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Search and Bidding Costs

  • Chun-Hui Miao EMAIL logo

Abstract

This paper studies consumer search behavior in markets where sellers must incur fixed costs to win a contract. We show that consumers face a commitment problem if their search intensities are not observed by sellers. Welfare is maximized when consumers can precommit to a limited number of searches, but in the absence of the ability to commit, consumers search more than the optimum. A decline in search costs can exacerbate the commitment problem and leave consumers potentially worse off.

JEL Classification: D40; L00

Acknowledgements

This paper was previously circulated under the title “Excessive Search”. I am grateful to seminar participants at the 2018 Midwest Theory Conference, USC – Columbia, and especially an anonymous referee for helpful comments and suggestions. All remaining errors are mine.

A Proof

Proof of Lemma 2.

Using the results from Lemma 1, we obtain that

(3)Epmin|n,nB=1αn+k=1nnkαk1αnkp_pˉpd11FnBpk=1αn+nα01k=1nn1k11αnkα1Fk1FnB1FdF=1αn+nb11αnnB+1nnB+1,

where α=1b1/nB1 and FnBp=1b/p1/nB11b1/nB1. Let x=nnB11,Epmin|n,nB can be rewritten as b1+1bx/x. Hence, xEpmin|n,nB=b1+x˜lnx˜x˜x2, where x˜=bx. Since 1+x˜lnx˜x˜>0 for all x˜0,1,xEpmin|n,nB as well as nEpmin|n,nB must be negative. Since x decreases with nB, nBEpmin|n,nB must be positive.   ■

Proof of Lemma 3.

By (3), gn,nB=nEpmin|n,nB=b1+x˜lnx˜x˜nnB+12, where x˜=bx and x=nnB11. There are two roots of n for hn=gn,n=s if and only if s<sˉ, where sˉ=0.298blnb. Denote them by n1 and n2, where n1<n2. We prove by showing that ihn1>0 and hn2<0;iig1n,n<0 for both n1 and n2.

i By definition, hn=b1bzz+bzlnb, where z=1n1. Let fz=b1bzz+bzlnb. It is easy to verify that limz0fz=limzfz=0 since b < 1. In addition, fz=bz2z˜+z˜ln2z˜z˜lnz˜1, where z˜=bz0,1. Note that z˜ is decreasing in z and that z˜+z˜ln2z˜z˜lnz˜10 when z˜0.166. This means that fz is unimodal, increasing when z < logb 0.166 and decreasing when z > logb 0.166. Thus, hn as well as fz is maximized when z = logb 0.166. The maximum is – 0.298b ln b. Hence, there are two roots of z for fz=s if and only if s < – 0.298b ln b. Denote them by z1 and z2, where z1>z2,fz1<0 and fz2>0. Equivalently, there are two roots for hn=s, where n1=1+1/z1 and n2=1+1/z2, with hn1>0 and hn2<0.

i i g 1 n , n = 2 n 2 E p min | n , n B | n = n B = z ˜ ln 2 z ˜ 2 z ˜ ln z ˜ + 2 z ˜ 2 n 1 b . Since z˜ln2z˜2z˜lnz˜+2z˜2<0 for all z˜0,1, we must have g1n,n<0 for all n > 1.   ■

Proof of Proposition 1.

i Since hn2=s and hn2<0 by Lemma 3i, n2 must decrease when s increases.

i i By Lemma 2, Epmin=bnn1b1/n1. Let z=1n1,Epmin can be written as b1bzz+1. Using L’Hopital’s rule, we can verify that 1bzz decreases with z. Therefore, Epmin increases with n. By i, n2 decreases with s. We thus conclude that Epmin decreases with s.

i i i Let k = n – 1, the total expected costs can be written as T=kb1/k+k+1b+k+1s, where k1b1/k+b1/klnb1/k=s/b. Thus, Ts=k+1+dkdss+bkkkb1/k+b1/klnb=k+11+skdkds. This means that Ts<0 if and only if ddsks<0. Since ddsks=dkdsddkks and ddkks=bk22k˜+2k˜lnk˜k˜ln2k˜>0, where k˜=b1/k, whether Ts<0 only depends on the sign of dkds. In the stable equilibrium, dkds<0 by i, hence Ts<0.   ■

