In this paper, we study the properties of optimal growth models à la Nelson and Phelps (1966) where the labor resources of an economy can be allocated freely either to production, technology adoption or capital maintenance. We first characterize the balanced growth paths of a benchmark model without maintenance services. Then we introduce te maintenance activity via the depreciation rate of capital. We characterize the optimal allocation of labor across the three activities. We prove that when technolgical shocks occur, equilibrium maintenance and adoption operate in opposite directions. The main prediction of the model is that though capital maintenance deepens the technological gap by diverting labor resources from adoption, it generally increases the long run output level at equilibrium
Boucekkine, R., Martinez, B., & Saglam, H. C. (2001). Technology and option, Capital Maintenance and the Technological Gap (IRES Discussion paper 2001-33). https://hdl.handle.net/2078.5/34791