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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 20:40, 25 January 2010
, 20:40, 25 January 2010→Search Theoretic Models of Price Dispersion
*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:<center><math>u(q) + y\,</math> where <math>y\,</math> is a numeraire good</center>*The indirect utility of consumers is:<center><math>V(p,M) = v(p) + M\,</math></center>
<center>where <math>v(\cdot)\,</math> in nonincreasing in <math>p\,</math>, and <math>M\,</math> is income.</center>
*By [http://en.wikipedia.org/wiki/Roy%27s_identity Roy's identity]:
*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 : <center><math>V(p,M) = v(p) + M - cn\,</math></center>
'''A note 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>. Taking the derivitive with respect to <math>p\,</math>:
<math>\frac{d(v(M,p))}{dp} = \frac{dv(M,p)}{dm} \cdot \frac{dM}{dp} + \frac{dv}{dp} = 0,\,</math> where
<math>\frac{dM}{dp} = \frac{de(p,u)}{dp}\,</math>.
<math>\therefore q(m,p) = -\frac{d}{dp(v(p))}\,</math>\\
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