Mathematics in economics: models and methods
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford, UK [u.a.]
Blackwell
1995
|
| Ausgabe: | Repr. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 508 S. graph. Darst. |
| ISBN: | 0631180559 0631180567 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804129414916603904 |
|---|---|
| adam_text | Contents
Acknowledgements xiii
Note on Conventions xv
Foreword by K. G. Binmore xvii
Part I Elementary Algebra 1
1 Sets and Numbers 3
1.1 Sets 3
1.2 Venn diagrams 4
1.3 Inequalities 6
1.4 Roots 9
1.5 Exercises 12
1.6 Answers 13
2 Matrices and Vectors 17
2.1 Matrices 17
2.2 Vectors 22
2.3 Lines and planes 25
2.4 Exercises 30
2.5 Answers 32
3 Modelling Consumer Choice 40
3.1 Commodity bundles 40
3.2 Price vectors 40
3.3 Budget set 41
3.4 Rationing, taxation and subsidies 43
3.5 Preferences 45
3.6 Optimal choice 51
3.7 Sales versus income tax 52
3.8 Marginal rate of substitution 52
3.9 Factors of production 56
3.10 Exercises 60
3.11 Answers 61
4 Discrete Variables 67
4.1 Discrete and continuous variables 67
viii Contents
4.2 Summation 69
4.3 Induction 71
4.4 Intertemporal choice 72
4.5 Discounting 74
4.6 Bonds 75
4.7 Binomial theorem 76
4.8 Polynomials 79
4.9 Population growth 82
4.10 Cobweb model 86
4.11 Linear homogeneous difference equations 88
4.12 Multiplier accelerator models 90
4.13 Summing differences 91
4.14 Exercises 94
4.15 Answers 97
5 Functions 103
5.1 Dependent and independent variables 103
5.2 Production functions 104
5.3 Returns to scale 105
5.4 Utility functions 107
5.5 Real variables 109
5.6 Demand functions 114
5.7 Market demand 117
5.8 Cost functions 119
5.9 Supply functions 122
5.10 Market supply 126
5.11 Vector variables 127
5.12 Operations on functions 129
5.13 Implicit functions 132
5.14 Discrete variables 132
5.15 Operators 133
5.16 Probability measures 133
5.17 Independent events 135
5.18 Random variables 137
5.19 Expectation 139
5.20 Risky consumer choice 141
5.21 Risk aversion 145
5.22 Exercises 146
5.23 Answers 149
6 Equilibrium 160
6.1 Supply and demand 160
6.2 Comparative statics 162
6.3 General equilibrium 166
6.4 Linear market equilibrium models 168
6.5 Homogeneous linear equations 170
6.6 Rank 174
6.7 Non homogeneous linear equations 177
6.8 Non homogeneous difference equations 181
Contents ix
6.9 Finding the inverse of a matrix 185
6.10 Input output analysis 189
6.11 Determinants a tool for solving equations 193
6.12 Exercises 201
6.13 Answers 204
7 Eigenvalues and Eigenvectors 209
7.1 Example: super power arms race 209
7.2 Eigenvalues 211
7.3 Arms race revisited 213
7.4 Diagonalization 214
7.5 Boom bust: a Markov process 216
7.6 Symmetric matrices 219
7.7 Quadratic forms 220
7.8 Positive definite forms 225
7.9 Matrices of size nxn 229
7.10 Exercises 233
7.11 Further exercises 234
7.12 Answers 238
Part II Elementary Calculus 247
8 Limits and their Uses 251
8.1 Large scale average cost 251
8.2 Marginal costs profitability 253
8.3 Definition of a limit 255
8.4 Exercises 258
8.5 Answers 259
9 Continuity and its Uses 260
9.1 The continuity condition 260
9.2 Discontinuous cost function 261
9.3 Discontinuous stock function 261
9.4 Right sided and left sided limits 262
9.5 Importance of continuity in economic models 263
9.6 Calculation of limits 265
9.7 Exercises 268
9.8 Answers 269
10 Uses of the Derivative 271
10.1 Instantaneous market indicators 271
10.2 Linearization: a tool for simplifying models 277
10.3 Why the marginal propensity to consume lies between
zero and unity 279
10.4 Marginal revenue versus average revenue; the mean
value theorem 280
10.5 Increasing functions facts and myths 282
10.6 Average revenue, marginal revenue inverse functions 284
10.7 Exercises 288
x Contents
10.8 Further exercises 291
10.9 Answers 293
11 Continuous Compounding and Exponential Growth 297
11.1 Interest compounded with a high frequency 297
11.2 Connection with differentiation 299
11.3 Cashing in an appreciating asset 301
11.4 Summing a flow of expenditure 304
11.5 Consumer surplus 305
11.6 Logarithms and how to double your money 311
11.7 Exercises 317
11.8 Answers 324
12 Partial Differentiation 332
12.1 Total versus partial change: analysis of two input costs 332
