A Note on Dynamic Optimization, Maintenance Expenditure and Quality of Capital

The dynamic interaction between investment–maintenance decisions and uncertainty about the capital's future productivity status is considered. Maintenance influences the flow of services provided by a stock of capital, affecting the firm's technological knowledge of capital productivity. In a simple Lerner–Haavelmo–Jorgenson framework with constant returns to scale and linear homogeneous cost of adjustment, two closed forms for the firm's market value are presented and the impact of uncertainty on investment–maintenance policy is analyzed. The optimal management strategy uses maintenance to sustain the profitability of existing capital. This smooths out investment fluctuations and lengthens the periods of time in which the firm invests. Nevertheless, since the random movement of quality of capital makes the marginal revenue products of capital decline over time and maintenance cannot offset this tendency, a stochastic switching time emerges at which the firm will find it optimal to stop investing and let the stock deplete.