSIAN 3 71 ABSOLUTE VERSUS RELATIVE
EXTREMA 372 EXERCISE 12.4 374 12.5 UTILITY MAXIMIZATION AND CONSUMER
DEMAND 374 FIRST-ORDER CONDITION 375 SECOND-ORDER CONDITION 376 XVI
CONTENTS COMPARATIVE-STATIC A NALYSIS 3 78 PROPORTIONATE CHANGES IN
PRICES AND INCOME 381 EXERCISE 12.5 382 12.6 HOMOGENEOUS FUNCTIONS 383
LINEAR HOMOGENEITY 383 COBB-DOUGLAS PRODUCTION FUNCTION 386 EXTENSIONS
OF THE RESULTS 388 EXERCISE 12.6 389 12.7 LEAST-COST COMBINATION OF
INPUTS 390 FIRST-ORDER CONDITION 390 SECOND-ORDER CONDITION 392 THE
EXPANSION PATH 392 HOMOTHETIC FUNCTIONS 394 ELASTICITY OF SUBSTITUTION
396 CES PRODUCTION FUNCTION 397 COBB-DOUGLAS FUNCTION AS A SPECIAL CASE
OF THE CES FUNCTION 399 EXERCISE 12.7 401 CHAPTER 13 FURTHER TOPICS IN
OPTIMIZATION THE ARROW-ENTHOVEN SUFFICIENCY THEOREM: QUASICONCAVE
PROGRAMMING 425 A CONSTRAINT-QUALIFICATION TEST 426 EXERCISE 13.4 427
13.5 MAXIMUM-VALUE FUNCTIONS AND THE ENVELOPE THEOREM 428 THE ENVELOPE
THEOREM FOR UNCONSTRAINED OPTIMIZATION 428 THE PROFIT FUNCTION 429
RECIPROCIT} CONDITIONS 430 THE ENVELOPE THEOREM FOR CONSTRAINED
OPTIMIZATION 432 INTERPRETATION OF THE LAGRANGE MULTIPLIER 434 1 3.6
DUALITY AND THE ENVELOPE THEOREM 435 THE PRIMAL PROBLEM 435 THE DUAL
PROBLEM 436 DUALITY 436 ROY S IDENTITY 43 7 SHEPHARD S LEMMA 438
EXERCISE 13.6 441 13.7 SOME CONCLUDING REMARKS 442 402 13.1 NONLINEAR
PROGRAMMING AND KUHN-TUCKER CONDITIONS 402 STEP I: EFFECT OF
NONNEGATIVITY RESTRICTIONS 403 STEP 2: EFFECT OF INEQUALITY CONSTRAINTS
404 INTERPRETATION OF THE KUHN-TUCKER CONDITIONS 408 THE N- VARIABLE,
M-CONSTRAINT CASE 409 EXERCISE 13.1 411 1 3.2 THE CONSTRAINT
QUALIFICATION 412 IRREGIDARITIES AT BOUNDATY POINTS 412 THE CONSTRAINT
QUALIFICATION 415 LINEAR CONSTRAINTS 416 EXERCISE 13.2 418 13.3 ECONOMIC
APPLICATIONS 418 WAR-TIME RATIONING 418 PEAK-LOAD PRICING 420 EXERCISE
13.3 423 13.4 SUFFICIENCY THEOREMS IN NONLINEAR PROGRAMMING 424 THE
KUHN-TUCKER SUFFICIENCY THEOREM: CONCAVE PROGRAMMING 424 PART FIVE
DYNAMIC ANALYSIS 443 CHAPTER 14 ECONOMIC DYNAMICS AND INTEGRAL CALCULUS
444 14.1 DYNAMICS AND INTEGRATION 444 14.2 INDEFINITE INTEGRALS 446 THE
NATURE OF INTEGRALS 446 BASIC RULES OF INTEGRATION 447 RULES OF
OPERATION 448 RULES INVOLVING SUBSTITUTION 451 EXERCISE 14.2 453 14.3
DEFINITE INTEGRALS 454 MEANING OF DEFINITE INTEGRALS 454 A DEFINITE
INTEGRAL AS AN AREA UNDER A CURRE 455 SOME PROPERTIES OF DEFINITE
INTEGRALS 458 ANOTHER LOOK AT THE INDEFINITE INTEGRAL 460 EXERCISE 14.3
460 CONTENTS XVII 14.4 IMPROPER INTEGRALS 461 INFINITE LIMITS OF
INTEGRATION 461 INFINITE INTEGRAND 463 EXERCISE 14.4 464 14.5 SOME
ECONOMIC APPLICATIONS OF INTEGRALS 464 FROM A MARGINAL FUNCTION TO A