12.2 Geometric meaning of the partial derivatives 334
12.3 Comparative statics: national income revisited 335
12.4 The chain rule: marginal product revisited 336
12.5 Implicit differentiation 340
12.6 Implicit differentiation: economic applications 343
12.7 Euler s theorem for homogeneous functions 344
12.8 Exercises 346
12.9 Answers 348
13 The Gradient 351
13.1 Tangent budget lines 351
13.2 Price vectors and normals 354
13.3 Normals to isoquant curves: the gradient 357
13.4 An application: the Edgeworth box 361
13.5 Tangent planes to surfaces 364
13.6 A directional marginal utility 369
13.7 Direction of fastest growth 373
13.8 Breaking the convention: differentials 375
13.9 Exercises 378
13.10 Answers 380
14 Taylor s Theorem an Approximation Tool 384
14.1 Double your money approximation and relative
smallness 384
14.2 Estimating error via the derivatives 385
14.3 Taylor s theorem: second order error 388
14.4 Taylor s theorem: higher order terms and (1 +x) 390
14.5 The constant elasticity of substitution production function
in the limit as p approaches zero 393
14.6 Concavity of/(x) from f (x) *s 0 394
14.7 Classification of stationary points: revision 395
14.8 Modelling a cost curve with a cubic 399
14.9 An exotic application: monopolistic barter 401
14.10 Exercises 406
14.11 Further exercises 409
14.12 Answers 410
Contents xi
15 Optimization in Two Variables 416
15.1 Interior optimum: stationarity 416
15.2 Classifying quadratic surfaces 418
15.3 Quadratic approximation of a surface locally 423
15.4 Classifying stationary points: local concavity 427
15.5 Global concavity 434
15.6 Boundary optimum: Lagrange multipliers 439
15.7 Worked examples 441
15.8 Lagrange multiplier as the marginal utility of money 445
15.9 More than two variables 446
15.10 Constrained optimization: a second order condition 450
15.11 Exercises 451
15.12 Further exercises 453
15.13 Answers 455
16 Economic Dynamics: Differential Equations 461
16.1 Domar s growth model 461
16.2 Off equilibrium: a paradox 463
16.3 Price adjustment in the market 464
16.4 Solow s growth model 465
16.5 Resume on differential equations 469
16.6 Some more tricks for order 1 475
16.7 A market with price trend anticipation 478
16.8 Second order differential equations with constant
coefficients 479
16.9 The market with price trend anticipation (continued) 482
16.10 Finding particular solutions 484
16.11 Higher orders 487
16.12 A final example: the Phillips relation 488
16.13 Exercises 492
16.14 Further exercises 494
16.15 Answers 496
Index of Symbols 503
Index 504
|
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| discipline | Wirtschaftswissenschaften |
| edition | Repr. |
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| spellingShingle | Ostaszewski, Adam Mathematics in economics models and methods Mathématiques économiques - Manuels d'enseignement supérieur ram Économie politique - Modèles mathématiques ram Mathematisches Modell (DE-588)4114528-8 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Wirtschaftsmodell (DE-588)4079348-5 gnd |
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| title | Mathematics in economics models and methods |
| title_auth | Mathematics in economics models and methods |
| title_exact_search | Mathematics in economics models and methods |
| title_full | Mathematics in economics models and methods Adam Ostaszewski |
| title_fullStr | Mathematics in economics models and methods Adam Ostaszewski |
| title_full_unstemmed | Mathematics in economics models and methods Adam Ostaszewski |
| title_short | Mathematics in economics |
| title_sort | mathematics in economics models and methods |
| title_sub | models and methods |
| topic | Mathématiques économiques - Manuels d'enseignement supérieur ram Économie politique - Modèles mathématiques ram Mathematisches Modell (DE-588)4114528-8 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Wirtschaftsmodell (DE-588)4079348-5 gnd |
| topic_facet | Mathématiques économiques - Manuels d'enseignement supérieur Économie politique - Modèles mathématiques Mathematisches Modell Wirtschaftsmathematik Wirtschaftsmodell |
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