Endogenous Markup, Per Capita Income and Population Size in the Gravity Equation

Wisarut Suwanprasert

doi:10.1515/bejte-2017-0166

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Endogenous Markup, Per Capita Income and Population Size in the Gravity Equation

Wisarut Suwanprasert

Published/Copyright: November 3, 2018

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From the journal The B.E. Journal of Theoretical Economics Volume 19 Issue 2

Abstract

While recent studies use asymmetric trade costs and non-homothetic preference to explain why trade grows strongly with income per capita, this paper proposes a new explanation using a random search framework based on Burdett and Judd (1983). I show that the values of international trade flows as a share of income are generally larger in high-income countries because the markups in high-income countries are generally larger than those in low-income countries. In addition, firms’ price setting strategy creates an endogenous wedge between bilateral trade flow and gains from trade.

Keywords: gravity equation; international trade; per capita income; search frictions

JEL Classification: F1

Acknowledgements

I am deeply grateful to Robert Staiger, Kamran Bilir, and Charles Engel for their invaluable guidance. I would like to thank Editor Burkhard C. Schipper and the anonymous referees for very useful and insightful comments. I also thank Joachim Zietz and seminar participants at University of Wisconsin-Madison, Thailand Development Research Institute (TDRI), Chulalongkorn University, Thammasat University and Midwest International Trade Conference for helpful discussions and suggestions. All remaining errors are my own.

Appendix

Lemma 1.

if α1>0 and α2>0, the probability density function of the price distribution fp has no mass point with the connected support p_,y.

Proof.

(1) fp has no mass point.

Suppose that fp has a mass point at p∗. Then the firm posting a price p∗ can profitably deviate by reducing its price to p∗−ϵ for an arbitrarily small ε > 0. It’s demand increases by α2σL/Nλ2fp∗ while its profit per unit drops by ε. This deviation is profitable when ε is sufficiently small. Therefore, fp has no mass point. This lemma confirms that firms must use only a mixed strategy in prices; a pure Nash strategy does not exist.

(2) fp is connected in the compact support p_,y

To start with, I show that the support is bounded and then that the support is connected.

Clearly the maximum price in the support of fp, pˉ, must be less than or equal to y so that consumers can afford to pay. Suppose pˉ<y. This firm always loses consumers who see two prices; its revenue is solely from customers who visit only this firm. Its profit from this market is simplified to Πpˉ=α1σL/Nλpˉ−c which is strictly increasing in pˉ. Hence, the highest-price firm always raises its price until pˉ=y. The minimum price, p_, must be non-negative, and hence is bounded from below by zero. In conclusion, the support is a closed subset of 0,y.

Suppose that fp is not connected, i.e., its support has an empty gap p1,p2, for p_<p1<p2<pˉ. Then the firm posting the price p1 has a profitable opportunity to increase its price to p1+ϵ. This deviation does not affect the firm’s demand because the probability that this firm can sell does not change. However, the deviation raises the profit per unit. □

Proposition 2.

An increase in the population size of the destination country increases the value of exports to that country through more transaction per export firms and more export firms. The elasticity of export value with respect to the population size of the destination country is positive and less than one. An increase in income per capita of the destination country increases the value of exports to that country through larger sale value per transaction and more export firms.

Proof.

The impacts of population size and per capita income on exports are as follows. The elasticity of exportation with respect to the population size of the destination country is

dlogTFABdlogLB=dlogα1+α2MNA,LBdlogNAdlogNAdlogLB+dlogα1+α2MNA,LBdlogLB+dlogTABdlogLB=1−λLBλyB−τcLAλyA−c+LBλyB−τc⏟More export firms+λ⏟More transactions per firm+0⏟Sale value per transaction

The elasticity of exportation with respect to the per capita income of the destination country is

dlogTFABdlogyB=dlogα1+α2MNA,LBdlogNAdlogNAdlogyB+dlogTABdlogLB=1−λλLBλyBLAλyA−c+LBλyB−τc⏟More export firms+0⏟More transactions per firm+α1yBα1yB+α2τc⏟Sale value per transaction

Proposition 3.

Larger population size increases aggregate welfare gains from trade but unambiguously reduces the gains from trade per consumer. The net effect of an increase in per capita on gains from trade per consumer is ambiguous.

Proof.

The proof proceeds in two steps; I start the analysis with population size and then look at per capita income. Following eq. (14), the elasticity of the gains from trade per consumer with respect to population size is

dlogWB/LBdlogLB=dlogα1+α2MNA,LB/LBdlogLB+dlogu−TABdlogLB=1−λLBλyB−τcLAλyA−c+LBλyB−τc⏟More export firms+λ−1⏟Negative congestion externality+0 0

The elasticity of the gains from trade per consumer with respect to per capita income is

dlogWB/LBdlogyB=dlogα1+α2MNA,LB/LBdlogyB+dlogu−TABdlogyB=1−λλLBλyBLAλyA−c+LBλyB−τc⏟More export firms−α1yBα1yB+α2τcTABu−TAB⏟Larger markup

Proposition 4.

