Mathematics for modern economics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Allan
1984
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 412 S. graph. Darst. |
| ISBN: | 0860030237 0860031241 0389205222 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface ix
Parti Differential Calculus 1
1 Algebra: The Language of Mathematics 3
Introductory Remarks 3
Sets 4
Basic Algebra 6
2 Functions of One Variable 13
Functions and their Graphs 13
Linear Functions 16
Quadratic Functions 21
Logarithmic and Exponential Functions 26
Composite Functions and Inverses 30
Limiting Values of Functions 31
Linear Simultaneous Equations 32
Exercises 35
3 Differentiation of Functions of a Single Variable 38
The Derivative 38
Rules for Differentiation 47
Problems 56
Exercises 58
v
vi Contents
4 Differentiation of Functions of Several Variables 60
Vectors 60
Functions of Several Variables and Partial Functions 63
Partial Differentiation 68
Implicit Functions and Implicit Differentiation 70
Direction and Total Derivatives 74
Problems 80
Exercises 81
5 Unconstrained Optimisation 83
Functions of One Variable 83
Functions of Several Variables 90
Non linear Simultaneous Equations 94
Tangents and Tangent Functions 96 j
Problems 99 I
Exercises 101 i
6 Difference and Differential Equations 103
Introduction 103
Difference Equations 104
Integration 114
First Order Differential Equations 123
Problems 129
Exercises 130 :
i
7 Concave and Convex Functions 132
Introduction 132 ¦¦
Concave Functions of a Single Variable 133
Concave Functions of Many Variables 143
Convex Functions 148
Problem 150
Exercises 150
Part II Constrained Optimisation 153
8 An Informal Introduction to Constrained Maximisation 155
Introduction 155
Maximisation of Utility Subject to a Budget Constraint 156
Cost Minimisation Subject to an Output Constraint 162
One Variable Constrained Maximisation 167
Problem 173
Contents vii
9 Lagrangian and Envelope Functions 174
Introduction 174
The Lagrangian Theorem and its Use 175
Interpreting the Lagrangian 177
The Envelope Function and the Lagrangian 179
The Concavity of the Envelope Function 181
The Proof of the Lagrangian Theorem 184
Problems 187
10 The Indirect Utility Function 190
Introduction 190
The Indirect Utility Function 191
Characteristic Properties of Indirect Utility Functions 195
Roy s Identity 199
Optimal Value Functions and Lagrangians 203
The Duality of Indirect and Direct Utility Functions 207
Problems 213
11 Expenditure, Cost and Profit Functions 215
Introduction 215
Expenditure Functions 215
The Cost Function 223
The Profit Function 231
Problems 242
12 The Envelope Theorem 245
Introduction 245
The Envelope Theorem 245
Applications to Consumer Behaviour 247
Applications to the Firm 249
Problems 252
13 Extensions to the Theory of Optimisation 258
Introduction 258
Monotonic Transformations and Indirect Concavity 259
Quasi Concavity 267
Lagrangians with Several Constraints and the Kuhn Tucker
Conditions 269
Problems 274
viii Contents
Part III Solutions to Problems: The Theory of the Consumer
and Firm 277
14 Consumer Theory 279
The Consumption Decision 279
Indirect Utility, Expenditure and Demand Function 283
Aggregation and the Structure of the Indirect
Utility Function 293
Intertemporal Consumption 296
Taxation 306
Consumer Surplus 309
Public Provision of Goods 312
Uncertainty 315
15 Costs and the Competitive Firm 319
Production Functions 319
The Perfectly Competitive Firm 337
16 Monopoly and Imperfect Competition 344
Monopoly 344
Imperfect Competition 355
Monopoly in the Input Market 364
Appendix 372
Introduction 372
Vectors and Matrices 372
Matrix Products 374
Determinants 377
Quadratic Forms 382
Length, Distance and Open Sets 383
Convex Sets and Concave Functions 387
Differentiation: The One Variable Case 389
Differentiation: Several Variables 393
Equality Constraints 396
Trigonometric Functions 396
Complex Numbers 399
Bibliography and Further Reading 406
Index 409
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:04:07Z |
| institution | BVB |
| isbn | 0860030237 0860031241 0389205222 |
| language | English |
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| physical | XII, 412 S. graph. Darst. |
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| publishDate | 1984 |
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| publisher | Allan |
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| spelling | Birchenhall, Chris Verfasser aut Mathematics for modern economics Chris Birchenhall and Paul Grout Oxford Allan 1984 XII, 412 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathématiques économiques Mathématiques économiques ram Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Wirtschaftsmathematik (DE-588)4066472-7 s DE-604 Grout, Paul Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002357983&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Birchenhall, Chris Grout, Paul Mathematics for modern economics Mathématiques économiques Mathématiques économiques ram Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| subject_GND | (DE-588)4066472-7 (DE-588)4151278-9 |
| title | Mathematics for modern economics |
| title_auth | Mathematics for modern economics |
| title_exact_search | Mathematics for modern economics |
| title_full | Mathematics for modern economics Chris Birchenhall and Paul Grout |
| title_fullStr | Mathematics for modern economics Chris Birchenhall and Paul Grout |
| title_full_unstemmed | Mathematics for modern economics Chris Birchenhall and Paul Grout |
| title_short | Mathematics for modern economics |
| title_sort | mathematics for modern economics |
| topic | Mathématiques économiques Mathématiques économiques ram Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| topic_facet | Mathématiques économiques Economics, Mathematical Wirtschaftsmathematik Einführung |
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