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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 15:11, 26 January 2010
, 15:11, 26 January 2010no edit summary
In addition <math>F\,</math> 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>.
===The Varian (1980) Model===
The Varian (1980) model gives customers ex-ante different information sets. Shoppers are informed consumers, and Loyals are uniformed consumers. Furthermore, Varian shows that these differences can exist when customers are acting optimally, provided the costs of becoming informed are ordered and surround the price (value) of information.
In the Varian (1980) model:
*<math>\phi = 0\,</math> (i.e. costless listing)
*<math>U > 0\,</math> (i.e. some uniformed customers) such that each firm is visited by <math>L=\frac{U}{n}\,</math> uniformed customers
We can use the distribution equations from before substituting in <math>L=\frac{U}{n}\,</math>:
<center><math>F(p) = \left ( 1 - \left ( \frac{(v-p)\frac{U}{n}}{(p-m)S} \right )^{\frac{1}{n-1}} \right )\,</math> on <math>[p_0,v]\,</math></center>
where:
<center><math>p_0 = m + (v-m)\frac{\frac{U}{n}}{\frac{U}{n}+S}\,</math></center>
Suppose that consumers have different costs of accessing the clearinghouse according to their types. The value of information at the clearinghouse can be seen to be:
<center><math>VOI^{(n)} = \mathbb{E}(p) - \mathbb{E} \left [ p_{min}^{(n)} \right ]\,</math></center>
If costs are such that <math>K_S\,</math> is the cost for the shoppers and <math>K_L\,</math> is the cost for the loyals, and then costs are such that:
<center><math>K_S \le VOI^{(n)} < K_L\,</math></center>
The shoppers will optimally use the clearinghouse and loyals optimally will not.
It is important to notice that the level of price dispersion is not a monotonic function of the consumer's information costs. When the costs become too high, no shoppers exist (i.e. no-one becomes informed) and all firms charge the monopoly price. Likewise when costs are zero, everyone becomes informed and all firms charge marginal cost (the Bertrand Paradox again).
<math>
