Space in economic analysis—from discrete to two-dimensional continuous theory

Trade across space is central to economic theory. Trade presumes the existence of a transport system. Already in the eighteenth and nineteenth centuries, economists such as Adam Smith and David Ricardo elaborated upon the gains from trade between two nations. It was the Law of Comparative Advantage in production that explained the gains from trade, according to Ricardo. Eli Heckscher and Bertil Ohlin reformulated Ricardian trade theory by treating spatially trapped resources in different locations as the root cause of the existence of comparative advantages. Their treatment of space-bridging frictions remained implicit, however. Stella Dafermos and Anna Nagurney addressed this neglect by transforming older theories of international trade into a very general class of network-based interregional models of trade and transportation. These were the so-called “variational inequality models.” The German economist Johann Heinrich von Thünen developed an early spatial alternative to mainstream trade theory. In 1826, he formulated a complete general equilibrium theory of transport, location, land use and trade in a continuous one-dimensional model. In the second half of the twentieth century, Martin Beckmann and Tönu Puu showed that von Thünen’s model is applicable to two-dimensional continuous space. Spatial economic theory, which in principle includes all theories of international and interregional trade, has evolved over time. Early implicit models evolved into models with discrete systems of regions and then into models with continuous one- or two-dimensional space. However, all of these theories and models assume the prior existence of a transport system. In this chapter we show that economic actors create networks of nodes (towns) and links (trading routes) because they expect various advantages to arise due to new opportunities for trade. Such network creation is a type of entrepreneurship that exhibits consequences that are unusually collective. Hence agglomerations of people and productive activities reflect accessibility differences and these differences are associated with unequal internal and external scale economies. We also show that there is a self-organizing process of network creation that makes cities more efficient over time.