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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 20:35, 25 January 2010
, 20:35, 25 January 2010→Search Theoretic Models of Price Dispersion
*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>
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]:
<center><math>q(p) \equiv -v'(p)\,</math>.</center>
*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 on the derivation of demand'''
Recall that: <center> <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>\frac{d/}{dp(v(M,p)) } = \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{de(p,u)/}{dp } = -\frac{dv/dp}{dv(M,p)/dm}\,</math> <math>\therefore q(m,p) = -\frac{d/}{dp(v(p))}\,</math>\\ </center>
<math></math>
