Cover image for Mathematics for economics and business : an interactive introduction
Title:
Mathematics for economics and business : an interactive introduction
Author:
Soper, Jean.
Personal Author:
Publication Information:
Oxford, UK ; Malden, Mass. : Blackwell Publishers, 1999.
Physical Description:
xx, 294 pages : illustrations ; 25 cm + 1 computer optical disc (4 3/4 in.).
Language:
English
ISBN:
9780631211891

9780631207818
Format :
Book

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HB135 .S573 1999 TEXT Adult Non-Fiction Central Closed Stacks
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Summary

Summary

Written for first-year undergraduates on economics and business courses, this book offers the ideal approach to understanding the mathematics relevant to them. It sets out all the basic mathematical techniques and explains the economic analysis or business context where each is used. By following the worked examples and tackling the practice problems, students will discover how to use and apply each of the techniques.


Table of Contents

Prefacep. x
Using this Book and the MathEcon Softwarep. xii
List of MathEcon Screensp. xvi
1 Functions in Economicsp. 1
1.1 Introductionp. 1
1.2 Coordinates and Graphsp. 2
Plotting negative valuesp. 3
1.3 Variables and Functionsp. 4
Substitution of x valuesp. 4
Power functionsp. 5
Linear functionsp. 6
Sketching functionsp. 7
1.4 Fractions and Sharingp. 10
Cancellingp. 11
Common denominatorp. 12
Addition and subtraction of fractionsp. 12
Multiplication and division of fractionsp. 13
1.5 Basic Rules of Algebrap. 15
Calculators and computersp. 16
Order within an expressionp. 16
Negative Numbersp. 17
Calculators and negative signsp. 18
Multiplying and dividing by 10p. 18
Factors and multiplying out bracketsp. 20
Accuracyp. 21
1.6 Powers and Indicesp. 23
Powers and your calculatorp. 25
1.7 Functions of More Than One Variablep. 26
1.8 Economic Variables and Functionsp. 26
1.9 Total and Average Revenuep. 27
1.10 Total and Average Costp. 29
1.11 Profitp. 32
1.12 Production Functions, Isoquants and the Average Product of Labourp. 33
Chapter 1 Answers to Practice Problemsp. 36
2 Equations in Economicsp. 43
2.1 Introductionp. 43
2.2 Rewriting and Solving Equationsp. 44
Solution in terms of other variablesp. 47
2.3 Substitutionp. 49
2.4 Demand and Supplyp. 50
Market equilibriump. 51
Changes in demand or supplyp. 52
Effects of a per unit taxp. 54
2.5 Cost-Volume-Profit Analysisp. 57
2.6 Linear Equationsp. 60
2.7 Budget Linesp. 64
2.8 Constant Substitution Along a Linep. 67
2.9 Quadratic Equationsp. 68
2.10 Intersection of MC with MR or AVCp. 71
2.11 Simultaneous Equationsp. 73
2.12 Simultaneous Equilibrium in Related Marketsp. 75
2.13 Exponential Functionsp. 78
2.14 Logarithmic Functionsp. 81
Chapter 2 Answers to Practice Problemsp. 84
3 Macroeconomic Modelsp. 93
3.1 Introductionp. 93
3.2 Notation and Model Specificationp. 94
3.3 Identifying Equilibrium Incomep. 102
3.4 Keynesian Cross Modelp. 103
3.5 IS-LM Analysisp. 107
Chapter 3 Answers to Practice Problemsp. 112
4 Changes, Rates, Finance and Seriesp. 117
4.1 Introductionp. 117
4.2 Percentage Changesp. 119
Proportionate changes and arc elasticityp. 120
4.3 Simple and Compound Interestp. 121
Simple interestp. 122
Compound interest, compounded annuallyp. 122
Compounding more frequentlyp. 124
