This article presents a micromodel of knowledge creation through the interactions among a group of people. The model features myopic agents in a pure externality model of interaction. Surprisingly, for a large set of initial conditions we find that the equilibrium process of knowledge creation converges to the most productive state, where the population splits into smaller groups of optimal size; close interaction takes place within each group only. This optimal size is larger as heterogeneity of knowledge is more important in the knowledge production process. Equilibrium paths are found analytically; they are a discontinuous function of initial heterogeneity.
Much of the literature on the endogenous generation of a city employs increasing returns to scale in order to obtain agglomeration. In contrast, the model considered here focuses on the role of marketplaces or trading centers in the agglomeration of population as cities. Gains to trade in combination with transportation and marketplace setup costs suffice to endogenously generate a city or cities with one or multiple marketplaces. It is assumed that consumers are fully mobile while production functions are location-specific. The exchange of commodities takes place in competitive markets at the marketplaces, while the number and locations of the marketplaces are determined endogenously using a core concept. Unlike the standard literature of urban economics, our model can deal with differences in geography by letting the setup costs of marketplaces and the transportation system depend on location. After showing that an equilibrium exists and that equilibrium allocations are the same as core allocations, we investigate the equilibrium number and locations of marketplaces, the population distribution, and land prices. In contrast with earlier literature, the results are general in the sense that specific functional forms are not needed to obtain existence of equilibrium, equilibria are first best, and equilibria are locally unique (in our examples).
2Where human beings organize their economy around market exchange, trade between city and country will be among the most powerful forces influencing cultural geography and environmental change. The ways people value the products of the soil, and decide how much it costs to get those products to market, together shape the landscape we inhabit. (Cronon, 1991, p. 50)
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