The Reinvestment Process in a Mass Where There is a Probability Law for the Lifetime of Each Capital Object

Abstract

In a mass of uniform capital objects such as e.g. telegraph poles, or a specific kind of machine component (cf. the examples given in Chapter 16) it will as a rule be possible to draw up on the basis of statistics a mortality curve (retirement curve) for such objects. It would then be plausible to assume that every new unit which is added to the mass is subjected to a probability distribution of this kind as long as it is in existence. We assume that it is the same curve for all units. This assumption that the durability is subject to a probability law is in one way more general than the assumption that the life-time for each object is a given number (determined by the durability of the old object which the new one is to replace). But on the other hand, we now make the more restrictive assumption that all units are alike. Thus we do not now have a possibility of distinguishing between different typical sorts of objects as we had in Chapter 17. For this reason the analytical schema we are now considering cannot be used for studying the movement in a very complex mass of capital objects (e.g. that of a country); but it provides a useful point of departure for discussing the movement in a fairly uniform mass of capital objects. If a mass with a few different types of object is involved, it is of great assistance to undertake an analysis separately for each part of the total mass.