A separable programming model incorporating linear demand functions for grains and vegetable oils: an analysis of United States agriculture in 1985

Applications of linear programming in analyzing and evaluating various policies related to agriculture have been numerous. The use of quadratic programming is relatively less common. The computational aspects of the problem present an important limitation on the use of quadratic programming when size of the model used is relatively large. In the present study, separable programming was applied to solve a quadratic programming model of U.S. agriculture. The quadratic objective function of the model was transformed into a separable function using eigenvalues and eigenvectors of the demand matrix. The quadratic programming model is formulated in such a way that number of constraints in the model is relatively small which facilitates application of separable programming to a broad spectrum of problems;The quadratic programming model is used to analyze the impact of alternative energy price and supply situations on the crop production sector of U.S. agriculture. In recent years, continuous rise in energy prices and prospects of reduction in fossil fuel-based energy supply are having numerous effects on the use of energy in all sectors of the economy and development of competing energy sources. In the present study, impact of alternative energy situations is analyzed on a number of variables related to agriculture which may be listed as follows: land, water, nitrogen and energy use in farming, regional crop production patterns, methods of farming, resource and output prices, energy and nonenergy related expenses in crop production, farm income and consumer expenditures on farm products at farm level;With increased energy prices, reduction in the use of inputs such as water and commercial fertilizer nitrogen which require energy was observed similarly. Reduction in irrigated farming and increase in acreages under minimum tillage were also observed as means of accomplishing reductions in energy use. But the decrease in energy used in farm production was very small relative to the increase in energy prices. Crop prices at farm-level, total cost of crop production, consumer expenditures at farm level and net farm income all increase due to increased energy prices;When energy supplies are reduced, the main results are similar to those observed when the energy prices increased. Regional level reduction in energy supply, rather than the national level reduction causes the nonenergy related cost of production to increase under the former alternative relative to the latter.