The rate of capital retirement: How is it related to the form of the survival function and the investment growth path?

We discuss the relationship between the retirement process of the capital, as formalized by its survival function, and the average retirement rate, and how this relationship is affected by changes in the investment path. The effect of the survival function on the age distribution of the capital goods, both those existing and those retired in each period, is also considered. These issues are illustrated by means of parametric (convex and concave) functions and numerical examples. We find that the retirement rate is a declining function of the growth rate of investment (except in the exponential decay case) and quite sensitive to the value of this parameter over a reasonable interval. Approximating the retirement rate by the inverse of the capital's maximal life-time or twice this value (`double declining balance') will in many cases produce very inaccurate results. The response of the capital/investment ratio and the retirement/investment ratio to changes in the investment growth rate and in the curvature of the survival function is also investigated. – Capital ; Retirement ; Survival function ; Age ;distribution ; Exponential decay ; Mortality rate