Maths for economics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2012
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIV, 674 S. Ill., graph. Darst. |
| ISBN: | 9780199602124 |
Staff View
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| 100 | 1 | |a Renshaw, Geoff |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Maths for economics |c Geoff Renshaw ; with contributions from Norman Ireland |
| 246 | 1 | 3 | |a Economics |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2012 | |
| 300 | |a XXIV, 674 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804148889297616896 |
|---|---|
| adam_text | Titel: Maths for economics
Autor: Renshaw, Geoffrey
Jahr: 2012
Detailed contents
About the author xiv 3 Linear equations 63
About the book xv 3.1 Introduction 63
How to use the book xvii 3.2 How we can manipulate equations 64
Chapter map xviii 3.3 Variables and parameters 69
Guided tour of the textbook features xx 3.4 Linear and non-linear equations 69
Guided tour of the Online Resource Centre xxii 35 Linear functions 72
Acknowledgements xxiv 36 Graphs of linear functions 73
3.7 The slope and intercept of a linear function 75
Part One Foundations 3-8 Graphical solution of linear equations 80
3.9 Simultaneous linear equations 81
1 Arithmetic 3 3.10 Graphical solution of simultaneous linear
1.1 Introduction 3 equations 84
1.2 Addition and subtraction with positive 3.11 Existence of a solution to a pair of linear
and negative numbers 4 simultaneous equations 87
1.3 Multiplication and division with positive 3.12 Three linear equations with three unknowns 90
and negative numbers 7 3.13 Economic applications 91
1.4 Brackets and when we need them 10 3.14 Demand and supply for a good 91
1.5 Factorization 13 3.15 The inverse demand and supply functions 94
1.6 Fractions 14 3.16 Comparative statics 97
1.7 Addition and subtraction of fractions 16 3.17 Macroeconomic equilibrium 102
1.8 Multiplication and division of fractions 20
1.9 Decimal numbers 24 * Quadratic equations 109
1.10 Adding, subtracting, multiplying, and 4.1 Introduction 109
dividing decimal numbers 26 4.2 Quadratic expressions 110
1.11 Fractions, proportions, and ratios 27 4.3 Factorizing quadratic expressions 112
1.12 Percentages 28 4.4 Quadratic equations 114
1.13 Index numbers 33 4.5 The formula for solving any quadratic
1.14 Powers and roots 35 equation 116
1.15 Standard index form 40 4.6 Cases where a quadratic expression
1.16 Some additional symbols 41 cannot be factorized 117
SELF-TEST EXERCISE 42 4-7 The case of the perfect square 118
2 Algebra 43
2.1 Introduction 43
2.2 Rules of algebra 44
4.8 Quadratic functions 120
4.9 The inverse quadratic function 122
4.10 Graphical solution of quadratic equations 123
4.11 Simultaneous quadratic equations 126
2.3 Addition and subtraction of algebraic 412 Graphical solution of simultaneous
exPresslons 44 quadratic equations 127
2.4 Multiplication and division of algebraic 4 13 Economic app|ication t : supp,y and demand 128
4.14 Economic application 2: costs and revenue 131
5 Some further equations and
expressions 45
2.5 Brackets and when we need them 47
2.6 Fractions 49
2.7 Addition and subtraction of fractions 50 techniques 134
2.8 Multiplication and division of fractions 52 51 Introduction 134
2.9 Powers and roots 55 52 The cubic function 135
2.10 Extending the idea of powers 56 5.3 Graphical solution of cubic equations 138
2.11 Negative and fractional powers 57 5 4 Application of the cubic function in
2.12 The sign of an 59 economics 141
2.13 Necessary and sufficient conditions 60 5.5 The rectangular hyperbola 142
APPENDIX: The Greek alphabet 62 5.6 Limits and continuity 143
5.7 Application of the rectangular hyperbola 8.8 The market demand function 229
in economics 147 8.9 Total revenue with monopoly 231
5.8 The circle and the ellipse 149 8.10 Marginal revenue with monopoly 232
5.9 Application of circle and ellipse in 8.11 Demand, total, and marginal revenue