TOTAL FUNCTION 464 INVESTMENT AND CAPITAL FORMATION 465 PRESENT VALUE OF
A CASH FLOW 468 PRESENT VALUE OF A PERPETUAL FLOW 470 EXERCISE 14.5 470
14.6 DOMAR GROWTH MODEL 471 THE FRAMEWORK 471 FINDING THE SOLUTION 472
THE RAZOR S EDGE 4 73 EXERCISE 14.6 474 CHAPTER 15 CONTINUOUS TIME:
FIRST-ORDER DIFFERENTIAL EQUATIONS 475 15.1 FIRST-ORDER LINEAR
DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENT AND CONSTANT TERM 475
THE HOMOGENEOUS CASE 476 THE NONHOMOGENEOUS CASE 476 VERIFICATION OF THE
SOLUTION 478 EXERCISE 15.1 479 15.2 DYNAMICS OF MARKET PRICE 479 THE
FRAMEWORK 480 THE TIME PATH 480 THE DYNAMIC STABILITY OF EQUILIBRIUM 481
AN ALTERNATIVE USE OF THE MODEL 482 EXERCISE 15.2 483 15.3 VARIABLE
COEFFICIENT AND VARIABLE TERM 483 THE HOMOGENEOUS CASE 484 THE
NONHOMOGENEOUS CASE 485 EXERCISE 15.3 486 15.4 EXACT DIFFERENTIAL
EQUATIONS 486 EXACT DIFFERENTIAL EQUATIONS 486 METHOD OF SOLUTION 487
INTEGRATING FACTOR 489 SOLUTION OF FIRST-ORDER LINEAR DIFFERENTIAL
EQUATIONS 490 EXERCISE 15.4 491 15.5 NONLINEAR DIFFERENTIAL EQUATIONS OF
THE FIRST ORDER AND FIRST DEGREE 492 EXACT DIFFERENTIAL EQUATIONS 492
SEPARABLE VARIABLES 492 EQUATIONS REDUCIBLE TO THE LINEAR FORM 493
EXERCISE 15.5 495 15.6 THE QUALITATIVE-GRAPHIC APPROACH 495 THE PHASE
DIAGRAM 495 TYPES OF TIME PATH 496 EXERCISE 15.6 498 15.7 SOLOW GROWTH
MODEL 498 THE FRAMEWORK 498 A QUALITATIVE-GRAPHIC ANALYSIS 500 A
QUANTITATIVE ILLUSTRATION 501 EXERCISE 15.7 502 CHAPTER 16 HIGHER-ORDER
DIFFERENTIAL EQUATIONS 503 16.1 SECOND-ORDER LINEAR DIFFERENTIAL
EQUATIONS WITH CONSTANT COEFFICIENTS AND CONSTANT TERM 504 THE
PARTICULAR INTEGRAL 504 THE COMPLEMENTARY FUNCTION 505 THE DYNAMIC
STABILITY OF EQUILIBRIUM 510 EXERCISE 16.1 511 16.2 COMPLEX NUMBERS AND
CIRCULAR FUNCTIONS 511 IMAGINARY AND COMPLEX NUMBERS 511 COMPLEX ROOTS
512 CIRCULAR FUNCTIONS 513 PROPERTIES OF THE SINE AND COSINE FUNCTIONS
515 EIDER RELATIONS 517 ALTERNATIVE REPRESENTATIONS OF COMPLEX NUMBERS
519 EXERCISE 16.2 521 16.3 ANALYSIS OF THE COMPLEX-ROOT CASE 522 THE
COMPLEMENTARY FUNCTION 522 AN EXAMPLE OF SOLUTION 524 THE TIME PATH 525
THE DYNAMIC STABILITY OF EQUILIBRIUM 527 EXERCISE 16.3 527 XVIII
CONTENTS 16.4 A MARKET MODEL WITH PRICE EXPECTATIONS 527 PRICE TREND AND
PRICE EXPECTATIONS 52 7 A SIMPLIFIED MODEL 528 THE TIME PATH OF PRICE
529 EXERCISE 16,4 532 16.5 THE INTERACTION OF INFLATION AND UNEMPLOYMENT
532 THE PHILLIPS RELATION 532 THE EXPECTATIONS-AUGMENTED PHILLIPS
RELATION 533 THE FEEDBACK FROM INFLATION TO UNEMPLOYMENT 534 THE TIME
PATH OFN 534 EXERCISE 16.5 537 1 6.6 DIFFERENTIAL EQUATIONS WITH A
VARIABLE TERM 538 METHOD OF UNDETERMINED COEFFICIENTS 538 A MODIFICATION
