Survival and Efficiency Curves for Capital and the Time-Age-Profile of Vintage Prices

The decline in the service flow from a stock of capital goods with age, due to the physical retirement of capital units and to the gradual loss of efficiency of each unit remaining, can be described by survival curves and efficiency curves. The paper reconsiders the relationship between these curves and the vintage prices of capital under neo-classical assumptions about perfect second-hand markets and malleability, using duality between quantities and prices. Three examples with parametric survival and efficiency curves are presented. Concavity of the survival and efficiency curves may be compatible with convexity of the age-price profile. This approach is contrasted with the frequently cited Hulten-Wykoff approach. Empirical illustrations, focusing on the convexity/concavity issue, are given