Location rent and the spatial distribution of economic activities: A nonlinear reformulation of the von Thunen paradigm (Johann Heinrich von Thuenen)

This thesis extends the classical von Thunen theory of agricultural rents to include input substitution and variable levels of cultivation intensity, resulting in variable levels of yield and nonlinear rent gradients. Under constant returns to scale and constant transport rates the rent gradient was found to be strictly convex to the origin, i.e., the central city, and labor inputs and yield were determined to be increasing, as one approaches the market, but at decreasing rates. These results confirm the Dunn-Isard conjecture as to the strict convexity of the rent gradient under nonlinear but homogeneous production functions. This model is further extended to non-agricultural, i.e., industrial rents, in accordance with transportation logistics which prescribe that all industrial inputs be distributed from the central market and all finished products be delivered back to the central market. Industrial production is also based upon nonlinear but homogeneous production functions, i.e., with constant returns to scale, and capital, labor, and land inputs, as well as intermediate product inputs purchased from other producers. Rent gradients in the urban sector were found to be strictly convex and labor and production density increased but at decreasing rates as one approaches the market center, echoing the same results found earlier in the agricultural sector. These results are supported by the hypothesis that specialization and the division of labor, particularly in manufacturing, yields sufficient economic advantages and incentives to provide for the mutual interdependence of individuals and firms, as well as the density of population and highly developed transportation systems which specialization requires. The validity of this hypothesis is demonstrated by an analysis which shows the formal equivalence between David Ricardo's analysis of the gains from trade based on comparative advantage and Adam Smith's analysis of the benefits of specialization and the division of labor. This analysis provides a means of accommodating a wide range of skills within an analytic framework based on non-homogeneous labor. The end result is the reformulation of the von Thunen model providing a seamless theory of location, rent, and the spatial distribution of economic activities in which the central city and its agricultural hinterland are mutually interdependent based upon interpersonal comparative advantage, specialization, and the division of labor.