economics 151 functions with monopoly 234
5.10 Inequalities 152 8.12 Demand, total, and marginal revenue
5.11 Examples of inequality problems 156 with perfect competition 235
5.12 Applications of inequalities in economics 159 8.13 Worked examples on demand, marginal,
and total revenue 236
8.14 Profit maximization 239
Part TWO Optimization With One 8.15 Profit maximization with monopoly 240
independent variable 8.16 Profit maximization using marginal cost
and marginal revenue 242
8.17 Profit maximization with perfect competition 244
8.18 Comparing the equilibria under monopoly
and perfect competition 246
8.19 Two common fallacies concerning profit
6 Derivatives and differentiation 165
6.1 Introduction 165
6.2 The difference quotient 166
6.3 Calculating the difference quotient 167 maximization 248
6.4 The slope of a curved line 16
maximization
8.20 The second order condition for profit
6.5 Finding the slope of the tangent 170 maximization 248
6.6 Generalization to any function of x 172 APPENDIX 8.1: The relationship between
6.7 Rules for evaluating the derivative of total cost, average cost, and marginal cost 253
a function 173
APPENDIX 8.2: The relationship between
6.8 Summary of rules of differentiation 182 price, total revenue, and marginal revenue 254
7 Derivatives in action 184 9 Elasticity 256
7.1 Introduction 184 9.1 Introduction 256
7.2 Increasing and decreasing functions 185 9.2 Absolute, proportionate, and percentage
7.3 Optimization: finding maximum and changes 257
minimum values 187 9.3 The arc elasticity of supply 259
7.4 A maximum value of a function 187 9.4 Elastic and inelastic supply 260
7.5 The derivative as a function of x 189 9.5 Elasticity as a rate of proportionate change 260
7.6 A minimum value of a function 189 9.6 Diagrammatic treatment 261
7.7 The second derivative 191 9.7 Shortcomings of arc elasticity 263
7.8 A rule for maximum and minimum 9.8 The point elasticity of supply 263
values 192
9.9 Reconciling the arc and point supply
7.9 Worked examples of maximum and elasticities 265
minimum values 192 9i0 Worked examples on supply elasticity 265
7.10 Points of inflection 195 9.11 The arc elasticity of demand 268
7.11 A rule for points of inflection 198 9.12 Elastic and inelastic demand 270
7.12 More about points of inflection 199 913 An alternative definition of demand elasticity 272
7.13 Convex and concave functions 206 914 The point elasticity of demand 273
7.14 An alternative notation for derivatives 209 9.15 Reconciling the arc and point demand
7.15 The differential and linear approximation 210 elasticities 274
9.16 Worked examples on demand elasticity 275
8 Economic applications of functions 917 Two simplifications 277
and derivatives 213
9.18 Marginal revenue and the elasticity of
8.1 Introduction 213 demand 279
8.2 The firm s total cost function 214 9.19 The elasticity of demand under perfect
8.3 The firm s average cost function 216 competition 282
8.4 Marginal cost 218 9-20 Worked examples on demand elasticity
8.5 The relationship between marginal and and marginal revenue 284
average cost 220 9.21 Other elasticities in economics 288
8.6 Worked examples of cost functions 222 9.22 The firm s total cost function 288
8.7 Demand, total revenue, and marginal 9.23 The aggregate consumption function 290
revenue 229 9.24 Generalizing the concept of elasticity 291
Part Three Mathematics of finance
13.3 The derivative of the natural logarithmic
function
and growth -13.4 Tne rate 0f proportionate change, or rate
of growth
10 Compound growth and present 13.5 Discrete growth
discounted value 297 13.6 Continuous growth
10.1 Introduction 297 13.7 Instantaneous, nominal, and effective
10.2 Arithmetic and geometric series 298 growth rates
10.3 An economic application 300 13.8 Semi-log graphs and the growth rate again
10.4 Simple and compound interest 304 13.9 An important special case
10.5 Applications of the compound growth 13.10 Logarithmic scales and elasticity
formula 307
10.6 Discrete versus continuous growth 309
