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Note that the strick inequality follows from the proof that <math>\Delta > 0\,</math>, and the weak inequality follows as <math>n^*\,</math> may not be optimal under <math>G\,</math>.
 
===The Rothschild Critique===
 
Rothschild (1973) pointed out that the search procedure used in Stigler (1961) may not be optimal. Specifically the customer's commitment to a fixed number of searches may not be credible. The strategy fails to incorporate new information as it becomes available: Once a sufficiently low price quote has been obtained, the benefit of additional searches may drop below the marginal cost.
 
<center>
'''Sequential search'''
In sequential search there is an optimal stopping rule.
Once search results have fallen below some threshold, called the reservation price, search stops.
Consumers know the distribution of prices, which is exogenously specified.
The reservation price is endogenously determined.
</center>
 
 
Recall that a firm's expected demand is: <math> Q(p) - \mu n^* K (1-F(p))^{n^*-1}\,</math>
 
 
Then a firm with constant marginal cost (m) has expected profits:
 
\pi(p) = (p-m)Q(p)
 
 
All firms have the same marginal cost and so the same expected profit function. The
 
===Diamond's Paradox===
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