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A Theory of Production, Matching, and Distribution

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  • Sephorah Mangin

Abstract

This paper presents a unified approach to production, matching, and distribution in an environment with labor market frictions. I use competing auctions as both a wage determination mechanism and a microfoundation for an aggregate production and matching technology. For any well-behaved distribution of firm productivities, I show that the aggregate production function exhibits standard neoclassical properties and an elasticity of substitution between capital and labor that is always less than or equal to one. If the distribution is Pareto or power law, this function is particularly tractable. In general, factor income shares vary with the degree of competition between firms to hire workers, the value of non-market activity, and characteristics of the underlying firm productivity distribution. Unlike Diamond-Mortensen-Pissarides style search models with Nash bargaining, production and distribution are endogenously tightly connected: the economy satisfies a generalized version of the Hosios condition.

Suggested Citation

  • Sephorah Mangin, 2015. "A Theory of Production, Matching, and Distribution," Monash Economics Working Papers 27-15, Monash University, Department of Economics.
  • Handle: RePEc:mos:moswps:2015-27
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    1. Christopher A. Pissarides, 2000. "Equilibrium Unemployment Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161877.
    2. McAfee, R. Preston & McMillan, John, 1987. "Auctions with a stochastic number of bidders," Journal of Economic Theory, Elsevier, vol. 43(1), pages 1-19, October.
    3. Albrecht, James & Gautier, Pieter & Vroman, Susan, 2012. "A note on Peters and Severinov, “Competition among sellers who offer auctions instead of prices”," Journal of Economic Theory, Elsevier, vol. 147(1), pages 389-392.
    4. Andrew B. Bernard & Jonathan Eaton & J. Bradford Jensen & Samuel Kortum, 2003. "Plants and Productivity in International Trade," American Economic Review, American Economic Association, vol. 93(4), pages 1268-1290, September.
    5. R. E. Hall, 1977. "An Aspect of the Economic Role of Unemployment," International Economic Association Series, in: G. C. Harcourt (ed.), The Microeconomic Foundations of Macroeconomics, chapter 11, pages 354-372, Palgrave Macmillan.
    6. Menzio, Guido & Shi, Shouyong, 2010. "Block recursive equilibria for stochastic models of search on the job," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1453-1494, July.
    7. Guido Menzio & Shouyong Shi, 2011. "Efficient Search on the Job and the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 119(3), pages 468-510.
    8. Peters, Michael & Severinov, Sergei, 1997. "Competition among Sellers Who Offer Auctions Instead of Prices," Journal of Economic Theory, Elsevier, vol. 75(1), pages 141-179, July.
    9. 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.
    10. Fabien Postel-Vinay & Jean-Marc Robin, 2002. "Equilibrium Wage Dispersion with Worker and Employer Heterogeneity," Econometrica, Econometric Society, vol. 70(6), pages 2295-2350, November.
    11. James Albrecht & Pieter Gautier & Susan Vroman, 2016. "Directed Search in the Housing Market," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 19, pages 218-231, January.
    12. Acemoglu, Daron & Shimer, Robert, 1999. "Holdups and Efficiency with Search Frictions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(4), pages 827-849, November.
    13. Mortensen, Dale & Pissarides, Christopher, 2011. "Job Creation and Job Destruction in the Theory of Unemployment," Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 1, pages 1-19.
    14. Xavier Gabaix, 2016. "Power Laws in Economics: An Introduction," Journal of Economic Perspectives, American Economic Association, vol. 30(1), pages 185-206, Winter.
    15. Xavier Gabaix & Augustin Landier, 2008. "Why has CEO Pay Increased So Much?," The Quarterly Journal of Economics, Oxford University Press, vol. 123(1), pages 49-100.
    16. Lester, Benjamin & Visschers, Ludo & Wolthoff, Ronald, 2015. "Meeting technologies and optimal trading mechanisms in competitive search markets," Journal of Economic Theory, Elsevier, vol. 155(C), pages 1-15.
    17. Galenianos, Manolis & Kircher, Philipp, 2009. "Directed search with multiple job applications," Journal of Economic Theory, Elsevier, vol. 144(2), pages 445-471, March.
    18. Antràs Pol, 2004. "Is the U.S. Aggregate Production Function Cobb-Douglas? New Estimates of the Elasticity of Substitution," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-36, April.
    19. Shouyong Shi, 2009. "Directed Search for Equilibrium Wage-Tenure Contracts," Econometrica, Econometric Society, vol. 77(2), pages 561-584, March.
    20. James Albrecht & Pieter A. Gautier & Susan Vroman, 2006. "Equilibrium Directed Search with Multiple Applications," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 869-891.
    21. Eeckhout, Jan & Kircher, Philipp, 2010. "Sorting versus screening: Search frictions and competing mechanisms," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1354-1385, July.
    22. Mangin, Sephorah & Sedláček, Petr, 2018. "Unemployment and the labor share," Journal of Monetary Economics, Elsevier, vol. 94(C), pages 41-59.
    23. Cai, Xiaoming & Gautier, Pieter A. & Wolthoff, Ronald P., 2017. "Search frictions, competing mechanisms and optimal market segmentation," Journal of Economic Theory, Elsevier, vol. 169(C), pages 453-473.
    24. Kohlbrecher, Britta & Merkl, Christian & Nordmeier, Daniela, 2016. "Revisiting the matching function," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 350-374.
    25. Ricardo Lagos, 2006. "A Model of TFP," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 983-1007.
    26. Brent Neiman, 2014. "The Global Decline of the Labor Share," The Quarterly Journal of Economics, Oxford University Press, vol. 129(1), pages 61-103.
    27. Shi, Shouyong, 2006. "Wage differentials, discrimination and efficiency," European Economic Review, Elsevier, vol. 50(4), pages 849-875, May.
    28. Arnaud Dupuy, 2012. "A Microfoundation for Production Functions: Assignment of Heterogeneous Workers to Heterogeneous Jobs," Economica, London School of Economics and Political Science, vol. 79(315), pages 534-556, July.
    29. Kenneth Burdett & Shouyong Shi & Randall Wright, 2001. "Pricing and Matching with Frictions," Journal of Political Economy, University of Chicago Press, vol. 109(5), pages 1060-1085, October.
