Answer to Question #217680 in Economics for Sahu

Question

Distinguish between the characteristics of first and second order difference equations. Give examples of economic problems that are solved with the help of each category of such equations.

Answer 1

Difference equations are one of the branches of mathematics that is of great applied importance. In addition to general mathematical and theoretical interest, difference equations have a wide practical

application. In particular, when solving problems related to the economy. Difference equations can be used to describe many processes of macroeconomic dynamics. For example, population growth (in the period under consideration), price growth dynamics, advertising distribution process, the production volume of a certain manufacturer, etc.

There is a phenomenon that is unique to difference equations and is not possible in differential equations. In difference equations, it is possible that the solution may not be an equilibrium point, but may reach unity after a finite number of iterations. In other words, a nonequilibrium state can go to an equilibrium state in a finite time.

In practice, situations often arise when the production cycle of a product lags behind the cycle of its implementation. This is typical for agriculture, for example. And in industrial production, the proposal is formed on the basis of the price in the previous period of time. Thus, the supply function S is time-shifted relative to the price P, i.e. we will assume that S (t) = S (P (t - I)), while the demand function D immediately corresponds to the price: D (t) = D (P (t))