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Mathematics in economics : models and methods

Mathematics in economics : models and methods

자료유형
단행본
개인저자
Ostaszewski, Adam. Binmore, K. G. , 1940-
서명 / 저자사항
Mathematics in economics : models and methods / Adam Ostaszewski.
발행사항
Oxford, UK ;   Cambridge, Mass. :   Blackwell ,   1993.  
형태사항
xix, 508 p. : ill. ; 25 cm.
ISBN
0631180559 (acid-free paper) 0631180567 (pbk. : acid-free paper) 9780631180562 (pbk.)
일반주기
"Based on lecture notes by K.G. Binmore and A. Ostaszewski."  
Includes index.  
일반주제명
Economics -- Mathematical models.
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001 000045557008
005 20091030105803
008 920914s1993 enka 001 0 eng
010 ▼a 92032454
020 ▼a 0631180559 (acid-free paper)
020 ▼a 0631180567 (pbk. : acid-free paper)
020 ▼a 9780631180562 (pbk.)
035 ▼a (KERIS)REF000013789381
040 ▼a DLC ▼c DLC ▼d DLC ▼d 211009
050 0 0 ▼a HB135 ▼b .O867 1993
082 0 0 ▼a 330/.01/5118 ▼2 22
090 ▼a 330.015118 ▼b O85m
100 1 ▼a Ostaszewski, Adam.
245 1 0 ▼a Mathematics in economics : ▼b models and methods / ▼c Adam Ostaszewski.
260 ▼a Oxford, UK ; ▼a Cambridge, Mass. : ▼b Blackwell , ▼c 1993.
300 ▼a xix, 508 p. : ▼b ill. ; ▼c 25 cm.
500 ▼a "Based on lecture notes by K.G. Binmore and A. Ostaszewski."
500 ▼a Includes index.
650 0 ▼a Economics ▼x Mathematical models.
700 1 ▼a Binmore, K. G. , ▼d 1940-
945 ▼a KINS

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No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 과학도서관/Sci-Info(2층서고)/ 청구기호 330.015118 O85m 등록번호 121186141 도서상태 대출가능 반납예정일 예약 서비스 B M

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목차


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 diagram = 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
  4.2 Summation = 69
  4.3 Induction = 71
  4.4 Inter-temporal 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
  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 Eigen-vectors = 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 n x n = 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
  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 iso-quant curves : the gradient = 357
  13.4 An application : the Edge-worth 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 (I + x)$$\^t$$ = 390
  14.5 The constant elasticity of substitution production function in the limit as $$\rho$$ approaches zero = 393
  14.6 Concavity of f(x) from f"(x)$$\leq$$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
 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 Rdsumd 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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