10.7 When interest is added more than once Part Four Optimization with tWO Or
per year 309 more independent variables
10.8 Present discounted value 314
10.9 Present value and economic behaviour 316
10.10 Present value of a series of future receipts 316
10.11 Present value of an infinite series 319
10.12 Market value of a perpetual bond 320
10.13 Calculating loan repayments 322
11 The exponential function and
logarithms 328
11.1 Introduction 328
11.2 The exponential function y = 10X 330
11.3 The function inverse to y= 10* 331
11.4 Properties of logarithms 333
11.5 Using your calculator to find common
logarithms 333
11.6 The graph of y= log10x 334
11.7 Rules for manipulating logs 335
11.8 Using logs to solve problems 337
11.9 Some more exponential functions 338
14 Functions of two or more
independent variables
14.1 Introduction
14.2 Functions with two independent variables
14.3 Examples of functions with two
independent variables
14.4 Partial derivatives
14.5 Evaluation of first order partial derivatives
14.6 Second order partial derivatives
14.7 Economic applications 1: the production
function
14.8 The shape of the production function
14.9 The Cobb-Douglas production function
14.10 Alternatives to the Cobb-Douglas form
14.11 Economic applications 2: the utility function
14.12 The shape of the utility function
14.13 The Cobb-Douglas utility function
APPENDIX 14.1: A variant of the partial
12 Continuous growth and the natural derivatives of the Cobb-Douglas function
exponential function 342
12.1 Introduction 342
12.2 Limitations of discrete compound growth 343 total differential, and applications
12.3 Continuous growth: the simplest case 343 15-1 deduction
12.4 Continuous growth: the general case 346 15-2 Maximum and minimum values
12.5 The graph of y=aerx 347 153 Saddle points
12.6 Natural logarithms 349 15A Tne total differential of z = f(x, y)
12.7 Rules for manipulating natural logs 351 155 Differentiating a function of a function
12.8 Natural exponentials and logs on your 15-6 Marginal revenue as a total derivative
calculator 351 15.7 Differentiating an implicit function
12.9 Continuous growth applications 353 15.8 Finding the slope of an iso-z section
12.10 Continuous discounting and present value 358 15-9 A shift from one iso-z section to another
12.11 Graphs with semi-log scale 361 15-10 Economic applications 1: the production
function
13 Derivatives of exponential and 15.11 Isoquants of the Cobb-Douglas production
logarithmic functions and their function
applications 368 15.12 Economic applications 2: the utility function
13.1 Introduction 368 15.13 The Cobb-Douglas utility function
13.2 The derivative of the natural exponential 15.14 Economic application 3: macroeconomic
function 369 equilibrium
15 Maximum and minimum values, the
15.15 The Keynesian multiplier 473 18.2 The definite integral 552
15.16 The IS curve and its slope 474 18.3 The indefinite integral 554
15.17 Comparative statics: shifts in the IS curve 475 18.4 Rules for finding the indefinite integral 555
18.5 Finding a definite integral 562
16 Constrained maximum and 18.6 Economic applications 1: deriving the
minimum values 479 total cost function from the marginal
16.1 Introduction 479 cost function 565
16.2 The problem, with a graphical solution 480 18.7 Economic applications 2: deriving total
16.3 Solution by implicit differentiation 482 revenue from the marginal revenue function 567
16.4 Solution by direct substitution 485 18-8 Economic applications 3: consumers surplus 569
16.5 The Lagrange multiplier method 486 18-9 Economic applications 4: producers surplus 570
16.6 Economic applications 1: cost minimization 490 18-10 Economic applications 5: present value of a
16.7 Economic applications 2: profit maximization 496 continuous stream of income 572
16.8 A worked example 501
16.9 Some problems with profit maximization 502
16.10 Profit maximization by a monopolist 508
16.11 Economic applications 3: utility maximization
