Economic Dynamics And Integral Calculus

The term dynamics, as applied to economic analysis, has had different meanings at different times and for different economists.* In standard usage today, however, the term refers to the type of analysis in which the object is either to trace and study the specific time paths of the variables or to determine whether, given sufficient time, these variables will tend to converge to certain (equilibrium) values. This type of information is important because it fills a serious gap that marred our study of statics and comparative statics. In the latter, we always make the arbitrary assumption that the process of economic adjustment inevitably leads to an equilibrium. In a dynamic analysis, the question of "attainability" is to be squarely faced, rather than assumed away.

One salient feature of dynamic analysis is the dating of the variables, which introduces the explicit consideration of time into the picture. This can be done in two ways: time can be considered either as a continuous variable or as a discrete variable. In the former case, something is happening to the variable at each point of time (such as in continuous interest compounding); whereas in the latter, the variable undergoes a change only once within a period of time (e.g., interest is

* Fritz Machlup, "Statics and Dynamics: Kaleidoscopic Words," Southern Economic Journal, October, 1959, pp. 91-110; reprinted in Machlup, Essays on Economic Semantics, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963, pp. 9-42.

added only at the end of every 6 months). One of these time concepts may be more appropriate than the other in certain contexts.

We shall discuss first the continuous-time case, to which the mathematical techniques of integral calculus and differential equations are pertinent. Later, in Chaps. 16 and 17, we shall turn to the discrete-time case, which utilizes the methods of difference equations.

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