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

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, …, C_n), where c_i 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 take us toward isolating the set of efficient consumption possibilities. To this end we first derive an alternative representation for the set of feasible consumption plans. This new representation tells us the precise nature of the set of efficient consumption points. Our solution to the problem is a general one and might be applied to the individual or the corporation. For after studying the set of efficient consumption patterns, the firm can choose that optimal pattern which maximizes the value of its equity. However, the solution is not a simple one, and for a planning horizon exceeding two periods, it is relatively difficult to portray the efficient set. In order to make the solution more applicable, we suggest solving for vectors of possible discount factors. Each of these discount factor vectors will correspond to a segment or facet of the efficient set. The investor is then asked to select that vector or combination of vectors appropriate to his time preference. The final step is the presentation to the individual of a facet of the efficient set. From this reduced efficient set the investor is asked to choose his optimal consumption point. The investment strategy selected is any one that satisfies all capital and technological constraints, given the chosen consumption vector. [ABSTRACT FROM AUTHOR]