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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 21:45, 25 January 2010
, 21:45, 25 January 2010no edit summary
The consumer seeks to minimize the expected cost (purchase + search) given by:
<center><math>\mathbb{E}(C) = K \mathbb{E}(p_{min}^{(n)}) + cn\,</math> </center>
<center>where <math>\mathbb{E}(p_{min}^{(n)}) = \mathbb{E}(min\{p_1,p_2,\ldots,p_n\}) \,</math> </center>
The distribution of the lowest <math>n\,</math> draws is: <center><math>F_{min}^{(n)}(p) = 1 - (1-F(p))^n\,</math> </center>
<center><math>\therefore \mathbb{E}(C) = K \int_{\underline{p}}^{\overline{p}} p dF_{min}^{(n)}(p) + cn\,</math></center><center><math>\therefore \mathbb{E}(C) = K \[ \underline{p} + \int_{\underline{p}}^{\overline{p}} 1-(1-F(p))^n dp \] + cn\,</math></center>
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