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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 22:09, 25 January 2010
, 22:09, 25 January 2010→The Stigler (1961) Model
<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>
To see this, first recall that <center><math>\mathbb{E}(X) = \int_{\underline{x}}^{\overline{x}} x f(x) dx \,</math></center>
Then use the [http://en.wikipedia.org/wiki/Integration_by_parts integration by parts ] formula <center><math>\int u\, \frac{dv}{dx}\; dx=uv-\int v\, \frac{du}{dx} \; dx\!</math></center>
<math>
