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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 15:21, 26 January 2010
, 15:21, 26 January 2010no edit summary
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).
===Baye and Morgan (2001)===
The Baye and Morgan (2001) model has optimizing firm, optimizing consumers and a monopolist gatekeeper. There is a nice 'story' to match this model that uses geographically distinct local markets that can serve the global market if they list with the gatekeeper. Loyal consumers shop locally, and shoppers are (potentially) global purchasers.
The assumptions are as follows:
*The gatekeeper optimally sets <math>\phi > 0\,</math>
*The gatekeeper optimally sets <math>L=0\,</math>
Substituting into the equations we find that:
Each firm lists with probability:
<center><math>\alpha = 1 - \left ( \frac{\frac{n-1}{n}\phi}{v-m)S} \right )^{\frac{1}{n-1}}\,</math> with <math>\alpha \in (0,1)\,</math></center>
The price distribution at the clearinghouse is:
<center><math>F(p) = \frac{1}{\alpha} \left ( 1 - \left ( \frac{\frac{n-1}{n}\phi + (v-p)L}{(p-m)S} \right )^{\frac{1}{n-1}} \right )\,</math> on <math>[p_0,v]\,</math></center>
where:
<center><math>p_0 = m + \frac{\frac{n-1}{n}}{S}\phi\,</math></center>
When a firm doesn't list it charges <math>v\,</math> and its equilibrium profits are:
<center><math>\mathbb{E}\pi = \frac{1}{n-1}\phi\,</math></center>
Price dispersion arises from the gatekeeper's incentives to set <math>\phi > 0\,</math>. The expected profits to firms are positive and proportional to <math>\phi\,</math>.
<math>