    30. Veronica Guerrieri & Robert Shimer & Randall Wright, 2010. "Adverse Selection in Competitive Search Equilibrium," Econometrica, Econometric Society, vol. 78(6), pages 1823-1862, November.
    31. Manolis Galenianos & Philipp Kircher, 2012. "On The Game‐Theoretic Foundations Of Competitive Search Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(1), pages 1-21, February.
    32. Espen R. Moen & Åsa Rosén, 2011. "Incentives in Competitive Search Equilibrium," Review of Economic Studies, Oxford University Press, vol. 78(2), pages 733-761.
    33. Kyungmin Kim & Philipp Kircher, 2015. "Efficient Competition Through Cheap Talk: The Case of Competing Auctions," Econometrica, Econometric Society, vol. 83(5), pages 1849-1875, September.
    34. Peters, Michael, 1991. "Ex Ante Price Offers in Matching Games Non-steady States," Econometrica, Econometric Society, vol. 59(5), pages 1425-1454, September.
    35. Maya Eden, 2017. "Misallocation and the Distribution of Global Volatility," American Economic Review, American Economic Association, vol. 107(2), pages 592-622, February.
    36. Fabien Postel-Vinay & Jean-Marc Robin, 2002. "Equilibrium wage dispersion with worker and employer heterogeneity," Post-Print hal-03587660, HAL.
    37. Fabien Postel-Vinay & Jean-Marc Robin, 2002. "Equilibrium Wage Dispersion with Worker and Employer Heterogeneity," Post-Print hal-03458567, HAL.
    38. Moen, Espen R, 1997. "Competitive Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 385-411, April.
    39. Ezra Oberfield & Devesh Raval, 2021. "Micro Data and Macro Technology," Econometrica, Econometric Society, vol. 89(2), pages 703-732, March.
    40. H. S. Houthakker, 1955. "The Pareto Distribution and the Cobb-Douglas Production Function in Activity Analysis," Review of Economic Studies, Oxford University Press, vol. 23(1), pages 27-31.
    41. Benoit Julien & John Kennes & Ian King, 2000. "Bidding for Labor," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(4), pages 619-649, October.
    42. James Albrecht & Pieter A. Gautier & Susan Vroman, 2014. "Efficient Entry in Competing Auctions," American Economic Review, American Economic Association, vol. 104(10), pages 3288-3296, October.
    43. Samuel S. Kortum, 1997. "Research, Patenting, and Technological Change," Econometrica, Econometric Society, vol. 65(6), pages 1389-1420, November.
    44. Francesco Caselli & Wilbur John Coleman II, 2006. "The World Technology Frontier," American Economic Review, American Economic Association, vol. 96(3), pages 499-522, June.
    45. Growiec, Jakub, 2008. "Production functions and distributions of unit factor productivities: Uncovering the link," Economics Letters, Elsevier, vol. 101(1), pages 87-90, October.
    46. Charles I. Jones, 2005. "The Shape of Production Functions and the Direction of Technical Change," The Quarterly Journal of Economics, Oxford University Press, vol. 120(2), pages 517-549.
    47. Ricardo Lagos, 2000. "An Alternative Approach to Search Frictions," Journal of Political Economy, University of Chicago Press, vol. 108(5), pages 851-873, October.
    48. Jonathan Eaton & Samuel S. Kortum & Sebastian Sotelo, 2012. "International Trade: Linking Micro and Macro," NBER Working Papers 17864, National Bureau of Economic Research, Inc.
    49. Randall Wright & Philipp Kircher & Benoit Julîen & Veronica Guerrieri, 2017. "Directed Search: A Guided Tour," NBER Working Papers 23884, National Bureau of Economic Research, Inc.
    50. Rainer Klump & Peter McAdam & Alpo Willman, 2012. "The Normalized Ces Production Function: Theory And Empirics," Journal of Economic Surveys, Wiley Blackwell, vol. 26(5), pages 769-799, December.
    51. Sherwin Rosen, 2005. "Substitution And Division Of Labour," World Scientific Book Chapters,in: An Inframarginal Approach To Trade Theory, chapter 3, pages 29-51 World Scientific Publishing Co. Pte. Ltd..
    52. Margaret Stevens, 2007. "New Microfoundations For The Aggregate Matching Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(3), pages 847-868, August.
    53. McAfee, R Preston, 1993. "Mechanism Design by Competing Sellers," Econometrica, Econometric Society, vol. 61(6), pages 1281-1312, November.
    54. Growiec, Jakub, 2013. "A microfoundation for normalized CES production functions with factor-augmenting technical change," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2336-2350.
    55. Asher Wolinsky, 1988. "Dynamic Markets with Competitive Bidding," Review of Economic Studies, Oxford University Press, vol. 55(1), pages 71-84.
    56. Mihai Banciu & Prakash Mirchandani, 2013. "Technical Note—New Results Concerning Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 61(4), pages 925-931, August.
    57. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    58. repec:hrv:faseco:34651705 is not listed on IDEAS
    59. James D. Montgomery, 1991. "Equilibrium Wage Dispersion and Interindustry Wage Differentials," The Quarterly Journal of Economics, Oxford University Press, vol. 106(1), pages 163-179.
    60. Shi, Shouyong, 2001. "Frictional Assignment. I. Efficiency," Journal of Economic Theory, Elsevier, vol. 98(2), pages 232-260, June.
    61. Robert Shimer, 2005. "The Assignment of Workers to Jobs in an Economy with Coordination Frictions," Journal of Political Economy, University of Chicago Press, vol. 113(5), pages 996-1025, October.
    62. Gerard R. Butters, 1977. "Equilibrium Distributions of Sales and Advertising Prices," Review of Economic Studies, Oxford University Press, vol. 44(3), pages 465-491.
    63. Arthur J. Hosios, 1990. "On The Efficiency of Matching and Related Models of Search and Unemployment," Review of Economic Studies, Oxford University Press, vol. 57(2), pages 279-298.
    64. Eaton, Jonathan & Kortum, Samuel, 1999. "International Technology Diffusion: Theory and Measurement," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 537-570, August.
    65. Coles, Melvyn G. & Eeckhout, Jan, 2003. "Indeterminacy and directed search," Journal of Economic Theory, Elsevier, vol. 111(2), pages 265-276, August.
    66. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
    67. Shouyong Shi, 2002. "A Directed Search Model of Inequality with Heterogeneous Skills and Skill-Biased Technology," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 467-491.
    68. Jonathan Eaton & Samuel Kortum, 2002. "Technology, Geography, and Trade," Econometrica, Econometric Society, vol. 70(5), pages 1741-1779, September.
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    Cited by:

