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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 15:57, 26 January 2010
, 15:57, 26 January 2010no edit summary
Price dispersion results from exogenous differences in preferences of consumers. Firm's wish to price at <math>v\,</math> for their loyal customers but if they did so, they could be undercut and loose their shoppers... however, this does not lead to the Bertrand outcome as at some point firms are better off pricing <math>v\,</math> and giving up on serving the shoppers. The equilibrium is therefore in mixed strategies - sometimes firms price low to attract shoppers and sometimes price high to maintain margins.
Loyal customers expect to pay the average of prices charged:
<center><math>\mathbb{E}(p) = \int_{p_0}^v p dF(p)\,</math></center>
Shoppers expect to pay the lowest of <math>n\,</math> draws from <math>F(p)\,</math>:
<center><math>\mathbb{E} \left [ p_{min}^{(n)} \right ] = \int_{p_0}^{v} p dF_{min}^{(n)}(p)\,</math></center>
As the number of competing firms increases prices increase because it is assumed that more loyals enter the market. The fraction of shoppers in the market is given by:
<center><math>\frac{S}{(S+nL)}\,</math></center>
In addition <math>F is stochastically ordered in <math>n\,</math>, so when there is <math>n+1\,</math> firms competing <math>F^{(n+1)}\,</math> [http://en.wikipedia.org/wiki/First-order_stochastic_dominance first-order stochastically dominates] <math>F^n\,</math>.
Finally it should be noted that the results in Rosenthal (1980) are essentially identical to those of the fixed-search model of Burdett and Judd (1983). In Burdett and Judd a fixed fraction of consumers sample only one firm and so can be considered "loyal", while the remainder sample two firms are are the "shoppers".
===The Varian (1980) Model===
<math>