539 EXERCISE 16,6 540 16.7 HIGHER-ORDER LINEAR DIFFERENTIAL EQUATIONS
540 FINDING THE SOLUTION 540 CONVERGENCE AND THE ROUTH THEOREM 542
EXERCISE 16.7 543 CHAPTER 17 DISCRETE TIME: FIRST-ORDER DIFFERENCE
EQUATIONS 544 1 7.1 DISCRETE TIME, DIFFERENCES, AND DIFFERENCE EQUATIONS
544 1 7.2 SOLVING A FIRST-ORDER DIFFERENCE EQUATION 546 ITERATIVE METHOD
546 GENERAL METHOD 548 EXERCISE 17.2 551 1 7.3 THE DYNAMIC STABILITY OF
EQUILIBRIUM 551 THE SIGNIFICANCE OFB 551 THE ROLE OF A 553 CONVERGENCE
TO EQUILIBRIUM 554 EXERCISE 17.3 554 17.4 THE COBWEB MODEL 555 THE MODEL
555 THE COBWEBS 556 EXERCISE 17.4 558 1 7.5 A MARKET MODEL WITH
INVENTORY 559 THE MODEL 559 THE TIME PATH 560 GRAPHICAL SUMMARY OF THE
RESULTS 561 EXERCISE 17.5 562 1 7.6 NONLINEAR DIFFERENCE EQUATIONS* THE
QUALITATIVE-GRAPHIC APPROACH 562 PHASE DIAGRAM 562 TYPES OF TIME PATH
564 A MARKET WITH A PRICE CEILING 565 EXERCISE 17.6 567 CHAPTER 18
HIGHER-ORDER DIFFERENCE EQUATIONS 568 18.1 SECOND-ORDER LINEAR
DIFFERENCE EQUATIONS WITH CONSTANT COEFFICIENTS AND CONSTANT TERM 569
PARTICULAR SOLUTION 569 COMPLEMENTARY FUNCTION 570 THE CONVERGENCE OF
THE TIME PATH 573 EXERCISE 18.1 575 18.2 SAMUELSON
MULTIPLIER-ACCELERATION INTERACTION MODEL 576 THE FRAMEWORK 576 THE
SOLUTION 577 CONVERGENCE VERSUS DIVERGENCE 578 A GRAPHICAL SUMMARY 580
EXERCISE 18.2 581 18.3 INFLATION AND UNEMPLOYMENT IN DISCRETE TIME 581
THE MODEL 581 THE DIFFERENCE EQUATION IN P 582 THE TIME PATH OFP 583 THE
ANALYSIS OF U 584 THE LONG-RUN PHILLIPS RELATION 585 EXERCISE 18.3 585
18.4 GENERALIZATIONS TO VARIABLE-TERM AND HIGHER-ORDER EQUATIONS 586
VARIABLE TERM IN THE FORM OF CM 586 VARIABLE TERM IN THE FORM CT 587
HIGHER-ORDER LINEAR DIFFERENCE EQUATIONS 588 CONVERGENCE AND THE SCHUR
THEOREM 589 EXERCISE 18.4 591 CONTENTS XIX CHAPTER 19 SIMULTANEOUS
DIFFERENTIAL EQUATIONS AND DIFFERENCE EQUATIONS 592 19.1 THE GENESIS OF
DYNAMIC SYSTEMS 592 INTERACTING PATTERNS OF CHANGE 592 THE
TRANSFORMATION OF A HIGH-ORDER DYNAMIC EQUATION 593 19.2 SOLVING
SIMULTANEOUS DYNAMIC EQUATIONS 594 SIMULTANEOUS DIFFERENCE EQUATIONS 594
MATRIX NOTATION 596 SIMULTANEOUS DIFFERENTIAL EQUATIONS 599 FURTHER
COMMENTS ON THE CHARACTERISTIC EQUATION 601 EXERCISE 19.2 602 19.3
DYNAMIC INPUT-OUTPUT MODELS 603 TIME LAG IN PRODUCTION 603 EXCESS DEMAND
AND OUTPUT ADJUSTMENT 605 CAPITAL FORMATION 607 EXERCISE 19.3 608 19.4
THE INFLATION-UNEMPLOYMENT MODEL ONCE MORE 609 SIMULTANEOUS DIFFERENTIAL
EQUATIONS 610 SOLUTION PATHS 610 SIMULTANEOUS DIFFERENCE EQUATIONS 612
SOLUTION PATHS 613 EXERCISE 19.4 614 1 9.5 TWO-VARIABLE PHASE DIAGRAMS
614 THE PHASE SPACE 615 THE DEMARCATION CURVES 615 STREAMLINES 617 TYPES