    1. Johannes Boehm, 2014. "The Impact of Contract Enforcement Costs on Outsourcing and Aggregate Productivity," 2014 Meeting Papers 340, Society for Economic Dynamics.
    2. Johannes Boehm, 2014. "The Impact of Contract Enforcement Costs on Outsourcing and Aggregate Productivity," 2014 Meeting Papers 340, Society for Economic Dynamics.
    3. Ezra Oberfield & Devesh Raval, 2021. "Micro Data and Macro Technology," Econometrica, Econometric Society, vol. 89(2), pages 703-732, March.
    4. Mangin, Sephorah & Sedláček, Petr, 2018. "Unemployment and the labor share," Journal of Monetary Economics, Elsevier, vol. 94(C), pages 41-59.
    5. Mangin, Sephorah & Julien, Benoît, 2021. "Efficiency in search and matching models: A generalized Hosios condition," Journal of Economic Theory, Elsevier, vol. 193(C).
    6. Johannes Boehm, 2014. "The Impact of Contract Enforcement Costs on Outsourcing and Aggregate Productivity," 2014 Meeting Papers 340, Society for Economic Dynamics.
    7. 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.
    8. Stephen J. DeCanio, 2022. "Simple efficiency-distribution models of production, with an application to robotics," SN Business & Economics, Springer, vol. 2(8), pages 1-16, August.
    9. Johannes Boehm, 2014. "The Impact of Contract Enforcement Costs on Outsourcing and Aggregate Productivity," 2014 Meeting Papers 340, Society for Economic Dynamics.
    10. DeCanio, Stephen J., 2016. "Robots and humans – complements or substitutes?," Journal of Macroeconomics, Elsevier, vol. 49(C), pages 280-291.

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    More about this item

    JEL classification:

    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity
    • E25 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Aggregate Factor Income Distribution
    • J64 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Unemployment: Models, Duration, Incidence, and Job Search

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