# Free entry ensures this let denote proportion of lo

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Unformatted text preview: at given a set of high-price ﬁrms (charing u ) and low-price ﬁrms (charging p c ), no individual ﬁrm wants to deviate. Free entry ensures this. Let β denote proportion of lo-price ﬁrms. Each high-price ﬁrm charges u and sells an amount qu = (1 − α)L (1 − α)L(1 − β ) = n(1 − β ) n (2) Each low-price ﬁrm charges p c and sells qc = αL + (1 − α)Lβ nβ EC 105. Industrial Organization. Fall 2011 (Matt Shum HSS, Lecture 12:Institute and price dispersion California Search of Technology) (3) September 9, 2011 11 / 25 Outline In equilibrium, enough ﬁrms of each type enter such that each ﬁrm makes zero proﬁts. Deﬁne quantities q a , q A such that (graph): AC (q a ) = u ; AC (q c ) = p c . (Quantities at which both hi- and lo-price ﬁrms make zero proﬁts.) With free entry, n and β must satisfy qa = qu = (1 − α)L AC (q c ); n qA = qc αL + (1 − α)Lβ nβ (4) Solving the two equations for n and β yields n= (1 − α)L ; qa β= αq a (1 − α)(q A − q a ) (5) N.B: arbitrary which ﬁrms become high or low price. Doesn’t specify process whereby price dispersion develops. As α → 0, then β → 0 (Diamond result) EC 105. Industrial Organization. Fall 2011 (Matt Shum HSS, Lecture 12:Institute and price dispersion California Search of Technology) September 9, 2011 12 / 25 Nonsequential vs. sequential search Two search models: Consider two search models: 1 Nonsequential search model: consumer commits to searching n stores before buying (from lowest-cost store). “Batch” search strategy. 2 Sequential search model: consumer decides after each search whether to buy at current store, or continue searching. EC 105. Industrial Organization. Fall 2011 (Matt Shum HSS, Lecture 12:Institute and price dispersion California Search of Technology) September 9, 2011 13 / 25 Nonsequential search model Main assumptions: Inﬁnite number (“continuum”) of ﬁrms and consumers Observed price distribution Fp is equilibrium mixed strategy on the part of ﬁrms, with bounds p , p . ¯ r : constant per-unit cost (wholesale cost), identical across ﬁrms Firms sell homogeneous products Each consumer buys one unit of the good Consumer i incurs cost ci to search one store; drawn independently from search cost distribution Fc First store is “free” qk : probability that consumer searches k stores before buying EC 105. Industrial Organization. Fall 2011 (Matt Shum HSS, Lecture 12:Institute and price dispersion California Search of Technology) September 9, 2011 14 / 25 Nonsequential search model Consumers in nonsequential model Consumer with search cost c who searches n stores incurs total cost c ∗ (n − 1) + E [min(p1 , . . . , pn )] p ¯ =c ∗ (n − 1) + p p · n(1 − Fp (p ))n−1 fp (p )dp . (6) This is decreasing in c . Search strategies characterized b...
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## This document was uploaded on 02/24/2014 for the course ECONOMICS macro econ at University of Florida.

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