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```Brief contents
Detailed contents	ix
How to use the book	xvii
Chapter map	xviii
Guided tour of the textbook features	xx
Guided tour of the Online Resource Centre	xxii
Acknowledgements	xxiii
Part One Foundations
1	Arithmetic	3
2	Algebra	43
3	Linear equations	63
5	Some further equations and techniques	134
Part Two Optimization with one independent variable
6	Derivatives and differentiation	165
7	Derivatives in action	184
8	Economic applications of functions and derivatives	213
9	Elasticity	256
Part Three Mathematics of finance and growth
10	Compound growth and present discounted value	297
11	The exponential function and logarithms	328
12	Continuous growth and the natural exponential function	342
13	Derivatives of exponential and logarithmic functions and their applications	368
Part Four Optimization with two or more independent variables
14	Functions of two or more independent variables	389
15	Maximum and minimum values, the total differential and applications	441
16	Constrained maximum and minimum values	479
17	Returns to scale and homogeneous functions; partial elasticities; logarithmic scales; growth accounting	519
Part Five Some further topics
18	Integration	551
19	Matrix algebra	577
20	Difference and differential equations	597
W21	Extensions and future directions (on the Online Resource Centre)	000
Appendix: Answers to chapter 1 self-test	623
Glossary	624
Index	632
Detailed contents
How to use the book	xvii
Chapter map	xviii
Guided tour of the textbook features	xx
Guided tour of the Online Resource Centre	xxii
Acknowledgements	xxiii
Part 1 Foundations
1	Arithmetic	3
1.1	Introduction	3
1.2	Addition and subtraction with positive and negative numbers	4
1.3	Multiplication and division with positive and negative numbers	7
1.4	Brackets and when we need them	10
1.5	Factorization	13
1.6	Fractions	14
1.7	Addition and subtraction of fractions	16
1.8	Multiplication and division of fractions	20
1.9	Decimal numbers	24
1.10	Adding, subtracting, multiplying, and dividing decimal numbers	26
1.11	Fractions, proportions, and ratios	27
1.12	Percentages	28
1.13	Index numbers	33
1.14	Powers and roots	35
1.15	Standard index form	40
Self-test exercises	42
2	Algebra	43
2.1	Introduction	43
2.2	Rules of algebra	44
2.3	Addition and subtraction of algebraic expressions	44
2.4	Multiplication and division of algebraic expressions	45
2.5	Brackets and when we need them	47
2.6	Fractions	49
2.7	Addition and subtraction of fractions	50
2.8	Multiplication and division of fractions	52
2.9	Powers and roots	55
2.10	Extending the idea of powers	56
2.11	Negative and fractional powers	57
2.12	The sign of an	59
2.13	Necessary and sufficient conditions	60
Appendix: The Greek alphabet	62
3	Linear equations	63
3.1	Introduction	63
3.2	How we can manipulate equations	64
3.3	Variables and parameters	69
3.4	Linear and non-linear equations	69
3.5	Linear functions	72
3.6	Graphs of linear functions	73
3.7	The slope and intercept of a linear function	75
3.8	Graphical solution of linear equations	80
3.9	Simultaneous linear equations	81
3.10	Graphical solution of simultaneous linear equations	84
3.11	Existence of a solution to a pair of linear simultaneous equations	87
3.12	Three linear equations with three unknowns	90
3.13	Economic applications	91
3.14	Demand and supply for a good	91
3.15	The inverse demand and supply functions	94
3.16	Comparative statics	97
3.17	Macroeconomic equilibrium	102
4.1	Introduction	109
4.5	The formula for solving any quadratic equation	116
4.6	Cases where a quadratic expression cannot be factorized	117
4.7	The case of the perfect square	118
4.9	The inverse quadratic function	122
4.10	Graphical solution of quadratic equations	123
4.12	Graphical solution of simultaneous quadratic equations	127
4.13	Economic application 1: supply and demand	128
4.14	Economic application 2: costs and revenue	131
5	Some further equations and techniques	134
5.1	Introduction	134
5.2	The cubic function	135
5.3	Graphical solution of cubic equations	138
5.4	Application of the cubic function in economics	141
5.5	The rectangular hyperbola	142
5.6	Limits and continuity	143
5.7	Application of the rectangular hyperbola in economics	146
5.8	The circle and the ellipse	149
5.9	Application of circle and ellipse in economics	151
5.10	Inequalities	152
5.11	Examples of inequality problems	156
5.12	Applications of inequalities in economics	159
Part 2 Optimization with one 	independent variable
6	Derivatives and differentiation	165
6.1	Introduction	165
