Von Thunen Biography Model Theory

Johann Heinrich Von Thünen Biography

Thunen Model, von Thunen Theory

Johann Heinrich von Thiinen (1783-1850) was a successful farmer and brilliant the­orist who worked in isolation on his agricultural estate in Mecklenburg, Germany. He understood, as few economists have before or since, the proper relation between theory and facts—which is the hallmark of any scientific investigation. It was this characteristic of his thought that endeared him to Alfred Marshall (see Chapter 14), who claimed to have "loved [him] above all my masters" (Memorials, p. 360). One of the things Marshall learned from von Thiinen was how to apply the principle that all forms of expenditure should be carried to the point at which the product of the last unit equals its cost: the total product is maximized only when resources are al­located equimarginally.

Von Thiinen is credited with a number of important and original anticipations of modern economic theory, such as the concepts of economic rent, diminishing returns, opportunity costs, and the marginal-productivity theory of wages. Above all else, however, he was a pioneer in the economic theory of location; so we will examine his contribution to marginal analysis primarily in that context.

Like Ricardo, von Thiinen recognized that differences in the cost of producing agricultural products result from utilization of land of different quality and location (i.e., distance from a central selling point). But whereas Ricardo focused on differ­ences in soil fertility, von Thiinen concentrated his analysis on differences in land location. At the same time, he recognized that those products that are bulky in rela­tion to value are more costly to transport than those that are less so and that some farm products cannot stand a long period in transit because of their perishability.

The problem, therefore, was to devise the best (most profitable) system of land utilization. Von Thunen's solution was so carefully worked out that he rightfully de­serves the distinction of being called the father of location theory in economics. His argument was couched in a theoretical construction, or model, which has the fol­lowing characteristics. A large town (market) is situated in the center of a fertile plain that has neither canals nor navigable rivers. The only means of conveyance is by horse-drawn wagon or a similar means of transport. All land within the plain is of equal fertility, and there are no other comparative advantages of production between plots. At a considerable distance from the city, the plain ends in an uncultivated wilderness. The town draws its produce from the plain, the inhabitants of which it supplies with manufactured products. There is no trade with the outside world.

A model developed by Melvin Greenhut shows how the boundaries of produc­tion are determined for two competing crops once the costs of production and trans­portation are known. In Figure 1 assume that O is the central market point in the middle of a homogeneous plain. OA is the cost of producing a dollar's worth of pota­toes and A'S is the cost of transporting the potatoes over a distance of OJ miles. Sim­ilarly, A"T and OAT represent an identical cost and distance in the opposite direction. AS and AT show the gradual increase in transport costs (and total costs) as the dis­tance from O increases. On the other hand, OB represents the cost of producing a dollar's worth of wheat, and B 'M (B"N) represents its transport cost for distance OX' (OX). The freight rate is assumed to be higher on potatoes than on wheat because the former yields a greater bulk per acre than the latter.

Von Thiinen's assumption of a uniform, homogeneous plain implies that labor and capital are equally productive at all locations and that the cost of production per acre of output is everywhere the same. From Figure 1 it will be seen that at a distance beyond OL, the delivered cost of a dollar's worth of potatoes (cost line AS) exceeds the delivered cost of a dollar's worth of wheat (cost line BM). Therefore, producers of potatoes will tend to locate to the west of L and to the east of H, whereas wheat producers will locate to the east of L and to the west of H.


Figure

Furthermore, if transport costs are the same in every direction, OL becomes the radius of a circle within which potato production will take place. In other words, von Thunen's model gives us the least-cost location for each crop within the isolated state. It also illustrates the principle of equimarginal allocation. Resources should be al­located to potato production only up to the point where the cost of producing a dol­lar's worth of potatoes equals the cost of producing a dollar's worth of wheat. Fi­nally, the model can be generalized to include more than two crops.

Von Thiinen's theory deals with the classical problem in location analysis, namely, the location of producers over an area that serves consumers at a central point. Al­though its assumptions are restrictive, it nevertheless marked a significant beginning in locational analysis and in mathematical economics. Moreover, Greenhut has shown that the analysis is not limited to agricultural locations but can be adapted to the locational decision of manufacturing concerns as well.