Stigler (1961) observed that when consumers are not perfectly informed about prices they will need to search amongst competing firms to discover favourable prices, and proposed that this search process could provide some explanation for the degree of price dispersion observed in real markets. More recently, numerous commentators have suggested that one impact of the introduction of e-commerce will be a reduction in mark-ups that can be sustained by firms due to the increased ease with which consumers are able to compare alternative prices. Unfortunately the dominant, and most challenging, result in the theoretical search literature gives no support to either conjecture.
Diamond (1971) showed that when consumers search sequentially for one commodity, and search costs are strictly positive, the unique equilibrium will be at the monopoly price. When search costs are zero, however, the model reduces to a Bertrand pricing game for which the unique solution is at the competitive price. Diamond’s result generates several uncomfortable implications. Neither equilibria displays price dispersion and there is no search undertaken in equilibrium, so Stigler's conjecture that the search process will sustain price dispersion appears to be unjustified. Second, whenever search costs are positive all firms charge the monopoly price, irrespective of the size of the industry or the actual cost of search. A reduction in search costs will have no impact on the equilibrium price charged, providing the cost of search remains positive. Third, there is a fundamental discontinuity in the equilibrium outcome at zero search costs, when search costs are strictly positive the monopoly price results but at zero search costs the competitive price results. While his results demonstrate, rather dramatically, the potential impact of weakening the assumption of perfect information just a little – it seems unrealistic to suggest that firms can exploit small information imperfections quite so extremely.
If price dispersion and consumer search are to exist in equilibrium then Diamond's result suggested that some additional mechanism is required. Several alternatives have been proposed, usually relying on some form of exogenously specified heterogeneity amongst agents in the economy. The most common technique is to assume heterogeneity in the consumers' cost of search and/or heterogeneity in the firms’ production costs.
Diamond's discontinuity problem can be overcome if some consumers have zero search costs and others have positive search costs. Equilibrium price dispersions can be achieved if a distribution of search costs amongst consumers is allowed and, crucially, that zero is an element of the support of the distribution. While not doubting the reality of differing search costs amongst consumers, there are a number of concerns I have with this escape route. First, consumers with zero search costs are, when making their consumption decisions, perfectly informed. This seems a rather undesirable, or at least one dimensional, way of analysing markets with imperfect information by assuming that only some consumers are imperfectly informed. Furthermore the resulting equilibria are dependent upon and, typically, very sensitive to, changes in the proportion of perfectly informed consumers. Conceptually there seems to be a big difference between analysing a situation where all consumers may (if they choose) access information more easily and one where the proportion of perfectly informed consumers grows.
Reinganum (1979) generates price dispersion through heterogeneity in producer costs, and many other authors6 combine a distribution of producer costs with a distribution of consumer search costs to generate price dispersion. The difficulty with this approach is that the differing production costs are exogenously specified and no explanation is given as to why differing production techniques survive in equilibrium. One interesting aspect of the model analysed in this paper is that the causality is reversed – we will see that consumer search, by generating price dispersion, may also generate the adoption of differing production techniques by ex-ante identical firms. It will be the process of consumer search that generates differing production techniques, rather than the reverse.
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