The point of departure from traditional theory in this study is the assumption made by Lrsch [5; pp. 62-65, 109-120, 136], and commonly accepted in the field, that agricultural settlement production units in a region are best considered to be "selfsufficient farms that are regularly distributed" throughout regional space. This assumption is the basis for Lrsch's hypothesized regular hexagonal pattern of market areas, with the smallest of these corresponding to the agricultural production unit itself, i.e., the individual farm. The now familiar diagram of this pattern is shown in Figure 1. L~Ssch's assumption, or more exactly the compatibility of this assumption with L/Ssch's other assumptions on the nature of the regional economy, was challenged by Isard [4; pp. 271-273] as early as 1955. Arguing inductively for the effe, cts of urbanization on a homogeneous region, Isard [4; p. 271] reasoned, "At a great distance from the core, market areas must be larger because not only are the production sites and industrial population fewer in number, but also, as a logical consequence of differential industrial population, agricultural activity is less intensive and agricultural population is more sparce than in the immediate hinterland of the central city. Thus we obtain a pattern of distorted hexagons." Isard depicted the resulting pattern of distorted hexagons and this is shown in Figure 2. However, he did not venture to generate the pattern mathematically from the conditions of the agricultural space economy that are assumed. Isard's model has since won broad acceptance in the field as the more realistic alternative to Lrsch's earlier work; see Haggett [3; pp. 121-125] and Morrill [6; pp. 175-184]. However, there have been to this author's knowledge no previous attempts to construct a deductive model to explain the nature of the distorted hexagon pattern. To be sure, the focus of concern for both Lrsch and Isard was the regional pattern of market areas, not specifically that of settlements. However, when the agricultural region is assumed to be composed of only discrete and homogeneous agricultural settlement production units, (i.e., villages rather than scattered farms), then these same units must be the quanta by which market areas are delineated. Thus the market area pattern for agricultural goods will correspond to the assumed pattern of agricultural settlement production units. This study can be said to attempt to quantify Isard's model and, in doing so, to relate it to that of Lrsch. The