OF EQUILIBRIUM 618 INFLATION AND MONETARY RULE A LA OBST 620 EXERCISE
19.5 623 19.6 LINEARIZATION OF A NONLINEAR DIFFERENTIAL- EQUATION SYSTEM
623 TAYLOR EXPANSION AND LINEARIZATION 624 THE REDUCED LINEARIZATION 625
LOCAL STABILITY ANALYSIS 625 EXERCISE 19.6 629 CHAPTER 20 OPTIMAL
CONTROL THEORY 631 20.1 THE NATURE OF OPTIMAL CONTROL 631 ILLUSTRATION:
A SIMPLE MACROECONOMIC MODEL 632 PONTRYAGIN S MAXIMUM PRINCIPLE 633 20.2
ALTERNATIVE TERMINAL CONDITIONS 639 FIXED TERMINAL POINT 639 HORIZONTAL
TERMINAL LINE 639 TRUNCATED VERTICAL TERMINAL LINE 639 TRUNCATED
HORIZONTAL TERMINAL LINE 640 EXERCISE 20.2 643 20.3 AUTONOMOUS PROBLEMS
644 20.4 ECONOMIC APPLICATIONS 645 LIFETIME UTILITY MAXIMIZATION 645
EXHAUSTIBLE RESOURCE 647 EXERCISE 20.4 649 20.5 INFINITE TIME HORIZON
649 NEOCLASSICAL OPTIMAL GROWTH MODEL 649 THE CURRENT-VALUE HAMILTONIAN
651 CONSTRUCTING A PHASE DIAGRAM 652 ANALYZING THE PHASE DIAGRAM 653
20.6 LIMITATIONS OF DYNAMIC ANALYSIS 654 THE GREEK ALPHABET 655
MATHEMATICAL SYMBOLS 656 A SHORT READING LIST 659 ANSWERS TO SELECTED
EXERCISES 662 INDEX 677
|
| any_adam_object | 1 |
| author | Chiang, Alpha C. 1927- Wainwright, Kevin |
| author_GND | (DE-588)13164940X |
| author_facet | Chiang, Alpha C. 1927- Wainwright, Kevin |
| author_role | aut aut |
| author_sort | Chiang, Alpha C. 1927- |
| author_variant | a c c ac acc k w kw |
| building | Verbundindex |
| bvnumber | BV019863140 |
| callnumber-first | H - Social Science |
| callnumber-label | HB135 |
| callnumber-raw | HB135 |
| callnumber-search | HB135 |
| callnumber-sort | HB 3135 |
| callnumber-subject | HB - Economic Theory and Demography |
| classification_rvk | SK 980 QH 100 QH 110 |
| classification_tum | MAT 902f WIR 522f |
| ctrlnum | (OCoLC)254965254 (DE-599)BVBBV019863140 |
| dewey-full | 330.0151 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 330 - Economics |
| dewey-raw | 330.0151 |
| dewey-search | 330.0151 |
| dewey-sort | 3330.0151 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 4. ed., international ed. |
| format | Book |
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| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV019863140 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:07:51Z |
| institution | BVB |
| isbn | 0071238239 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013187615 |
| oclc_num | 254965254 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-20 DE-384 DE-1029 DE-91G DE-BY-TUM DE-N2 DE-739 DE-521 DE-634 DE-945 DE-2070s DE-91 DE-BY-TUM DE-1047 DE-Re13 DE-BY-UBR DE-92 DE-83 DE-M49 DE-BY-TUM DE-29T DE-573 |
