The aggregation of capital over vintages in a model of embodied technical progress

The paper considers how to measure capital in a model where technical progress is embodied in new units of capital. This embodiment model also assumes that once new units of capital are installed, it cannot be “unbolted” and sold on the second hand market. A significant difference between this Solow–Harper model and the traditional capital services model due to Jorgenson and his coworkers is that rising real wage rates will generally induce early retirement of assets; i.e., this model can provide an explanation for obsolescence. The paper studies how to aggregate over vintages and how to measure depreciation in the context of this embodiment model. These problems are more complicated than the corresponding problems in the traditional capital services model because the age of retirement of an asset is endogenous in the embodiment model. The paper uses duality theory to simplify the exposition.