Capital maintenance and investment: Complements or substitutes?

This paper studies the properties of demand for capital maintenance services and its interaction with investment under variable capital utilization rate and adjustment costs. The depreciation rate varies with the maintenance effort and the utilization rate of capital. We show that the properties of the demand functions for maintenance services and capital goods depend closely on the sign of the cross derivative of the depreciation function, i.e., on whether the marginal efficiency of maintenance decreases or increases when the rate of capital utilization rises. In our model, it is impossible to reconcile some unquestionable empirical facts and some minimal regularity conditions on the demand function for maintenance services if this cross derivative is positive. In all cases, investment and maintenance are gross complements.