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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 04:39, 26 January 2010
, 04:39, 26 January 2010→Reinganum (1979) Revisited
===Reinganum (1979) Revisited===
Recall that Reinganum (1979) has firms with marginal costs drawn from a distribution <math>G(m)\,</math>. Suppose that an individual firm's cost is <math>m_j\,</math>, and that a fraction <math>\lambda\,</math> (, where <math>\lambda \in \left [0,1 \right )\,</math>) , of firms price above <math>r\,</math>. Then, with a mass <math>\mu \,</math> of consumers as before:
\end{cases}
</math></center>
It is instrumental to temporarily ignore that a firm's demand is zero above r. The profit maximizing price from above is (from the first order condition):
\left [(p_j-m_j) q'(p_j) + q(p_j)\right ] \left ( \frac{\mu}{1 - \lambda} \right = 0
Which implies (given the consumer's demand function above):
p_j=\left ( \frac{\epsilon}{1+\epsilon} \right ) m_j
If firm's were to do this then consumers would face a distribution of prices:
\hat{F}(p)=G \left (p \left ( \frac{\epsilon}{1+\epsilon} \right ) \right)
on the interval:
\left [ \frac{\undeline{m}\epsilon}{1+\epsilon} , \frac{\overline{m}\epsilon}{1+\epsilon} \right ]
<math>
