The optimal economic lifetime of vintage capital in the presence of operating costs, technological progress, and learning

This paper studies the optimal vintage specific investment and disinvestment decision of a firm. The decision is formulated as a distributed optimal control problem with a constraint on the state variable. The economic model takes into accounts maintenance and operating costs, technological progress and learning. It allows firms to purchase not only the latest technology but also previous year vintages and completely disinvest old machines. It does not assume that the firms keep machines of all vintages as other similar models do. An analytical expression for the optimal economic lifetime of capital is derived and the qualitative dynamics of the optimal investment and disinvestment rules is analyzed.