A benchmark AK optimal growth model with maintenance expenditures and endogenous utilization of capital is considered within an explicit vintage capital framework. Scrapping is endogenous, and the model allows for a clean distinction between age and usage dependent capital depreciation and obsolescence. It is also shown than in this set-up past investment profile completely determines the size of current maintenance expenditures. Among other findings, a closed-form solution to optimal dynamics is provided taking advantage of very recent development in optimal control of infinite dimensional systems. More importantly, and in contrast 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 investment and maintenance do move together in the short-run in response to neutral technological shocks, which seems to be more consistent with the data.
Boucekkine, R., Fabbri, G., & Gozzi, F. (2010). Maintenance and investment:Complements or substitutes? A reappraisal. Journal of Economic Dynamics and Control, 34(12), 2420-2439. https://doi.org/10.1016/j.jedc.2010.06.007 (Original work published 2010)