Basic Mathematics for Economists

Basic Mathematics for Economists

Автор(ы): Rosser M.

Год изд.: 2003
Издание: 2
Описание: Economics students will welcome the new edition of this excellent textbook. Given that many students come into economics courses without having studied mathematics for a number of years, this clearly written book will help to develop quantitative skills in even the least numerate student up to the required level for a general Economics or Business Studies course. All explanations of mathematical concepts are set out in the context of applications in economics. This new edition incorporates several new features, including new sections on: financial mathematics; continuous growth; matrix algebra.
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1 Introduction
1.1 Why study mathematics?
1.2 Calculators and computers
1.3 Using the book
2 Arithmetic
2.1 Revision of basic concepts
2.2 Multiple operations
2.3 Brackets
2.4 Fractions
2.5 Elasticity of demand
2.6 Decimals
2.7 Negative numbers
2.8 Powers
2.9 Roots and fractional powers
2.10 Logarithms
3 Introduction to algebra
3.1 Representation
3.2 Evaluation
3.3 Simplification: addition and subtraction
3.4 Simplification: multiplication
3.5 Simplification: factorizing
3.6 Simplification: division
3.7 Solving simple equations
3.8 The summation sign J2
3.9 Inequality signs
4 Graphs and functions
4.1 Functions
4.2 Inverse functions
4.3 Graphs of linear functions
4.4 Fitting linear functions
4.5 Slope
4.6 Budget constraints
4.7 Non-linear functions
4.8 Composite functions
4.9 Using Excel to plot functions
4.10 Functions with two independent variables
4.11 Summing functions horizontally
5 Linear equations
5.1 Simultaneous linear equation systems
5.2 Solving simultaneous linear equations
5.3 Graphical solution
5.4 Equating to same variable
5.5 Substitution
5.6 Row operations
5.7 More than two unknowns
5.8 Which method?
5.9 Comparative statics and the reduced form of an economic model
5.10 Price discrimination
5.11 Multiplant monopoly Appendix: linear programming
6 Quadratic equations
6.1 Solving quadratic equations
6.2 Graphical solution
6.3 Factorization
6.4 The quadratic formula
6.5 Quadratic simultaneous equations
6.6 Polynomials
7 Financial mathematics: series, time and investment
7.1 Discrete and continuous growth
7.2 Interest
7.3 Part year investment and the annual equivalent rate
7.4 Time periods, initial amounts and interest rates
7.5 Investment appraisal: net present value
7.6 The internal rate of return
7.7 Geometric series and annuities
7.8 Perpetual annuities
7.9 Loan repayments
7.10 Other applications of growth and decline
8 Introduction to calculus
8.1 The differential calculus
8.2 Rules for differentiation
8.3 Marginal revenue and total revenue
8.4 Marginal cost and total cost
8.5 Profit maximization
8.6 Respecifying functions
8.7 Point elasticity of demand
8.8 Tax yield
8.9 The Keynesian multiplier
9 Unconstrained optimization
9.1 First-order conditions for a maximum
9.2 Second-order condition for a maximum
9.3 Second-order condition for a minimum
9.4 Summary of second-order conditions
9.5 Profit maximization
9.6 Inventory control
9.7 Comparative static effects of taxes
10 Partial differentiation
10.1 Partial differentiation and the marginal product
10.2 Further applications of partial differentiation
10.3 Second-order partial derivatives
10.4 Unconstrained optimization: functions with two variables
10.5 Total differentials and total derivatives
11 Constrained optimization
11.1 Constrained optimization and resource allocation
11.2 Constrained optimization by substitution
11.3 The Lagrange multiplier: constrained maximization with two variables
11.4 The Lagrange multiplier: second-order conditions
11.5 Constrained minimization using the Lagrange multiplier
11.6 Constrained optimization with more than two variables
12 Further topics in calculus
12.1 Overview
12.2 The chain rule
12.3 The product rule
12.4 The quotient rule
12.5 Individual labour supply
12.6 Integration
12.7 Definite integrals
13 Dynamics and difference equations
13.1 Dynamic economic analysis
13.2 The cobweb: iterative solutions
13.3 The cobweb: difference equation solutions
13.4 The lagged Keynesian macroeconomic model
13.5 Duopoly price adjustment
14 Exponential functions, continuous growth and differential equations
14.1 Continuous growth and the exponential function
14.2 Accumulated final values after continuous growth
14.3 Continuous growth rates and initial amounts
14.4 Natural logarithms
14.5 Differentiation of logarithmic functions
14.6 Continuous time and differential equations
14.7 Solution of homogeneous differential equations
14.8 Solution of non-homogeneous differential equations
14.9 Continuous adjustment of market price
14.10 Continuous adjustment in a Keynesian macroeconomic model
15 Matrix algebra
15.7 Introduction to matrices and vectors
15.2 Basic principles of matrix multiplication
15.3 Matrix multiplication — the general case
15.4 The matrix inverse and the solution of simultaneous equations
15.5 Determinants
15.6 Minors, cofactors and the Laplace expansion
15.7 The transpose matrix, the cofactor matrix, the adjoint and the matrix inverse formula
15.8 Application of the matrix inverse to the solution of linear simultaneous equations
15.9 Cramer’s rule
15.10 Second-order conditions and the Hessian matrix
15.11 Constrained optimization and the bordered Hessian
Symbols and terminology

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