Graph ec 105 industrial organization fall 2011 matt

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Unformatted text preview: y cutoff-points, where consumer indifferent between n and n + 1 must have cost cn = E [min(p1 , . . . , pn )] − E [min(p1 , . . . , pn+1 )]. and c1 > c2 > c3 > · · · . Similarly, define qn = Fc (cn−1 ) − Fc (cn ) (fraction of consumers searching n ˜ stores). Graph. EC 105. Industrial Organization. Fall 2011 (Matt Shum HSS, Lecture 12:Institute and price dispersion California Search of Technology) September 9, 2011 15 / 25 L-SEARCH MODEL Nonsequential search model ch costs of the indifferent consumers, where a consumer with search costs September 9, 2011 16 / 25 EC 105. Industrial Organization. Fall 2011 (Matt Shum HSS, Lecture 12:Institute and price dispersion California Search of Technology) Nonsequential search model Firms in nonsequential model Firm’s profit from charging p is: ∞ Π(p ) = (p − r ) k =1 qk · k · (1 − Fp (p ))k −1 , ˜ ¯ ∀p ∈ [p , p ] For mixed strategy, firms must be indifferent btw all p : ∞ (¯ − r )˜1 = (p − r ) p q k =1 qk · k · (1 − Fp (p ))k −1 , ˜ EC 105. Industrial Organization. Fall 2011 (Matt Shum HSS, Lecture 12:Institute and price dispersion California Search of Technology) ∀p ∈ [p , p ) ¯ September 9, 2011 (7) 17 / 25 Nonsequential search model Estimating search costs Observe data Pn ≡ (p1 , . . . pn ). Sorted in increasing order. 1 ˆ ˜ Empirical price distribution Fp = Freq (p ≤ p ) = n i 1(pi ≤ p ).. ˜ Take p = p1 and p = pn ¯ Consumer cutpoints c1 , c2 , . . . can be estimated directly by simulating from observed prices Pn . This are “absissae” of search cost CDF. Corresponding “ordinates” recovered from firms’ indifference condition. Assume that consumers search at most K (< N − 1) stores. Then can solve for q1 , . . . , qK from ˜ ˜ K −1 (¯ − r )˜1 = (pi − r ) p q k =1 ˆ qk · k · (1 − Fp (pi ))k −1 , ˜ ∀pi , i = 1, . . . , n − 1. n − 1 equations with K unknowns. EC 105. Industrial Organization. Fall 2011 (Matt Shum HSS, Lecture 12:Institute and price dispersion California Search of Technology) September 9, 2011 18 / 25 we cannot identify the shape of the distribution for these people. For example, we know nothing Nonsequential search model about the shape of the search-cost distribution above the 52nd quantile for the Stokey-Lucas book, and above the 65th quantile for the Lazear book. Table 3 presents the maximum likelihood estimates for the sequential-search model. Comparing these results to those obtained from the nonsequential-search models, we see that the sequential-search model predicts higher magnitudes for search costs: as an example, the median Nonsequential model: results TABLE 2 Search-Cost Distribution Estimates for Nonsequential-Search Model Selling Product Ka Mb ˜c q1 ˜ q3 MEL Cost r Value 49.52 (12.45) ...
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