THE SPATIAL STRUCTURE OF AGRICULTURAL ACTIVITIES1

MEMBERS of the geographic profession have long been concerned with the spatial structure of human activities and have produced an extensive body of literature dealing with agriculture in general.2 These geographic studies of the spatial structure of agriculture have made a significant number of concepts available to the research worker, but nowhere does there appear any explicit proof of one of the basic theorems, namely: that for every spatial location there is some jointly optimum intensity of land use, type of land use, and group of markets, the selection of which by the agricultural entrepreneur leads to spatially ordered patterns of land use. This paper presents rigorous examinations of proofs of the existence theorem stated above. The establishment of a rigorous proof of this theorem provides an important link in the development of concepts pertaining to the spatial structure of agriculture. The establishment of a rigorous proof of the existence theorem provides a second important contribution by spelling out the context of information and concepts within which the theorem holds. The context within which the theorem may be proved provides a guide to