Constructal theory of economics structure generation in space and time

This paper extends to economics the constructal theory of generation of shape 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 minimization in the transport of goods between a point and an area, it is possible to anticipate the dendritic pattern of transport routes that cover the area, and the shapes and numbers of the interstitial areas of the dendrite. 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 pattern of routes and their interstices, but also the optimal size of the smallest (elemental) interstitial area. Every geometric detail of the dendritic structures is the result of a single (deterministic) generating principle. The refining of the performance of a rough design (e.g., rectangles-in-rectangle) pushes the design toward a structure that resembles a theoretically fractal structure (triangle-in-triangle). The concluding section shows that the 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 structures that occur spontaneously over a vast territory, from geophysics to biology and economics.