Mark Voronovitsky and Shlomo Maital
"People see what others do, and may be influenced by it."
Paul Ormerod, Butterfly Economics (1998)
"How many times have you walked away from a new
restaurant because it was almost empty? Most people
prefer to wait for a table at a restaurant that is crowded,
rather than eat in an empty one...If the place was really good,
goes the thinking, there would be a line out the door..."
Al Ries and Laura Ries. 22 Immutable
Laws of Branding (1996)
For more than a century, since Alfred Marshall (1881) and Leon Walras (1874; 1954), price and income held center stage in the theory of demand. Marshall specifically ignored social, interpersonal effects in demand -- perhaps because he felt it would complicate his elegantly simple price-quantity diagram (Leibenstein, 1950, p. 186). But with the growth of urban society, spending money became increasingly a social activity, taking place in settings (like shopping malls and restaurants) where others were similarly engaged. As discretionary income grows, the proportion of consumer spending devoted to price-sensitive basic commodities declines. At the same time the proportion allocated to services and 'experiences' grows (Gilmour and Pine, 1998). Indeed, many business strategies are focused precisely on escaping the world of price-sensitive commodities, and advancing into services and experiences where price is almost immaterial. Such experiences are almost invariably social in nature.
Scholars have sought to model and understand demand as a social activity, where interactions with others are a more important determinant of individual demand than the price of the product. Leibenstein's (1950) "bandwagon" effect ["the extent to which the demand for a commodity is increased due to the fact that others are also consuming the same commodity", p. 189] was an early contribution. And of course, long ago Thorstein Veblen's Theory of the Leisure Class pioneered in the sociological analysis of demand as conspicuous consumption.
Two principal themes exist in the modern 'social demand' literature: Becker (1991) and Kirman (1993, 1997). Becker shows that prices may not rise in the face of excess demand (expressed, for instance, as long queues at restaurants), if individual demand depends on the aggregate demand of all consumers. Kirman shows that buyers (in his example, ants choosing between two food piles) may cluster randomly at each of two sites in turn, when one buyer tells another about a great site. These two approaches differ in the type of social interaction that drives demand and in the structure of information. Becker posits that people tend to buy what others buy, requiring knowledge of total demand; and Kirman posits that people buy what one or more other people say or do (requiring only limited information on total demand). A largely independent literature on capital markets shows how Becker-like effects can generate financial panics and bubbles.
One common theme unites these separate strands of research: The commonness of 'avalances', in which demand rushes to one product or venue, while equally quickly abandoning another. Variations of this phenomenon are described as bubbles, bandwagons, cascades, contagions, or herd effects, or 'critical mass'. Such 'avalances' conflict with conventional demand theory under perfect information, where prices adjust rapidly to clear markets and prevent rapid 'emptying' of a restaurant or store, or common stock. They help explain in part why prices change far less frequently than the theory of demand and perfect competition predict.
In this paper, we seek to integrate the Becker and Kirman approaches and model why many successful restaurants, theatres and similar enterprises do not raise prices even in the face of excess demand. We assume there is a given probability each consumer will choose one of two restaurants. This probability depends on quantity of the consumers preferring the first restaurant at the previous moment of time and also on the relative prices of the two restaurants. The dynamics of distribution of probabilities are described by a uniform Markov chain. It is shown that a steady distribution exists in the Markov chain and that the chain converges to steady distribution from any initial distribution. We show the existence of a equilibrium state, where it is not profitable for any restaurant to change its prices, though almost all consumers prefer only one of the two restaurants.