A decrease in iceberg transportation costs unambiguouslyincreases the number of export firms but its effect on the expected value of trade flow per firm is ambiguous.The elasticity of exportation with respect to transportation costs is ambiguous.

Proof.

Using the expression of trade flow in eq. (10), the elasticity of exportation with respect to an iceberg trade cost is

dlogTFABdlogτ=dlogα1+α2MNA,LBdlogNAdlogNAdlogτ+dlogTABdlogτ=−1−λλLBλτcLAλyA−c+LBλyB−τc⏟More export firms+α2τcα1yB+α2τc⏟Lower value of trade flow

Proposition 5.

The elasticity of welfare with respect to a reduction of transportation costs is larger than the elasticity of exportation with respect to a reduction of the transportation costs. A decrease in iceberg transportation costs increases welfare in the importing country.

Proof.

Equation (15) compares two elasticities, and eq. (16) shows the total effect on welfare. □

Proposition 6.

The total value of imports is increasing in α1∗ and α2∗. A change in α1∗ ambiguously changes the welfare of the importing country, but a change in α2∗ always improves the welfare of the importing country.

Proof.

Using eqs. 10 and 13,

dlogTFABdlogα1∗=α1∗α1∗+α2∗+1−λλα1∗LBλyB−τcα1LAλyA−c+α1∗LBλyB−τc⏟The Extensive Margin+α1∗yBα1∗yB+α2∗τc−α1∗α1∗+α2∗⏟The Intensive MargindlogWBdlogα1∗=α1∗α1∗+α2∗+1−λλα1∗LBλyB−τcα1LAλyA−c+α1∗LBλyB−τc⏟The Extensive Margin−α1∗α2∗yB−τcu−TABα1∗+α2∗α1∗yB+α2∗τc⏟The Intensive Margin

dlogTFABdlogα2∗=α2∗α1∗+α2∗⏟The Extensive Margin−α1∗α2∗yB−τcα1∗+α2∗α1∗yB+α2∗τc⏟The Intensive Margin=α2∗τcα1∗yB+α2∗τcdlogWBdlogα2∗=α2∗α1∗+α2∗⏟The Extensive Margin+α1∗α2∗yB−τcu−TABα1∗+α2∗α1∗yB+α2∗τc⏟The Intensive Margin

References

Akerman, Anders and Rikard Forslid. 2009. “Firm Heterogeneity and Country Size Dependent Market Entry Costs.” CCES Discussion Paper Series 11: Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.Search in Google Scholar

Alessandria, George. 2004. “International Deviations from the Law of One Price: The Role of Search Frictions and Market Share.” International Economic Review 45 (4): 1263–91.10.1111/j.0020-6598.2004.00305.xSearch in Google Scholar

Alessandria, George. 2009 . “Consumer Search, Price Dispersion and International Relative Price Fluctuations.” International Economic Review 50: 803– 829.10.1111/j.1468-2354.2009.00549.xSearch in Google Scholar

Alessandria, George, and Joseph P. Kaboski. 2011. “Pricing-to-Market and the Failure of Absolute PPP.” American Economic Journal: Macroeconomics 3 (1): 91–127.10.21799/frbp.wp.2007.29Search in Google Scholar

Allen, T. (2014). “Information Frictions in Trade.” Econometrica, 82 (6): 2041–2083.10.3982/ECTA10984Search in Google Scholar

Arkolakis, Costa, Arnaud Costinot, and Andres Rodriguez-Clare. 2012. “New Trade Models, Same Old Gains?” American Economic Review 102 (1): 94–130.10.1257/aer.102.1.94Search in Google Scholar

Bernard, Andrew B., Jonathan Eaton, J. Bradford Jensen, and Samuel Kortum. 2003. “Plants and Productivity in International Trade.” American Economic Review 93 (4): 1268–90.10.1257/000282803769206296Search in Google Scholar

Arkolakis, Costa, Arnaud Costinot, Dave Donaldson, and Andrés Rodr&’ıguez-Clare. 2018. “The Elusive Pro-Competitive Effects of Trade.” The Review of Economic Studies forthcoming.10.3386/w21370Search in Google Scholar

Bertoletti, Paolo, Federico Etro, and Ina Simonovska. 2018. “International Trade with Indirect Additivity.” American Economic Journal: Microeconomics 2017 10 (2): 1–57.10.3386/w21984Search in Google Scholar

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

Stevens, Luminita, and Chahrour, Ryan, 2015. “Equilibrium Price Dispersion and the Border Effect.” Staff Report 522, Federal Reserve Bank of Minneapolis.Search in Google Scholar

