The Investment-Consumption Decision under Capital Rationing: An Efficient Set Analysis

Abstract

The investment decision under capital rationing has been of intense interest to individuals in the field of finance. A major research problem in this area is the specification of a criterion function for solving the capital rationing problem. Lorie and Savage [8] and Weingartner [11] argued that when faced with capital rationing, the firm's objective should be the maximization of the present value of its investments' cash flows. What was troubling to some about this formulation is the assumption that the discount rate, necessary for the calculation of the present value of an investment's cash flows, is known before the problem of project selection is undertaken. Baumol and Quandt (B-Q) [1] confronted this problem directly. First, they reminded their readers that Hirschleifer [5] had shown that the appropriate discount rate in a pure capital rationing problem is given by the slope of the investment opportunity curve at its point of tangency with the investor's highest indifference curve, and this rate cannot be discovered until the utility function is specified fully and the final consumption vector determined. Hence, B-Q claim (as Hirschleifer does) that under capital rationing the discount rate cannot be an external variable but must be an internal variable, which, among other things, is a function of the available projects and the actual capital constraints.3 As a way to circumvent this problem, B-Q offer the individual's utility of consumption flows over time as a substitute objective function. However, in B-Q's formulation, one needs to specify fully the individual's utility function, a task which is difficult. The purpose of this paper is to focus on the efficient set of consumption vectors when the problem is the maximization of U(c1, c2, ..., cJ), where ci is consumption in period i, and U is some general utility function. We assume nothing about the specific form of the utility function. The only assumption we make is that more consumption is preferred to less. Our method attempts to determine how far analysis can