A DYNAMIC CONTRIBUTION TO von THÜNEN’S SPATIAL ECONOMY
OSCAR ORELLANA E. (Mathematic Department, Universidad Técnica Federico Santa María,
Valparaíso-Chile, e-mail: [email protected]).
JAIME GLARÍA B. (Electronic Department, Universidad Técnica Federico Santa María,
Valparaíso- Chile, e-mail: [email protected]).
ABSTRACT: In 2000, Edwin S. Mills brought back the urban economy studies to the
beginning of the 19 century, reviewing several foundational publications like: “Die
räumliche Ordnung der Wirtschaft” by August Lösch (1906-1945), in 1940; “Die zentralen
Orte in Süddeutschland” by Walter Christaller (1893-1969), in 1933; “Principles of
Economics” by Alfred Marshall (1842-1924), in 1920; and “Progress and Poverty” by Henry
George (1839-1897), in 1874, back to “Der isolierte Staat in Beziehung auf Landwirtschaft
und Nationalökonomie” by Johann Heinrich von Thünen (1783-1850), in 1826.
Von Thünen postulated a theory about the spatial ordering of production relating it with
the production rent, u, understood as:
u= r • (p- c- C•x),
where r is a product flow from its production center to a unique consumption urban
center; p is the product price at the urban center; c is the production cost; C is the freight
rate (including damages) from the production center to the urban one; and x is the
distance between both centers.
The basic argument in von Thünen´s theory is that the rate C and the distance x from the
urban center need to be balanced out, and such necessity of balance compels the
products with higher transportation cost to be produced (in stationary state) where the
land is more expensive (near the urban center) and those products with a lower rate,
where the land is cheaper (far from the town).
Even though Mills warned about the tendency of modern studies to abandon the spatial
ordering, and explained such tendency as due to both the exhaustion of the monocentric
case and the difficulty of the multicentric case, here we coincide with the contrary efforts
performed by Fujita, Krugman and Venables in their book: “The Spatial Economy”.
Accordingly, we attempt to contribute a light dynamic theory about the evolution of the
spatial ordering, coming back to a unique consumption center (one town), multiple
centers of production (agricultural land) distanced from the consumption center, one after
the other along an otherwise isolated territory, and several possible products (vegetables,
fruits, cereals, , etc.) in each of the production centers.
In our attempt, we add the cost of the land to the production costs, and let the land price
evolve with the other variables. Moreover, we replace the production rents, the flows of
products, the price of the land and the productivity by their respective linear densities, to
promote the calculation by means of spatial integration. On top of that, we explicitly
declare units of measure for all the variables, with the objective of reducing the
interpretation errors.
At the end, we put into play the money interests and the prices, selling and buying of land,
we calculate the evolution for all these variables and the ones that von Thünen considered
stationary, we enable the inclusion of the investigation of the product offer and demand
at the urban center, and we guess that the extension of the theory to multicenter cases
that compete among each other to satisfy their demands is not too difficult. These last
two aspects are under current investigation by the authors of this work.
Some of the simulations results of our dynamic equations are shown below.
Evolution of the linear density of land price according to distance and time, p T(x,t).
Linear densities of production rents ignoring land price when t=1000, rn(x,1000)(pn(1000)cn(1000)-Cn,1x), shown by thin lines; the same densities in von Thünen’s stationary
scenario, shown by thick lines.