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'''The Stigler (1961) Model''' The first special case examined in the general framework is that of Stigler (1961):#Each consumer purchases <math>K \ge 1\,</math> units, so that <math>q(p) = -v'(p) = K\,</math> #Fixed sample search is used#The distribution of firms' prices is given exogenously by the non-degenerate CDF <math>F(p)\,</math> on <math>[\underline{p}, \overline{p}]\,</math>.  <center>''Fixed sample search'' In a fixed sample search the consumer commits to conducting <math>n\,</math> searches and then buys from the firm offering the lowest price.</center> The consumer seeks to minimize the expected cost (purchase + search) given by:<center><math>\mathbb{E}(C) = K \mathbb{E}\(p_min^(n)\) + cn\,</math>where <math>\mathbb{E}\(p_min^(n)\) = \mathbb{E}\(min\{p_1,p_2,\ldots,p_n\}\) \,</math>The distribution of the lowest <math>n\,</math> draws is: <math>F_min^(n)(p) = 1 - (1-F(p))^n\,</math> <math>\,</math>