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A Model of search price Dispersion We assume that the consumers do not know which store is a discount and which is expensive unless they conduct a search at a cost of s. However, consumers do know the average store price. Thus, if a consumer does not conduct a search, he knows to expect that random shopping would result in paying an average price of p. Each consumer buys one unit and wishes to minimize the price he or she pays for the product plus the search cost. Formally, denoting by L'(a, P)the loss function of consumer type S. sE [L, H. we assume that L'= PD+as if he or she searches for the lowest price p if he or she purchases from a randomly chosen store (16.2) The parameter a measures the relative importance of the search cost in consumer preferences Clearly, since each consumer s minimizes (16.2), a type s consumer will search for. the lowest price if pD tassp, that is, if the sum of the discount price plus the search cost does not exceed the average price(which equals the expected price of purchasing from a randomly chosen store). In contrast, if PD+as >F, then clearly, buying at random is cheaper for consumer s than searching and buying from the discount store (Note: The expected number of searches to get the lowest price is 1/3 (0+1+2=1.)A Model of Search & Price Dispersion (Note:The expected number of searches to get the lowest price is 1/3*(0+1+2)=1.)
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