Basic mathematics for economists

Rosser, M. J. 1949- (author.). Lis, Piotr, (author.).

Record details

ISBN: 9780415485913
ISBN: 0415485916
ISBN: 9780415485920
ISBN: 0415485924
ISBN: 9781315641713
Physical Description: print
xii, 607 pages : illustrations ; 25 cm
Edition: Third edition.
Publisher: Abingdon, Oxon ; Routledge, 2016.

Content descriptions

General Note:

Includes index.

Formatted Contents Note:

Machine generated contents note: 1. Introduction -- 1.1. Why study mathematics? -- 1.2. Calculators and computers -- 1.3. Using this 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. summation sign S and price indexes -- 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 a spreadsheet to plot functions -- 4.10. Functions with two independent variables -- 4.11. Summing functions horizontally -- 5. Simultaneous linear equations -- 5.1. Systems of simultaneous linear equations -- 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 -- 5A. Appendix: linear programming -- 5A.1. Constrained maximization -- 5A.2. Constrained minimization -- 5A.3. Mixed constraints -- 5A.4. More than two variables -- 6. Quadratic equations -- 6.1. Solving quadratic equations -- 6.2. Graphical solution -- 6.3. Factorization -- 6.4. 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. internal rate of return -- 7.7. Geometric series and annuities -- 7.8. Perpetual annuities -- 7.9. Pension pots, annuity income and drawdown pensions -- 7.10. Drawdown pension income -- 7.11. Loan repayments and mortgages -- 7.12. Savings schemes -- 7.13. Sinking fund savings schemes -- 7.14. Other applications of growth and decline -- 7A. Appendix: asset valuation -- 7A.1. Valuation of bonds -- 7A.2. Valuation of shares -- 8. Introduction to calculus -- 8.1. 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. Re-specifying functions -- 8.7. Point elasticity of demand -- 8.8. Tax yield -- 8.9. Keynesian multiplier -- 9. Unconstrained optimization -- 9.1. First-order conditions for a maximum -- 9.2. Second-order conditions for a maximum -- 9.3. Second-order conditions 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. Lagrange multiplier: constrained maximization with two variables -- 11.4. 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 differentiation and integration -- 12.1. Overview -- 12.2. chain rule -- 12.3. product rule -- 12.4. quotient rule -- 12.5. Integration -- 12.6. Definite integrals -- 12.7. Integration by substitution and integration by parts -- 13. Dynamics and difference equations -- 13.1. Dynamic economic analysis -- 13.2. cobweb: iterative solutions -- 13.3. cobweb: difference equation solutions -- 13.4. 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 -- 15.1. Introduction to matrices and vectors -- 15.2. Basic principles of matrix multiplication -- 15.3. Matrix multiplication -- the general case -- 15.4. matrix inverse and the solution of simultaneous equations -- 15.5. Determinants -- 15.6. Minors, cofactors and the Laplace expansion -- 15.7. 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 -- 15.12. Input-output analysis -- 15.13. Multiple industry input-output models.