De Loecker, Jan, Pinelopi K. Goldberg, Amit K. Khandelwal, Nina Pavcnik, et al. 2016. “Prices, Markups, and Trade Reform.” Econometrica 84: 445–510.10.3982/ECTA11042Search in Google Scholar

Dingel, Jonathan I. 2014. “The Determinants of Quality Specialization” Unpublished Manuscript.10.2139/ssrn.2621678Search in Google Scholar

Lukasz A Drozd, and Jaromir B Nosal. 2012 (2). “Understanding International Prices: Customers as Capital.” American Economic Review 102 (1): 364–395.10.1257/aer.102.1.364Search in Google Scholar

Eaton, Jonathan, and Samuel Kortum. 2002. “Technology, Geography, and Trade.” Econometrica 70 (5): 1741–79.10.1111/1468-0262.00352Search in Google Scholar

Edmond, Chris, Virgiliu Midrigan, and Daniel Yi Xu. 2015. “Competition, Markups, and the Gains from International Trade.” American Economic Review 105 (10): 3183–221.10.1257/aer.20120549Search in Google Scholar

Fajgelbaum, Pablo, Gene M. Grossman, and Elhanan Helpman. 2011. “Income Distribution, Product Quality, and International Trade.” Journal of Political Economics 119 (4): 721–65.10.1086/662628Search in Google Scholar

Fieler, Ana C. 2011. “Nonhomotheticity and Bilateral Trade: Evidence and a Quantitative Explanation.” Econometrica 79 (4): 1069–101.10.3982/ECTA8346Search in Google Scholar

Feenstra, Robert, and David E. Weinstein. 2017. “Globalization, Markups, and US Welfare.” Journal of Political Economy 125 (4): 1040–74.10.1086/692695Search in Google Scholar

Head, Allen, and Alok Kumar. 2005. “Price Dispersion, Inflation, and Welfare.” International Economic Review 46: 533–72.10.1111/j.1468-2354.2005.00333.xSearch in Google Scholar

Head, Allen, Lucy Qian Liu, Guido Menzio, and Randall Wright. 2012. “Sticky Prices: A New Monetarist Approach.” Journal of the European Economic Association 10 (5): 939–73.10.1111/j.1542-4774.2012.01081.xSearch in Google Scholar

Hummels, David, and Volodymyr Lugovskyy. 2009. “International Pricing in a Generalized Model of Ideal Variety.” Journal of Money, Credit and Banking 41: 3–33.10.1111/j.1538-4616.2008.00197.xSearch in Google Scholar

Hunter, Linda and James R. Markusen. 1988. Per-Capita Income as a Determinant of Trade Empirical Methods for International Economics, 89–109. Cambridge: MIT Press.Search in Google Scholar

Kaplan, Greg, and Guido Menzio. 2016 (6). “Shopping Externalities and Self-Fulfilling Unemployment Fluctuations.” Journal of Political Economy 124 (3): 771–825. DOI: 10.1086/685909.Search in Google Scholar

Krugman, Paul 1980. “Scale Economies, Product Differentiation, and the Pattern of Trade.” The American Economic Review 70 (5): 950–959.10.7551/mitpress/5933.003.0005Search in Google Scholar

Manova, Kalina, and Zhiwei Zhang. 2012. “Export Prices across Firms and Destinations.” Quarterly Journal of Economics 127 (1): 379–436.10.1093/qje/qjr051Search in Google Scholar

Markusen, James R. 2013. “Putting Per-Capita Income Back into Trade Theory.” Journal of International Economics 90 (2): 255–65.10.1016/j.jinteco.2013.04.003Search in Google Scholar

Markusen, James R., and Randall M. Wigle. 1990. “Explaining the Volume of North-South Trade.” Economic Journal 100 (403): 1206–15.10.2307/2233968Search in Google Scholar

Melitz, Marc J. 2003. “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity.” Econometrica 71 (6): 1695–725.10.1111/1468-0262.00467Search in Google Scholar

Melitz, Marc J., and Giancarlo I. P. Ottaviano. 2008. “Market Size, Trade, and Productivity.” Review of Economic Studies 75 (1): 295–316.10.1111/j.1467-937X.2007.00463.xSearch in Google Scholar

Kaplan, Greg, and Guido Menzio. 2016. “Shopping Externalities and Self-Fulfilling Unemployment Fluctuations.” Journal of Political Economy 124 (3): 771–825.10.1086/685909Search in Google Scholar

Simonovska, Ina. 2015. “Income Differences and Prices of Tradables: Insights from an Online Retailer.” Review of Economic Studies 82 (4): 1612–56.10.1093/restud/rdv015Search in Google Scholar

Waugh, Michael E. 2010. “International Trade and Income Differences.” American Economic Review 100 (5): 2093–124.10.1257/aer.100.5.2093Search in Google Scholar

Published Online: 2018-11-03

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https://doi.org/10.1515/bejte-2017-0166

Keywords for this article

gravity equation; international trade; per capita income; search frictions