6.2	The difference quotient	166
6.3	Calculating the difference quotient	167
6.4	The slope of a curved line	168
6.5	Finding the slope of the tangent	170
6.6	Generalization to any function of x	172
6.7	Rules for evaluating the derivative of a function	173
6.8	Summary of rules of differentiation	182
7	Derivatives in action	184
7.1	Introduction	184
7.2	Increasing and decreasing functions	185
7.3	Optimization: finding maximum and minimum values	187
7.4	A maximum value of a function	187
7.5	The derivative as a function of x	188
7.6	A minimum value of a function	189
7.7	The second derivative	191
7.8	A rule for maximum and minimum values	191
7.9	Worked examples of maximum and minimum values	192
7.10	Points of inflection	195
7.11	A rule for points of inflection	198
7.12	More about points of inflection	199
7.13	Convex and concave functions	206
7.14	An alternative notation for derivatives	209
7.15	The differential and linear approximation	210
8	Economic applications of functions and derivatives	213
8.1	Introduction	213
8.2	The firm's total cost function	214
8.3	The firm's average cost function	216
8.4	Marginal cost	218
8.5	The relationship between marginal and average cost	220
8.6	Worked examples of cost functions	222
8.7	Demand, total revenue, and marginal revenue	229
8.8	The market demand function	229
8.9	Total revenue with monopoly	231
8.10	Marginal revenue with monopoly	232
8.11	Demand, total and marginal revenue functions with monopoly	234
8.12	Demand, total and marginal revenue with perfect competition	235
8.13	Worked examples on demand, marginal and total revenue	236
8.14	Profit maximization	239
8.15	Profit maximization with monopoly	240
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 maximization	248
8.20	The second order condition for profit maximization	248
Appendix 8.1: The relationship between total cost, average cost, and marginal cost	253
Appendix 8.2: The relationship between price, total revenue, and marginal revenue	254
9	Elasticity	256
9.1	Introduction	256
9.2	Absolute, proportionate, and percentage changes	257
9.3	The arc elasticity of supply	259
9.4	Elastic and inelastic supply	260
9.5	Elasticity as a rate of proportionate change	260
9.6	Diagrammatic treatment	261
9.7	Shortcomings of arc elasticity	263
9.8	The point elasticity of supply	263
9.9	Reconciling the arc and point supply elasticities	265
9.10	Worked examples on supply elasticity	265
9.11	The arc elasticity of demand	268
9.12	Elastic and inelastic demand	270
9.13	An alternative definition of demand elasticity	272
9.14	The point elasticity of demand	273
9.15	Reconciling the arc and point demand elasticities	274
9.16	Worked examples on demand elasticity	275
9.17	Marginal revenue and the elasticity of demand	279
9.18	The elasticity of demand under perfect competition	282
9.19	Worked examples on demand elasticity and marginal revenue	284
9.20	Other elasticities in economics	288
9.21	The firm's total cost function	288
9.22	The aggregate consumption function	290
9.23	Generalizing the concept of elasticity	292
Part 3 Mathematics of finance 	and growth
10	Compound growth and present discounted value	297
10.1	Introduction	297
10.2	Arithmetic and geometric series	298
10.3	An economic application	300
10.4	Simple and compound interest	304
10.5	Applications of the compound growth formula	307
10.6	Discrete versus continuous growth	309
10.7	When interest is added more than once per year	309
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 = 10x	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
12	Continuous growth and the natural exponential function	342
12.1	Introduction	342
12.2	Limitations of discrete compound growth	343
12.3	Continuous growth: the simplest case	343
12.4	Continuous growth: the general case	346
12.5	The graph of y = aerx	347
12.6	Natural logarithms	349
12.7	Rules for manipulating natural logs	351
12.8	Natural exponentials and logs on your calculator	351
12.9	Continuous growth applications	353
12.10	Continuous discounting and present value	358
12.11	Graphs with semi-log scale	361
13	Derivatives of exponential and logarithmic functions and their applications	368
13.1	Introduction	368
13.2	The derivative of the natural exponential function	369
13.3	The derivative of the natural logarithmic function	370
13.4	The rate of proportionate change, or rate of growth	371
13.5	Discrete growth	371
13.6	Continuous growth	374
13.7	Instantaneous and nominal growth rates compared	377
13.8	Semi-log graphs and the growth rate again	378
13.9	An important special case	379
