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The consumer seeks to minimize the expected cost (purchase + search) given by:
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<math>E(C) = K E(p_{min}^{(n)}) + cn\,</math>
<center><math>E(C) = K E(p_{min}^{(n)}) + cn\,</math> </center> <center>where <math>E(p_{min}^{(n)}) = E(min\{p_1,p_2,\ldots,p_n\}) \,</math> </center> The distribution of the lowest <math>n\,</math> draws is: <center><math>F_{min}^{(n)}(p) = 1 - (1-F(p))^n\,</math> </center>
The distribution of the lowest <math>n\,</math> draws is: <math>F_{min}^{(n)}(p) = 1 - (1-F(p))^n\,</math>
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\,</math>
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