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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 04:01, 26 January 2010
, 04:01, 26 January 2010→Sequential Search Models
'''Case 1)''' <math>h(\overline{p}) < 0\,\,</math> and <math> \int_{\underline{p}}^{\overline{p}} v(p)dF(p) < c\,</math>. In this case it is better not to search.
'''Case 2)''' <math>h(\overline{p}) < 0\,</math> and <math>\int_{\underline{p}}^{\overline{p}} v(p)dF(p) \ge c\,</math>. In this case the net benefit at the current price is negative, but the consumer is best off by searching until they get a price quote at (or below) <math>\underline{p}\,</math>.
<center><math>h(\underline{p}) = -c < 0\,</math></center>
<center><math>h(\overline(p)) \ge 0\,</math></center>
<center><math>h'(z) = B'(z) > 0\,</math></center>
Using the equation above to find the optimal <math>r \,</math> (i.e. taking the first order condition), and then differentiating with respect to <math>c\,</math>, we can determine an interesting comparative static:
<center><math>\frac{\partial r}{\partial c} = \frac{1}{q(r)F(r)} = \frac{1}{Kr^{\epsilon}F(r)} > 0\,</math></center>
Therefore a the reservation price is increasing in search costs. Note the special case where <math>q(r)=1 \,</math> leads to a magnification effect, but attenuation effects are also possible.