Capital accumulation and firm growth: a polyperiod linear programming analysis of farms in the peanut area of southeastern Virginia

Abstract

In order to determine the optimum allocation of resource combination of productive enterprises, capital flows; and growth trends on a typical Southeastern Virginia farm. a polyperiod linear programming technique using the IBM 7040 computer, was applied. The input-output matrix was subdivided into four five-year production period1, resulting in a 20-year planning horizon.

Optimum solutions were obtained for the maximization of profit (net returns) and net worth using various discount rates and resource restrictions. Since profit maximization is probably the primary goal of most farm operators, emphasis is given to decision and growth trends resulting from the use of various discount rates which estimate present value of future returns. Emphasis was placed on capital flows and accumulation and firm growth.

Several conclusions may be drawn from the optimum solutions obtained: 1) the greater the discount rate used on maximum net returns, the closer the solution parallels maximum net worth results; 2) capital accumulation is much greater at low discount rates; and 3) firm growth is most rapid when the operator's objective is the maximization of net worth

Several general points were established with reference to new methodology. Polyperiod linear programming is an efficient and useful mathematical device for decision purposes -- resource allocations and enterprise combinations -- and also realistically reflects the accumulation and flows of capital and trends in firm growth, Built-in features allow planning on a more valid basis since many economic factors enter the analysis to reduce some of the risks and uncertainties encountered when dealing with the future.