| owner_facet | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-20 DE-384 DE-1029 DE-91G DE-BY-TUM DE-N2 DE-739 DE-521 DE-634 DE-945 DE-2070s DE-91 DE-BY-TUM DE-1047 DE-Re13 DE-BY-UBR DE-92 DE-83 DE-M49 DE-BY-TUM DE-29T DE-573 |
| physical | XIX, 688 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | McGraw-Hill |
| record_format | marc |
| spelling | Chiang, Alpha C. 1927- Verfasser (DE-588)13164940X aut Fundamental methods of mathematical economics Alpha C. Chiang ; Kevin Wainwright 4. ed., international ed. Boston, Mass. [u.a.] McGraw-Hill 2005 XIX, 688 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wirtschaftsmathematik Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Wirtschaftswissenschaften (DE-588)4066528-8 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Wirtschaftswissenschaften (DE-588)4066528-8 s Mathematische Methode (DE-588)4155620-3 s DE-604 Wirtschaftsmathematik (DE-588)4066472-7 s 2\p DE-604 Mathematik (DE-588)4037944-9 s 3\p DE-604 Wainwright, Kevin Verfasser aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013187615&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chiang, Alpha C. 1927- Wainwright, Kevin Fundamental methods of mathematical economics Wirtschaftsmathematik Mathematische Methode (DE-588)4155620-3 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Wirtschaftswissenschaften (DE-588)4066528-8 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4155620-3 (DE-588)4066472-7 (DE-588)4066528-8 (DE-588)4037944-9 (DE-588)4123623-3 |
| title | Fundamental methods of mathematical economics |
| title_auth | Fundamental methods of mathematical economics |
| title_exact_search | Fundamental methods of mathematical economics |
| title_full | Fundamental methods of mathematical economics Alpha C. Chiang ; Kevin Wainwright |
| title_fullStr | Fundamental methods of mathematical economics Alpha C. Chiang ; Kevin Wainwright |
| title_full_unstemmed | Fundamental methods of mathematical economics Alpha C. Chiang ; Kevin Wainwright |
| title_short | Fundamental methods of mathematical economics |
| title_sort | fundamental methods of mathematical economics |
| topic | Wirtschaftsmathematik Mathematische Methode (DE-588)4155620-3 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Wirtschaftswissenschaften (DE-588)4066528-8 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Wirtschaftsmathematik Mathematische Methode Wirtschaftswissenschaften Mathematik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013187615&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT chiangalphac fundamentalmethodsofmathematicaleconomics AT wainwrightkevin fundamentalmethodsofmathematicaleconomics |