References

Anderson, S. P., and R. Renault. 2000. “Consumer Information and Firm Pricing: Negative Externalities from Improved Information.” International Economic Review 41 (3): 721–42.10.1111/1468-2354.00081Search in Google Scholar

Armstrong, M., and J. Zhou. 2011. “Paying for Prominence.” The Economic Journal 121 (556): F368–F395.10.1111/j.1468-0297.2011.02469.xSearch in Google Scholar

Bagwell, K. 1995. “Commitment and Observability in Games.” Games and Economic Behavior 8 (2): 271–80.10.1016/S0899-8256(05)80001-6Search in Google Scholar

Bakos, J. Y. 1997. “Reducing Buyer Search Costs: Implications for Electronic Marketplaces.” Management Science 43 (12): 1676–92.10.1287/mnsc.43.12.1676Search in Google Scholar

Brown, J. R., and A. Goolsbee. 2002. “Does the Internet Make Markets More Competitive? Evidence from the Life Insurance Industry.” Journal of Political Economy 110 (3): 481–507.10.1086/339714Search in Google Scholar

Burdett, K., and K. L. Judd. 1983. “Equilibrium Price Dispersion.” Econometrica 51 (4): 955–69.10.2307/1912045Search in Google Scholar

Chen, Y., and T. Zhang. 2011. “Equilibrium Price Dispersion with Heterogeneous Searchers.” International Journal of Industrial Organization 29 (6): 645–54.10.1016/j.ijindorg.2011.03.007Search in Google Scholar

Choi, M., A. Y. Dai, and K. Kim. 2018. “Consumer Search and Price Competition.” Econometrica 86 (4): 1257–81.10.3982/ECTA14837Search in Google Scholar

Coase, R. H. 1972. “Durability and Monopoly.” Journal of Law and Economics 15 (1): 143–49.10.1086/466731Search in Google Scholar

Diamond, P. A. 1971. “A Model of Price Adjustment.” Journal of Economic Theory 3 (2): 156–68.10.1016/0022-0531(71)90013-5Search in Google Scholar

Fershtman, C., and A. Fishman. 1992. “Price Cycles and Booms: Dynamic Search Equilibrium.” The American Economic Review 82 (5): 1221–33.Search in Google Scholar

Garcia, D., J. Honda, and M. Janssen. 2017. “The Double Diamond Paradox.” American Economic Journal: Microeconomics 9 (3): 63–99.10.1257/mic.20150299Search in Google Scholar

Gastwirth, J. L. 1976. “On Probabilistic Models of Consumer Search for Information.” The Quarterly Journal of Economics 90 (1): 38–50.10.2307/1886085Search in Google Scholar

Gautier, P. A., and J. L. Moraga-González. 2018. “Search Intensity, Wage Dispersion and the Minimum Wage.” Labour Economics 50: 80–86.10.1016/j.labeco.2017.04.003Search in Google Scholar

Haan, M., J.-L. Moraga-González, and V. Petrikaite. 2017. “A Model of Directed Consumer Search.” Discussion paper, CEPR Discussion Papers.10.1016/j.ijindorg.2018.09.001Search in Google Scholar

Honka, E. 2014. “Quantifying Search and Switching Costs in the US Auto Insurance Industry.” The RAND Journal of Economics 45 (4): 847–84.10.1111/1756-2171.12073Search in Google Scholar

Honka, E., and P. Chintagunta. 2017. “Simultaneous or sequential? Search strategies in the US Auto Insurance Industry.” Marketing Science 36 (1): 21–42.10.1287/mksc.2016.0995Search in Google Scholar

Hortaçsu, A., and C. Syverson. 2004. “Product Differentiation, Search Costs, and Competition in the Mutual Fund Industry: A Case Study of S&P 500 Index Funds.” The Quarterly Journal of Economics 119 (2): 403–56.10.3386/w9728Search in Google Scholar