19 Matrix algebra 577
19.1 Introduction 577
19.2 Definitions and notation 578
by the consumer 510 19-3 Transpose of a matrix 579
16.12 Deriving the consumer s demand functions 512 19-4 Addition/subtraction of two matrices 579
19.5 Multiplication of two matrices 580
17 Returns to scale and homogeneous 19.6 Vector multiplication 582
functions; partial elasticities; growth 19 7 Scalar multiplication 583
accounting; logarithmic scales 519 19.8 Matrix algebra as a compact notation 583
17.1 Introduction 519 19.9 The determinant of a square matrix 584
17.2 The production function and returns to scale 520 19.10 The inverse of a square matrix 587
17.3 Homogeneous functions 522 19.11 Using matrix inversion to solve linear
17.4 Properties of homogeneous functions 525 simultaneous equations 589
17.5 Partial elasticities 531 19.12 Cramer s rule 590
17.6 Partial elasticities of demand 532 19.13 A macroeconomic application 592
17.7 The proportionate differential of a function 534 19.14 Conclusions 594
17.8 Growth accounting 537
17.9 Elasticity and logs 539 20 Difference and differential equations 597
17.10 Partial elasticities and logarithmic scales 540 20.1 Introduction 597
17.11 The proportionate differential and logs 542 20.2 Difference equations 598
17.12 Log linearity with several variables 544 20.3 Qualitative analysis 601
20.4 The cobweb model of supply and demand 605
20.5 Conclusions on the cobweb model 610
Part Five Some further topics 20.6 Differential equations 612
20.7 Qualitative analysis 615
18 Integration 551 20.8 Dynamic stability of a market 616
18.1 Introduction 551 20.9 Conclusions on market stability 619
W21 Extensions and future directions APPENDIX 21.3: The firm s maximum profit
(on the Online Resource Centre) function with two products
21.1 Introduction APPENDIX 21.4: Removing the imaginary number
21.2 Functions and analysis
21.3 Comparative statics
21.4 Second order difference equations
APPENDIX 21.1: Proof of Taylor s theorem Answers to progress exercises 623
APPENDIX 21.2: Using Taylor s formula to relate Answers to chapter 1 self-test 657
production function forms Glossary 658
Index 667
|
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| dewey-full | 330.01/51 |
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| dewey-ones | 330 - Economics |
| dewey-raw | 330.01/51 |
| dewey-search | 330.01/51 |
| dewey-sort | 3330.01 251 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
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| isbn | 9780199602124 |
| language | English |
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| spelling | Renshaw, Geoff Verfasser aut Maths for economics Geoff Renshaw ; with contributions from Norman Ireland Economics 3. ed. Oxford [u.a.] Oxford Univ. Press 2012 XXIV, 674 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Wirtschaftsmathematik (DE-588)4066472-7 s b DE-604 Ireland, Norman J. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024785040&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 |
| spellingShingle | Renshaw, Geoff Maths for economics Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| subject_GND | (DE-588)4066472-7 (DE-588)4123623-3 |
| title | Maths for economics |
| title_alt | Economics |
| title_auth | Maths for economics |
| title_exact_search | Maths for economics |
| title_full | Maths for economics Geoff Renshaw ; with contributions from Norman Ireland |
| title_fullStr | Maths for economics Geoff Renshaw ; with contributions from Norman Ireland |
| title_full_unstemmed | Maths for economics Geoff Renshaw ; with contributions from Norman Ireland |
| title_short | Maths for economics |
| title_sort | maths for economics |
| topic | Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| topic_facet | Wirtschaftsmathematik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024785040&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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