An optimal investment and financial control model: theoretical solutions and an application

Abstract

This dissertation is devoted to the study of a dynamic (discrete-time) investment and financial control problem over a fixed decision-making interval. In the model, the objective of the firm is to maximize the value of the final capacity plus the amount of savings in the terminal year less the amount of the final indebtedness outstanding. The state variables are farming capacity, indebtedness and savings, while the controls are purchases of new capacity and borrowing (or repayment). There are six difference equations defining changes in farming capacity, indebtedness incurred, and savings, and three sets of inequality constraints restricting the values of the states and controls. The basic model is developed in Chapter II, while in Chapter III, the decision rules are derived including proofs. The results are then interpreted economically in Chapter IV. In Chapter V, the basic model is transformed into a mathematical programming problem. Chapter VI is devoted to an application of the model to farming on the Texas High Plains where they are irrigating from the Ground Water Reservoir: Subdivision No. 1. Here, the farming areas and their characteristics are described, the various estimates of the parameters are calculated (or specified for the problem). Solutions to four parametric variations are computed and discussed. The results indicate the possible sobering effects of depletion of the underground aquifer. There just would not be much growth of farms in Subdivision No. 1 if the model is reflective of farming in this area and the values of the parameters materialize.