There are several basic concepts which lie at the heart of economic theory. They are the "economic atom" which is usually considered to be the individual, profits, money, price and markets and the more complex organism the firm. Much of economic theory is based on utility maximizing individuals and profit maximizing firms. The concept of a utility function attributes to individuals a considerable amount of sophistication. The proof of its existence poses many difficult problems in observation and measurement. In this study of market and price formation we consider simplistic social individuals who must buy to eat and who look for where to shop for the best price. In this foray into dynamics we opt for a simple model of consumer price formation. Our firms are concerned with survival rather than a sophisticated profit maximization. Yet we relate these simple behaviors to the more conventional and complex ones.
A natural way to approach the economic physics of monopolistic competition is to introduce space explicitly. For much of economic analysis of competition space and information are critical factors. The basic aspects of markets involve an intermix of factors, such as transportation costs and delivery times which depend explicitly on physical space. But for pure information, physical distance is less important than direct connection. For questions concerning the growth of market areas, the spatial representation is appropriate. Consideration of space is sufficient to provide a justification of Chamberlin's model of monopolistic competition as is evident from the work of Hotelling [1]. Furthermore it is reasonably natural to consider space on a grid with some form of minimal distance. Many of the instabilities found in economic models such as the Bertrand model are not present with an appropriate grid.
When investigating these topics, one quickly finds that many aspects of price formation can be understood in terms of generalized evolutionary dynamics. In consequence, our first models in this paper study spatial competition and cluster formation without the generation of price (Sec. 3). This generates cluster size distributions, which can be compared to real world data. We spend some time investigating theoretical models which can explain our simulation data (Sec. 4). We then, finally, move on to price formation, where we implement the price dynamics ``on top'' of the already analyzed spatial competition models (Sec. 5). The paper is concluded by a discussion and a summary.