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Unformatted text preview: y cutoﬀpoints,
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 LSEARCH 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 searchcost distribution above the 52nd quantile for the StokeyLucas book,
and above the 65th quantile for the Lazear book.
Table 3 presents the maximum likelihood estimates for the sequentialsearch model. Comparing these results to those obtained from the nonsequentialsearch models, we see that the
sequentialsearch model predicts higher magnitudes for search costs: as an example, the median Nonsequential model: results
TABLE 2 SearchCost Distribution Estimates for NonsequentialSearch Model
Selling Product Ka Mb ˜c
q1 ˜
q3 MEL Cost r Value 49.52 (12.45)...
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