Linear and Nonlinear Spatial Models in Agricultural Competition, Land Use, and Production Potential

Abstract

the analysis of land-use patterns, interregional competition, supply potential, and other spatial aspects of the agricultural industry. The landuse studies of the 1930's [15], studies of interregional competition in the dairy industry in the same decade [11], and the capacity studies during World War II [7] are all early examples of this interest. Because of lack of data and limited computational capacity, these early studies were unable either to include all relevant competitive products and important producing areas or to incorporate enough simultaneous regional interdependencies. Data deficiencies (both quantitative and qualitative) still impose limitations, but modern computers have eliminated many of the computational restrictions. In the mid-1950's, for example, we had difficulty finding a computer which could solve a problem with only 210 restraints and 310 real variables. Now, thanks to improved computers and decomposition algorithms, a model with 4,000 restraints and 37,000 variables does not exhaust computer capacity. Unfortunately, there has been no comparable improvement in the supply of data. Although other types of models are used, most spatial models, linear or nonlinear, and most supply-response (representative-farm) models are activity-analysis models. Spatial models use a region as the basic producing unit; supply-response models use an individual (representative or typical) farm. Supply-response models try to predict market supply under a given set of market conditions-ignoring, for the most part, interactions between farms in different regions or, for that matter, between farms in the same region. Spatial models try to take account of interregional competitive forces by explicitly including demand restraints and permitting interregional commodity shipments. Insofar as they are inconsistent with regional