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The optimal consumer strategy is:
'''Case 1)'''{{pad|4em}} &nbsp;&nbsp; <math>h(\overline{p}) < 0 and \int_{\underline{p}}^{\overline{p}} v(p)dF(p) < c\,</math>. In this case it is better not to search.
'''Case 2)'''{{pad|4em}} &nbsp;&nbsp; <math>h(\overline{p}) < 0 and \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>.
'''Case 3)'''{{pad|4em}} &nbsp;&nbsp; <math>h(\overline{p}) > 0\,</math>. This is the interior solution. The customer should search until they get a reservation price <math>r\,</math> given by:
<center><math>h(r) = \int_{\underline{p}}^{r} (v(p) - v(r))dF(p) - c = 0\,</math></center>
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