Optimal Capital Policy with Bounded Investment Plans

Abstract

The neoclassical theory of optimal capital accumulation commonly employs the assumption that the level of investment by the firm is bounded neither above nor below.2 Arrow [2] has considered irreversible investment in which case the investment plan is bounded below by zero and he provided a characterization of the optimal capital policy on both those intervals of time where the bound was effective and on those intervals where the bound was not effective. In this paper we consider the optimal capital policy of a firm maximizing its present value over an infinite horizon under perfect certainty, when the investment plan is bounded both above and below. The upper bound is such that the amount invested by the firm at any moment of time is limited by current profits. It turns out that this bound has some interesting implications in terms of a comparison with the traditional case of unbounded investment plans. The interest in investment plans which are bounded above stems from the observation that a number of capital market imperfections lead precisely to such bounds.3 In particular we show that situations in which either the firm faces a non-price capital rationing constraint or the absence of a capital market in which firms may borrow there exists an upper bound on investment plans equivalent to the one mentioned above. Capital market imperfections such as these are not uncommon. Credit rationing, for example, was found to be an empirically significant phenomenon by Jaffee and Modigliani [4] and has often beeni noted as one of the more common forms of capital market imperfections facing firms. It is perhaps not insignificant then that in the applied business finance literature the investment problem is often treated as allocating a fixed amount of investment funds among various projects. In order to provide a characterization of the optimal capital policy of the firm with bounded investment plans, we use as reference a firm identical in all other respects, but whose investment plans are not constrained as in the case of a perfect capital market. Now it is not immediately obvious in a dynamic model how one should go about comparing two investment plans. The question we wish to address is whether the bound on investment plans imposed by the capital market