Continuous compoundingp. 125
4.4 Annual Percentage Ratep. 127
4.5 Nominal and Real Interest Ratesp. 129
4.6 Growth Rates and Logarithmsp. 131
Finding growth rates and time periodsp. 133
4.7 Depreciationp. 134
Straight line depreciationp. 135
Reducing balance method of depreciationp. 135
4.8 Net Present Valuep. 136
Internal rate of returnp. 138
4.9 Seriesp. 139
4.10 Savings and Loans with Regular Paymentsp. 141
Sinking fundp. 143
Annuitiesp. 144
Mortgage repaymentsp. 145
4.11 Prices of Bills and Bonds and the Rate of Interestp. 146
Billsp. 146
Bondsp. 147
Chapter 4 Answers to Practice Problemsp. 149
5 Differentiation in Economicsp. 152
5.1 Introductionp. 152
5.2 Why Economists use Differentiationp. 153
5.3 The Basic Rules of Differentiationp. 154
The constant rulep. 155
Power-function rulep. 156
Sum-difference rulep. 159
Linear-function rulep. 161
Inverse-function rulep. 162
5.4 Application to Economic Analysisp. 163
5.5 Utility Functionsp. 164
5.6 Revenue Functionsp. 166
5.7 Short-run Production Functionsp. 170
5.8 Cost Functionsp. 171
5.9 Point Elasticity of Demand and of Supplyp. 174
5.10 Investment Multiplierp. 182
Chapter 5 Answers to Practice Problemsp. 184
6 Maximum and Minimum Valuesp. 189
6.1 Introductionp. 189
6.2 Identifying Maximum and Minimum Turning Pointsp. 190
6.3 Maximum Total Revenuep. 194
6.4 Maximum Profitp. 195
Taxationp. 196
6.5 Minimum Average Costp. 199
6.6 Efficient Use of Labourp. 201
6.7 Tax Rate which Maximizes Tax Revenuep. 203
6.8 Minimizing Total Inventory Costsp. 204
Chapter 6 Answers to Practice Problemsp. 205
7 Further Rules of Differentiationp. 209
7.1 Introductionp. 209
7.2 The Chain Rulep. 210
7.3 The Product Rulep. 211
7.4 The Quotient Rulep. 213
7.5 Marginal Revenue, Price Elasticity and Maximum Total Revenuep. 214
7.6 Optimal Production and Cost Relationshipsp. 217
MC = W/MPL and MVP = P . MPLp. 218
Marginal and average costp. 220
7.7 Exponential and Natural Logarithmic Functionsp. 222
7.8 Applications to Economic Analysisp. 224
Chapter 7 Answers to Practice Problemsp. 225
8 Partial Differentiation in Economicsp. 230
8.1 Introductionp. 230
8.2 Partial Derivativesp. 231
8.3 Elasticitiesp. 233
8.4 Small Increments Formulap. 235
8.5 Multipliersp. 236
8.6 Differentials and Implicit Differentiationp. 244
8.7 Slope of an Indifference Curvep. 245
8.8 Long-run Production Functionsp. 247
Returns to scalep. 248
Homogeneous functionsp. 249
Cobb Douglas production functionsp. 251
8.9 Logarithmic Demand Functionsp. 252
8.10 Second Order Partial Derivativesp. 253
8.11 Optimization of Multivariate Functionsp. 255
8.12 Price Discriminating Monopolyp. 257
Chapter 8 Answers to Practice Problemsp. 259
9 Constrained Maxima and Minimap. 264
9.1 Introductionp. 264
9.2 Substitution Methodp. 266
9.3 Lagrange Multiplier Methodp. 267
Further results from the Lagrange multiplier methodp. 270
Chapter 9 Answers to Practice Problemsp. 272
10 Integration in Economicsp. 276
10.1 Introductionp. 276
10.2 Rules of Integrationp. 277
Integration notationp. 277
Constant of integrationp. 278
Power function examplesp. 278
Further rules of integrationp. 279
10.3 Finding Total Functions from Marginal Functionsp. 281
10.4 Area Under a Curvep. 284
10.5 Definite Integrals in Economicsp. 286
Total revenuep. 286
Consumer surplusp. 287
Producer surplusp. 287
Chapter 10 Answers to Practice Problemsp. 288
Indexp. 291