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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 04:24, 26 January 2010
, 04:24, 26 January 2010no edit summary
*Consumers engage in optimal sequential search
*Firms all charge the unique monopoly price <math>p^*\,</math>
*The A consumer with the highest marginal cost <math>\overline{m}\,</math> still earns sufficient enough surplus at the monopoly price to cover the cost of one price quotesearch:<center><math>v \left ( \frac{\epsilon}{1+\epsilon}\overline{m} \right p^*) > c\,</math></center> In Diamond's model all firms charge the monopoly price and all consumers visit exactly one store. This is a Nash equilibrium: Given the stopping rule of consumers the firm's best response is to charge the monopoly price; Given the monopoly price, the consumers' best response is to search just once and then buy. This is unique as a firm posting below the monopoly price would want to deviate up by an epsilon - the consumers would still buy and the firm would make more.
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in the presence of any search frictions whatsoever the monopoly price is the equilibrium.
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===The Reiganum (1979) Model===
Reiganum (1979) showed that price dispersion could exist with sequential search as well as with optimizing consumers and optimizing firms.
Consider the following special case of our environment:
*Consumers have identical demands:
<center><math>-v'(p)=q(p)=Kp^{\epsilon}\,</math>, where <math>\epsilon < -1\,</math> and <math>K > 0\,</math></center>
*Consumers engage in optimal sequential search
*Firms have heterogeneous (private) marginal costs drawn from <math>G(m)\,</math> on <math>[\underline{m},\overline{m}]\,</math>
*The consumer with the highest marginal cost <math>\overline{m}\,</math> still earns sufficient surplus to cover the cost of one price quote:
<center><math>v \left ( \frac{\epsilon}{1+\epsilon}\overline{m} \right ) > c\,</math></center>
Reiganum (1979) shows that under these assumptions there is an equilibrium in which firms optimally set prices, consumers engage in optimal sequential search, and yet there is still price dispersion. We return to the Reiganum (1979) model after a discussion of sequential search.
===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>\lamda\,</math> (<math>\lamda \in \left [0,1 \right )\,</math>) of firms price above <math>r. Then:
<center><math>\mathbb{E}\pi_j = \begin{cases}(p_j-m_j)q(p_j)\left ( \frac{\mu}{1-lamda} \right ) & mbox{if}\; p_j \le r \\0 & mbox{if}\; p_j > r /end{cases}\,</math></center>
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