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'''A note on the derivation of demand'''
Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 20:43, 25 January 2010
, 20:43, 25 January 2010→Search Theoretic Models of Price Dispersion
==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
*The final indirect utility of the customer is: <center><math>V(p,M) = v(p) + M - cn\,</math></center>
Recall that <math>M=e(p,u)\,</math>,
Taking the derivitive with respect to <math>p\,</math>:
<center><math>\frac{d(v(M,p))}{dp} = \frac{dv(M,p)}{dm} \cdot \frac{dM}{dp} + \frac{dv(M,p)}{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{\frac{dv(M,p)}{dp}}{\frac{dv(M,p)}{dm}}\,</math> <math>\therefore q(m,p) = -\frac{d}{dp(v(p))}\,</math>\\
<math>\therefore q(m,p) = -\frac{d}{dp(v(p))}\,</math> in our case.
</center>
<math></math>
