Constructal theory of economics structure generation in space and time

This paper extends to economics the constructal theory of generation of sha pe and structure in natural flow systems that connect one point to a finite size area or volume. It is shown that by invoking the principle of cost mi nimization in the transport of goods between a point and an area, it is pos sible to anticipate the dendritic pattern of transport routes that cover th e area, and the shapes and numbers of the interstitial areas of the dendrit e. It is also shown that by maximizing the revenue in transactions between a point and an area, it is possible to derive not only the dendritic patter n of routes and their interstices, but also the optimal size of the smalles t (elemental) interstitial area. Every geometric detail of the dendritic st ructures is the result of a single (deterministic) generating principle. Th e refining of the performance of a rough design (e.g,, rectangles-in-rectan gle) pushes the design toward a structure that resembles a theoretically fr actal structure (triangle-in-triangle). The concluding section shows that t he law of optimal refraction of transport routes is a manifestation of the same principle and can be used to optimize further the dendritic patterns. The chief conclusion is that the constructal law of physics has a powerful and established analog in economics: the law of parsimony. The constructal theory extended in this paper unites the naturally organized flow structure s that occur spontaneously over a vast territory, from geophysics to biolog y and economics. (C) 2000 Elsevier Science Ltd. All rights reserved.