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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 20:25, 25 January 2010
, 20:25, 25 January 2010no edit summary
Baye et al. (2006) provides a survey of models of search and clearing-house that exhibit price dispersion. The survey is undertaken through two specializable frameworks, one for search and one for cleaning-houses, which are then adapted to show the key results from the literature. There are a number of equivalent results across the two frameworks.
==Search Theoretic Models of Price Dispersion==
The general framework used through-out is as follows:
A continuum of price-setting firms with unit measure compete selling an homogenous product
A mass <math>\mu</math> is interested in purchasing the product
Consumers have quasi-linear utility <math>u(q) + y</math> where <math>y\,</math> is a numeraire good
The indirect utility of consumers is <math>V(p,M) = v(p) + M\,</math>
where <math>v(\cdot)\,</math> in nonincreasing in <math>p\,</math>, and <math>M\,</math> is income.
By [http://en.wikipedia.org/wiki/Roy%27s_identity Roy's identity]:
<math>q(p) \equiv -v'(p)\,</math>.
There is a search cost <math>c\,</math> per price quote
The customer purchases after <math>n\,</math> price quotes
The final indirect utility of the customer is <math>V(p,M) = v(p) + M - cn\,</math>
'''A on the derivation of demand'''
Recall that <math>M=e(p,u)\,</math>, so that <math>v(e(p,u),p)=u\,</math> when the expenditure function is evaluated at <math>p\,</math> and <math>u\,</math>.
<math>d/dp(v(M,p)) = dv(M,p)/dm \cdot dM/dp + dv/dp = 0, where dM/dp = de(p,u)/dp\,</math>.
<math>\therefore q(m,p) = de(p,u)/dp = -frac{dv/dp}{dv(M,p)/dm}\,</math>
<math>\therefore q(m,p) = -d/dp(v(p))\,</math>
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