Difference Equations

Abstract

A general definition of a difference equation was given in the last chapter. We shall now restrict ourselves to a study of certain kinds of difference equations which frequently occur in economics. Because most of the equations we are likely to meet involve time, we shall find it convenient to refer to an independent variable which increases by equal amounts as “ time ”, but the method of solution is independent of the nature of this variable provided that it does increase by equal amounts. The equations may relate the value of some variable (such as income) at one moment to the value at some other moment. More usually they will relate the value during a period to the value during some other period. The important point is that either time is subdivided into a number of equal periods which are such that we can meaningfully compare the income (say) of one period with the income of another period or a series of evenly spaced instants is chosen such that we can meaningfully compare the population (say) at one instant with the population at another. In what follows we shall think of time as being divided into periods, partly for verbal convenience and partly to facilitate reference to economic examples. We may think of each period as being a day, a month, two months, or any other finite period.

And each the other’s difference bears.

Andrew Mabvell: Eyes and Tears