Janssen, M., and S. Shelegia. 2015. “Consumer Search and Double Marginalization.” American Economic Review 105 (6): 1683–710.10.1257/aer.20121317Search in Google Scholar

Janssen, M. C. W., and J. L. Moraga-González. 2004. “Strategic Pricing, Consumer Search and the Number of Firms.” Review of Economic Studies 71 (4): 1089–118.10.1111/0034-6527.00315Search in Google Scholar

Lang, K., and R. W. Rosenthal. 1991. “The Contractors’ Game.” The RAND Journal of Economics 22 (3): 329–38.10.2307/2601050Search in Google Scholar

Lester, B. 2011. “Information and Prices with Capacity Constraints.” American Economic Review 101 (4): 1591–600.10.1257/aer.101.4.1591Search in Google Scholar

los Santos, B. D., A. Hortaçsu, and M. R. Wildenbeest. 2012. “Testing Models of Consumer Search Using Data on Web Browsing and Purchasing Behavior.” American Economic Review 102 (6): 2955–80.10.1257/aer.102.6.2955Search in Google Scholar

Manning, R., and P. B. Morgan. 1982. “Search and Consumer Theory.” The Review of Economic Studies 49 (2): 203–16.10.2307/2297270Search in Google Scholar

McCall, J. J. 1970. “Economics of Information and Job Search.” The Quarterly Journal of Economics 84 (1): 113–26.10.2307/1879403Search in Google Scholar

Moraga-González, J. L., Z. Sándor, and M. R. Wildenbeest. 2017. “Prices and Heterogeneous Search Costs.” The RAND Journal of Economics 48 (1): 125–46.10.1111/1756-2171.12170Search in Google Scholar

Morgan, P., and R. Manning. 1985. “Optimal Search.” Econometrica 53 (4): 923–44.10.2307/1912661Search in Google Scholar

Rosenthal, R. W. 1980. “A model in which an Increase in the Number of Sellers Leads to a Higher Price.” Econometrica 48 (6): 1575–79.10.2307/1912828Search in Google Scholar

Rothschild, M. 1974. “Searching for the Lowest Price When the Distribution of Prices Is Unknown.” Journal of Political Economy 82 (4): 689–711.10.1016/B978-0-12-214850-7.50033-4Search in Google Scholar

Shen, J. 2015. “Ex-Ante Preference in a Consumer Search Market.” Working Paper.10.2139/ssrn.2826011Search in Google Scholar

Stahl, D. O. 1989. “Oligopolistic Pricing with Sequential Consumer Search.” The American Economic Review 79 (4): 700–12.Search in Google Scholar

Stigler, G. J. 1961. “The Economics of Information.” Journal of Political Economy 69 (3): 213–25.10.1007/978-3-642-51565-1_86Search in Google Scholar

Waldman, M. 2003. “Durable Goods Theory for Real World Markets.” Journal of Economic Perspectives 17 (1): 131–54.10.1257/089533003321164985Search in Google Scholar

Wolinsky, A. 2005. “Procurement via Sequential Search.” Journal of Political Economy 113 (4): 785–810.10.1086/430887Search in Google Scholar

Wolthoff, R. 2017. “Applications and Interviews: Firms’ Recruiting Decisions in a Frictional Labour Market.” The Review of Economic Studies 85 (2): 1314–51.10.1093/restud/rdx045Search in Google Scholar

Woodward, S. 2008. “A Study of Closing Costs for FHA Mortgages.” Discussion paper, The Urban Institute.Search in Google Scholar

Yang, H. 2013. “Targeted Search and the Long Tail Effect.” The RAND Journal of Economics 44 (4): 733–56.10.1111/1756-2171.12036Search in Google Scholar

Zhou, J. 2014. “Multiproduct Search and the Joint Search Effect.” American Economic Review 104 (9): 2918–39.10.1257/aer.104.9.2918Search in Google Scholar

Published Online: 2020-03-25

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