The primal-dual methodology of Samuelson (1965) is extended and applied to a nonautonomous variational calculus problem with a fixed vector of initial stocks, fixed initial and terminal time values, a free vector of terminal stocks, and a time-independent vector of parameters. It is shown that if the solution of the variational problem is smooth enough, the qualitative effects of parameter perturbations on the entire optimal arcs can be represented by a generalized Slutsky-type matrix, which holds in integral form and is symmetric negative semidefinite. Sufficient conditions for the optimal value function to be convex in the parameters are also given.

This study estimates rates of deterioration and depreciation for a sample of used privately owned single- and twin-engine aircraft over the period 1971–1991. The adoption of a strict liability standard in the 1970s lead to a 775% increase in liability expenses for the manufacturers of private planes between 1977 and 1985, resulting in sharp increases in the prices of new and used planes throughout the late 1970s and 1980s. This period of rapid price inflation coincides with a decrease in the depreciation rates for used single- and twin-engine aircraft after 1975. In addition, our results indicate that the rate of deterioration is positively related to the required cost of engine maintenance. These findings call into question the commonly invoked assumption that depreciation rates may be treated as exogenously determined constants, and lend support to the hypothesis that deterioration and depreciation rates respond systematically to key economic variables.