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6054 results in Econometrics and mathematical methods

Page 14 of 303

  • 27 - First-Order Differential Equations

  • Martin Anthony, London School of Economics and Political Science, Norman Biggs, London School of Economics and Political Science
  • Book:
    Mathematics for Economics and Finance
    Published online:
    24 May 2024
    Print publication:
    30 May 2024, pp 301-318

  • Summary

    Regarding the key components of macroeconomics as continuous (rather than discrete) and considering the corresponding dynamics leads to differential equations. In this chapter, we focus on first-order differential equations and consider two methods (applicable to certain types of equation): separation and the use of integrating factors. We look at economic applications to continuous-time price adjustment and continuous cash flows.

  • 29 - Coupled Systems and Diagonalisation

  • Martin Anthony, London School of Economics and Political Science, Norman Biggs, London School of Economics and Political Science
  • Book:
    Mathematics for Economics and Finance
    Published online:
    24 May 2024
    Print publication:
    30 May 2024, pp 334-346

  • Summary

    A mathematical discrete-time population model is presented, which leads to a system of two interlinked, or coupled, recurrence equations. We then turn to the general issue of how to solve such systems. One approach is to reduce the two coupled equations to a single second-order equation and solve using the techniques already developed, but there is another more sophisticated way. To this end, we introduce eigenvalues and eigenvectors, show how to find them and explain how they can be used to diagonalise a matrix.

Mathematics for Economics and Finance
  • Methods and Modelling
  • 2nd edition
  • Martin Anthony, Norman Biggs
  • Published online:
    24 May 2024
    Print publication:
    30 May 2024
  • Accessible, concise, and interactive, this book introduces the mathematical methods that are indispensable in economics and finance. Fully updated to be as student friendly as possible, this edition contains extensive problems, worked examples and exercises (with full solutions at the end of the book). Two brand new chapters cover coupled systems of recurrence/differential equations, and matrix diagonalisation. All topics are motivated by problems from economics and finance, demonstrating to students how they can apply the mathematical techniques covered. For undergraduate students of economics, mathematics, or both, this book will be welcomed for its clarity and breadth and the many opportunities it provides for readers to practise and test their understanding.

Page 14 of 303