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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 16:07, 11 April 2010
, 16:07, 11 April 2010Reverted edits by Ed (Talk) to last version by 136.152.161.214
<center>where <math>\mathbb{E}(p_{min}^{(n)}) = \mathbb{E}(min\{p_1,p_2,\ldots,p_n\}) \,</math>, that is the expected minimum price from n draws</center>
The distribution of the lowest <math>n\,</math> draws is: <center><math>F_{min}^{(n)}(p) = 1 - (1-F(p))^n\,</math>, where <math>(1-F(p))^n\,</math> is the probability that <math>P\,</math> is less than <math>p\,</math> for all <math>n\,</math> draws. </center>
Note that the strick inequality follows from the proof that <math>\Delta > 0\,</math>, and the weak inequality follows as <math>n^*\,</math> may not be optimal under <math>G\,</math>.
===The Rothschild Critique===
<center><math>\alpha = 1 - \left ( \frac{\frac{n-1}{n-1}\phi}{(v-m)S} \right )^{\frac{1}{n-1}}\,</math></center> This is obtained by equating the inside and outside options and solving for <math>\alpha\,</math>. The outside option is: <center><math>(v-m)\left(L-\frac{S}{n}(1-\alpha)^{n-1}\right)\,</math></center> :where <math>(v-m)\,</math> is the mark-up, <math>\frac{S}{n}\,</math> is the traffic if no-one else lists and <math>(1-\alpha)^{n-1}\,</math> is the probability that no-one else lists. The inside option is: <center><math>(v-m)\left(L - S(1-\alpha)^{n-1}\right)-\phi\,</math></center> :where <math>S\,</math> is the traffic obtained from listing and <math>\phi\,</math> is the cost of listing.
If a firm lists then its price is drawn from:
<center><math>p_0 = m + (v-m)\frac{L}{L+S} + \frac{\frac{n-1}{n-1}}{L+S}\phi\,</math></center>
