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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)

4 bytes added , 20:36, 25 January 2010

'''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>.

<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>\\

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