Capital maintenance and investment: Complements or substitutes

A benchmark AK optimal growth model with maintenance expenditures and endogenous utilization of capital is considered within an explicit vin-tage capital framework. Scrapping is endogenous, and the model allows for a clean distinction between age and usage dependent capital deprecia-tion and obsolescence. It is also shown that in this set-up past investment profile completely determines the size of current maintenance expendi-tures. Among other findings, a closed-form solution to optimal dynam-ics is provided taking advantage of very recent development in optimal control of infinite dimensional systems. More importantly, and in con-trast to the pre-existing literature, we study investment and maintenance co-movements without any postulated ad-hoc depreciation function. In particular using impulse response experiments, we find that optimal in-vestment and maintenance do move together in the short-run in response to neutral technological shocks, which seems to be more consistent with the data