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Functional Forms for Tractable Economic Models and the Cost Structure of International Trade

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  • Michal Fabinger
  • E. Glen Weyl

Abstract

We present functional forms allowing a broader range of analytic solutions to common economic equilibrium problems. These can increase the realism of pen-and-paper solutions or speed large-scale numerical solutions as computational subroutines. We use the latter approach to build a tractable heterogeneous firm model of international trade accommodating economies of scale in export and diseconomies of scale in production, providing a natural, unified solution to several puzzles concerning trade costs. We briefly highlight applications in a range of other fields. Our method of generating analytic solutions is a discrete approximation to a logarithmically modified Laplace transform of equilibrium conditions.

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  • Michal Fabinger & E. Glen Weyl, 2016. "Functional Forms for Tractable Economic Models and the Cost Structure of International Trade," Papers 1611.02270, arXiv.org, revised Aug 2018.
    • Handle: RePEc:arx:papers:1611.02270
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    1. Gabaix, Xavier & Laibson, David & Li, Deyuan & Li, Hongyi & Resnick, Sidney & de Vries, Casper G., 2016. "The impact of competition on prices with numerous firms," Journal of Economic Theory, Elsevier, vol. 165(C), pages 1-24.
    2. Thomas Chaney, 2014. "The Network Structure of International Trade," American Economic Review, American Economic Association, vol. 104(11), pages 3600-3634, November.
    3. Gregory S. Crawford & Robin S. Lee & Michael D. Whinston & Ali Yurukoglu, 2018. "The Welfare Effects of Vertical Integration in Multichannel Television Markets," Econometrica, Econometric Society, vol. 86(3), pages 891-954, May.
    4. Hart, Oliver & Moore, John, 1990. "Property Rights and the Nature of the Firm," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1119-1158, December.
    5. Farrell, Joseph & Shapiro, Carl, 1988. "Horizontal Mergers: An Equilibrium Analysis," Department of Economics, Working Paper Series qt0tp305nx, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    6. Anthony B. Atkinson & Thomas Piketty & Emmanuel Saez, 2011. "Top Incomes in the Long Run of History," Journal of Economic Literature, American Economic Association, vol. 49(1), pages 3-71, March.
    7. Nuno Cassola & Ali Hortaçsu & Jakub Kastl, 2013. "The 2007 Subprime Market Crisis Through the Lens of European Central Bank Auctions for Short‐Term Funds," Econometrica, Econometric Society, vol. 81(4), pages 1309-1345, July.
    8. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
    9. Krugman, Paul, 1980. "Scale Economies, Product Differentiation, and the Pattern of Trade," American Economic Review, American Economic Association, vol. 70(5), pages 950-959, December.
    10. Florian Scheuer & Kent Smetters, 2014. "Could a Website Really Have Doomed the Health Exchanges? Multiple Equilibria, Initial Conditions and the Construction of the Fine," NBER Working Papers 19835, National Bureau of Economic Research, Inc.
    11. Farrell, Joseph & Shapiro, Carl, 1990. "Horizontal Mergers: An Equilibrium Analysis," American Economic Review, American Economic Association, vol. 80(1), pages 107-126, March.
    12. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    13. Liran Einav & Amy Finkelstein & Mark R. Cullen, 2010. "Estimating Welfare in Insurance Markets Using Variation in Prices," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 877-921.
    14. Adachi, Takanori & Ebina, Takeshi, 2014. "Cost pass-through and inverse demand curvature in vertical relationships with upstream and downstream competition," Economics Letters, Elsevier, vol. 124(3), pages 465-468.
    15. Hajargasht, Gholamreza & Griffiths, William E., 2013. "Pareto–lognormal distributions: Inequality, poverty, and estimation from grouped income data," Economic Modelling, Elsevier, vol. 33(C), pages 593-604.
    16. Lars A. Stole & Jeffrey Zwiebel, 1996. "Intra-firm Bargaining under Non-binding Contracts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(3), pages 375-410.
    17. Jean-Charles Rochet & Jean Tirole, 2003. "Platform Competition in Two-Sided Markets," Journal of the European Economic Association, MIT Press, vol. 1(4), pages 990-1029, June.
    18. Michael A. Salinger, 1988. "Vertical Mergers and Market Foreclosure," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(2), pages 345-356.
    19. Aoyama,Hideaki & Fujiwara,Yoshi & Ikeda,Yuichi & Iyetomi,Hiroshi & Souma,Wataru Preface by-Name:Yoshikawa,Hiroshi, 2010. "Econophysics and Companies," Cambridge Books, Cambridge University Press, number 9780521191494, January.
    20. Elhanan Helpman & Oleg Itskhoki, 2010. "Labour Market Rigidities, Trade and Unemployment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(3), pages 1100-1137.
    21. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    22. Elhanan Helpman & Marc Melitz & Yona Rubinstein, 2008. "Estimating Trade Flows: Trading Partners and Trading Volumes," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(2), pages 441-487.
    23. Joseph J. Spengler, 1950. "Vertical Integration and Antitrust Policy," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 347-347.
    24. Neale Mahoney & E. Glen Weyl, 2014. "Imperfect Competition in Selection Markets," NBER Working Papers 20411, National Bureau of Economic Research, Inc.
    25. Elhanan Helpman & Oleg Itskhoki & Stephen Redding, 2010. "Inequality and Unemployment in a Global Economy," Econometrica, Econometric Society, vol. 78(4), pages 1239-1283, July.
    26. Grossman, Sanford J & Hart, Oliver D, 1986. "The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 691-719, August.
    27. David M. Cutler & Sarah J. Reber, 1998. "Paying for Health Insurance: The Trade-Off between Competition and Adverse Selection," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 113(2), pages 433-466.
    28. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
    29. Costas Arkolakis, 2010. "Market Penetration Costs and the New Consumers Margin in International Trade," Journal of Political Economy, University of Chicago Press, vol. 118(6), pages 1151-1199.
    30. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    31. Michael Kremer & Christopher M. Snyder, 2015. "Preventives Versus Treatments," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 130(3), pages 1167-1239.
    32. George A. Akerlof, 1970. "The Market for "Lemons": Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 84(3), pages 488-500.
    33. repec:hal:spmain:info:hdl:2441/7an8r1ubqs93caeqs80puld0tp is not listed on IDEAS
    34. Eric Budish & Benjamin N. Roin & Heidi Williams, 2015. "Do Firms Underinvest in Long-Term Research? Evidence from Cancer Clinical Trials," American Economic Review, American Economic Association, vol. 105(7), pages 2044-2085, July.
    35. Peter Diamond & Emmanuel Saez, 2011. "The Case for a Progressive Tax: From Basic Research to Policy Recommendations," Journal of Economic Perspectives, American Economic Association, vol. 25(4), pages 165-190, Fall.
    36. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    37. Marc J. Melitz, 2003. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," Econometrica, Econometric Society, vol. 71(6), pages 1695-1725, November.
    38. Behrens, Kristian & Murata, Yasusada, 2007. "General equilibrium models of monopolistic competition: A new approach," Journal of Economic Theory, Elsevier, vol. 136(1), pages 776-787, September.
    39. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    40. Toda, Alexis Akira, 2012. "The double power law in income distribution: Explanations and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 364-381.
    41. Rikard Forslid & Toshihiro Okubo, 2016. "Big is Beautiful when Exporting," Review of International Economics, Wiley Blackwell, vol. 24(2), pages 330-343, May.
    42. Lloyd, P.J., 1998. "The Origins of the Von Thunen-Mill-Pareto-Wicksell-Cobb-Douglas Function," Department of Economics - Working Papers Series 660, The University of Melbourne.
    43. Iñaki Aguirre & Simon Cowan & John Vickers, 2010. "Monopoly Price Discrimination and Demand Curvature," American Economic Review, American Economic Association, vol. 100(4), pages 1601-1615, September.
    44. Quint, Daniel, 2014. "Imperfect competition with complements and substitutes," Journal of Economic Theory, Elsevier, vol. 152(C), pages 266-290.
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    Cited by:

