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p_j=\left ( \frac{\epsilon}{1+\epsilon} \right ) m_j
Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 04:41, 26 January 2010
, 04:41, 26 January 2010→Reinganum (1979) Revisited
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It is instrumental to temporarily ignore that a firm's demand is zero above <math>r\,</math>. The profit maximizing price from above is (from the first order condition):
<center><math>\left [(p_j-m_j) q'(p_j) + q(p_j)\right ] \left ( \frac{\mu}{1 - \lambda} \right = 0\,</math></center>
Which implies (given the consumer's demand function above):
<center><math>p_j=\left ( \frac{\epsilon}{1+\epsilon} \right ) m_j\,</math></center>
If firm's were to do this then consumers would face a distribution of prices:
<center><math>\hat{F}(p)=G \left (p \left ( \frac{\epsilon}{1+\epsilon} \right ) \right) \,</math> on the interval: <math>\left [ \frac{\undeline{m}\epsilon}{1+\epsilon} , \frac{\overline{m}\epsilon}{1+\epsilon} \right ]\,</math></center>
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