Capital accumulation and financing programs in a neoclassical investment model

Abstract

The classical theory of capital assumes that the installation or removal of capital goods is free of restrictions. Thus, investment behavior is independent of the level of accumulated capital, and any level of investment is possible which will optimize the firm's objectives. This is referred to by Jorgenson as a decomposable technology. Using the calculus of variation, Jorgenson [t967] derived the conditions of optimal capital accumulation for a present value maximizing firm. Under the classical assumptions, the optimal firm size can be attained instantaneously without restrictions. Several ways have been used in the literature to restrict the speed of capital adjustment to the optimal level. For example, Arrow [ 1968] introduced the concept of irreversibility of investment so that investment is non-negative at any given point in time. Gould [1968] introduced a quadratic installation cost function which varies with gross investment, thus placing indirectly a restriction on the firm's rate of investment. Treadway [1969] introduced a cost function of a more general nature dependent upon n e t investment which has a similar inhibiting effect upon firm expansion. Lucas [1967] considered an adjustment factor imbedded in a neoclassical production function. More recently, Wong [1975] and Appelbaum and Harris [1978] studied models in which investment is bounded above by current retained profits. Inequality constraints have also been introduced which bound investment level at each instant of time between zero and a maxi-