    1. Takanori Adachi & Muhammad Michal Fabinger, 2017. "Multi-Dimensional Pass-Through, Incidence, and the Welfare Burden of Taxation in Oligopoly," CIRJE F-Series CIRJE-F-1040, CIRJE, Faculty of Economics, University of Tokyo.
    2. Takanori Adachi & Michal Fabinger, 2017. "Multi-Dimensional Pass-Through, Incidence, and the Welfare Burden of Taxation in Oligopoly," CIRJE F-Series CIRJE-F-1040, CIRJE, Faculty of Economics, University of Tokyo.
    3. William Griffiths & Duangkamon Chotikapanich & Gholamreza Hajargasht, 2022. "A note on inequality measures for mixtures of double Pareto–lognormal distributions," Australian Economic Papers, Wiley Blackwell, vol. 61(2), pages 280-290, June.
    4. Takanori Adachi & Michal Fabinger, 2019. "Output and Welfare Implications of Oligopolistic Third-Degree Price Discrimination," Working Papers e139, Tokyo Center for Economic Research.
    5. Takanori Adachi & Michal Fabinger, 2017. "Multi-Dimensional Pass-Through and Welfare Measures under Imperfect Competition," Papers 1702.04967, arXiv.org, revised Dec 2018.
    6. Simon Cowan, 2023. "Welfare-increasing monopolization," Economics Series Working Papers 1006, University of Oxford, Department of Economics.
    7. William Griffiths & Duangkamon Chotikapanich & Gholamreza Hajargasht, 2021. "A Note on Inequality Measures for Mixtures of Double Pareto-Lognormal Distributions," Monash Econometrics and Business Statistics Working Papers 14/21, Monash University, Department of Econometrics and Business Statistics.

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