13.10	Logarithmic scales and elasticity	381
Part 4 Optimization with two or 	more independent variables
14	Functions of two or more independent variables	389
14.1	Introduction	389
14.2	Functions with two independent variables	390
14.3	Examples of functions with two independent variables	393
14.4	Partial derivatives	398
14.5	Evaluation of first order partial derivatives	401
14.6	Second order partial derivatives	403
14.7	Economic applications 1: the production function	411
14.8	The shape of the production function	411
14.9	The Cobb-Douglas production function	420
14.10	Alternatives to the Cobb-Douglas form	425
14.11	Economic applications 2: the utility function	428
14.12	The shape of the utility function	429
14.13	The Cobb-Douglas utility function	434
Appendix 14.1: A variant of the partial derivatives of the Cobb-Douglas function	439
15	Maximum and minimum values, the total differential, and applications	441
15.1	Introduction	441
15.2	Maximum and minimum values	442
15.4	The total differential of z = f(x, y)	452
15.5	Differentiating a function of a function	457
15.6	Marginal revenue as a total derivative	458
15.7	Differentiating an implicit function	460
15.8	Finding the slope of an iso-z section	463
15.9	A shift from one iso-z section to another	463
15.10	Economic applications 1: the production function	465
15.11	Isoquants of the Cobb-Douglas production function	468
15.12	Economic applications 2: the utility function	470
15.13	The Cobb-Douglas utility function	472
15.14	Economic application 3: macroeconomic equilibrium	473
15.15	The Keynesian multiplier	473
15.16	The IS curve and its slope	474
15.17	Comparative statics: shifts in the IS curve	475
16	Constrained maximum and minimum values	479
16.1	Introduction	479
16.2	The problem, with a graphical solution	480
16.3	Solution by implicit differentiation	482
16.4	Solution by direct substitution	485
16.5	The Lagrange multiplier method	486
16.6	Economic applications 1: cost minimization by the firm	490
16.7	Economic applications 2: profit maximization	496
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 by the consumer	510
16.12	Deriving the consumer's demand functions	512
17	Returns to scale and homogeneous functions; partial elasticities; growth accounting; logarithmic scales	519
17.1	Introduction	519
17.2	The production function and returns to scale	520
17.3	Homogeneous functions	522
17.4	Properties of homogeneous functions	525
17.5	Partial elasticities	531
17.6	Partial elasticities of demand	532
17.7	The proportionate differential of a function	534
17.8	Growth accounting	537
17.9	Elasticity and logs	539
17.10	Partial elasticities and logarithmic scales	540
17.11	The proportionate differential and logs	542
17.12	Log linearity with several variables	544
Part 5 Some further topics
18	Integration	551
18.1	Introduction	551
18.2	The definite integral	552
18.3	The indefinite integral	554
18.4	Rules for finding the indefinite integral	555
18.5	Finding a definite integral	562
18.6	Economic applications 1: deriving the total cost function from the marginal cost function	565
18.7	Economic applications 2: deriving total revenue from the marginal revenue function	567
18.8	Economic applications 3: consumers' surplus	569
18.9	Economic applications 4: producers' surplus	570
18.10	Economic applications 5: present value of a continuous stream of income	572
19	Matrix algebra	577
19.1	Introduction	577
19.2	Definitions and notation	578
19.3	Transpose of a matrix	579
19.4	Addition/subtraction of two matrices	579
19.5	Multiplication of two matrices	580
19.6	Vector multiplication	582
19.7	Scalar multiplication	583
19.8	Matrix algebra as a compact notation	583
19.9	The determinant of a square matrix	584
19.10	The inverse of a square matrix	587
19.11	Using matrix inversion to solve linear simultaneous equations	589
19.12	Cramer's rule	590
19.13	A macroeconomic application	592
19.14	Conclusions	594
20	Difference and differential equations	597
20.1	Introduction	597
20.2	Difference equations	598
20.3	Qualitative analysis	601
20.4	The cobweb model of supply and demand	605
20.5	Conclusions on the cobweb model	610
20.6	Differential equations	612
20.7	Qualitative analysis	615
20.8	Dynamic stability of a market	616
20.9	Conclusions on market stability	620
W21	Extensions and future directions (on the Online Resource Centre)	000
Appendix: Answers to chapter 1 self-test	623
Glossary	624
Index	632
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Library of Congress Subject Headings for this publication:

Economics, Mathematical.