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Equilibrium in Production Chains with Multiple Upstream Partners

Author

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  • Meng Yu
  • Junnan Zhang
Abstract
In this paper, we extend and improve the production chain model introduced by Kikuchi et al. (2018). Utilizing the theory of monotone concave operators, we prove the existence, uniqueness, and global stability of equilibrium price, hence improving their results on production networks with multiple upstream partners. We propose an algorithm for computing the equilibrium price function that is more than ten times faster than successive evaluations of the operator. The model is then generalized to a stochastic setting that offers richer implications for the distribution of firms in a production network.

Suggested Citation

  • Meng Yu & Junnan Zhang, 2019. "Equilibrium in Production Chains with Multiple Upstream Partners," Papers 1908.08208, arXiv.org.
    • Handle: RePEc:arx:papers:1908.08208
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    References listed on IDEAS

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    1. Morand, Olivier F. & Reffett, Kevin L., 2003. "Existence and uniqueness of equilibrium in nonoptimal unbounded infinite horizon economies," Journal of Monetary Economics, Elsevier, vol. 50(6), pages 1351-1373, September.
    2. Gary S. Becker & Kevin M. Murphy, 1994. "The Division of Labor, Coordination Costs, and Knowledge," NBER Chapters, in: Human Capital: A Theoretical and Empirical Analysis with Special Reference to Education, Third Edition, pages 299-322, National Bureau of Economic Research, Inc.
    3. Baldwin, Richard & Venables, Anthony J., 2013. "Spiders and snakes: Offshoring and agglomeration in the global economy," Journal of International Economics, Elsevier, vol. 90(2), pages 245-254.
    4. Datta, Manjira & Mirman, Leonard J. & Reffett, Kevin L., 2002. "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Journal of Economic Theory, Elsevier, vol. 103(2), pages 377-410, April.
    5. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2013. "A constructive geometrical approach to the uniqueness of Markov stationary equilibrium in stochastic games of intergenerational altruism," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1019-1039.
    6. Manjira Datta & Leonard Mirman & Olivier Morand & Kevin Reffett, 2002. "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Annals of Operations Research, Springer, vol. 114(1), pages 117-144, August.
    7. Daron Acemoglu & Asuman Ozdaglar & Alireza Tahbaz-Salehi, 2015. "Systemic Risk and Stability in Financial Networks," American Economic Review, American Economic Association, vol. 105(2), pages 564-608, February.
    8. Kikuchi, Tomoo & Nishimura, Kazuo & Stachurski, John, 2018. "Span of control, transaction costs and the structure of production chains," Theoretical Economics, Econometric Society, vol. 13(2), May.
    9. Daron Acemoglu & Vasco M. Carvalho & Asuman Ozdaglar & Alireza Tahbaz‐Salehi, 2012. "The Network Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 80(5), pages 1977-2016, September.
    10. Saki Bigio, 2013. "Financial Frictions in Production Networks," 2013 Meeting Papers 121, Society for Economic Dynamics.
    11. Jaroslav Borovička & John Stachurski, 2020. "Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities," Journal of Finance, American Finance Association, vol. 75(3), pages 1457-1493, June.
    12. Daron Acemoglu & Asuman Ozdaglar & Alireza Tahbaz-Salehi, 2015. "Networks, Shocks, and Systemic Risk," NBER Working Papers 20931, National Bureau of Economic Research, Inc.
    13. Jeffrey M. Lacker & Stacey L. Schreft, 1991. "Money, trade credit and asset prices," Working Paper 91-04, Federal Reserve Bank of Richmond.
    14. Nicola Pavoni & Christopher Sleet & Matthias Messner, 2018. "The Dual Approach to Recursive Optimization: Theory and Examples," Econometrica, Econometric Society, vol. 86(1), pages 133-172, January.
    15. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
    16. Coleman, Wilbur II, 2000. "Uniqueness of an Equilibrium in Infinite-Horizon Economies Subject to Taxes and Externalities," Journal of Economic Theory, Elsevier, vol. 95(1), pages 71-78, November.
    17. Robert E. Lucas Jr., 1978. "On the Size Distribution of Business Firms," Bell Journal of Economics, The RAND Corporation, vol. 9(2), pages 508-523, Autumn.
    18. Marinacci, Massimo & Montrucchio, Luigi, 2010. "Unique solutions for stochastic recursive utilities," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1776-1804, September.
    19. Antonio Ciccone, 2002. "Input Chains and Industrialization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 565-587.
    20. Bloise, Gaetano & Vailakis, Yiannis, 2018. "Convex dynamic programming with (bounded) recursive utility," Journal of Economic Theory, Elsevier, vol. 173(C), pages 118-141.
    21. Dedrick, Jason & Kraemer, Kenneth L. & Linden, Greg, 2011. "The distribution of value in the mobile phone supply chain," Telecommunications Policy, Elsevier, vol. 35(6), pages 505-521, July.
    22. Charles I. Jones, 2011. "Intermediate Goods and Weak Links in the Theory of Economic Development," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(2), pages 1-28, April.
    23. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    24. Massimo Marinacci & Luigi Montrucchio, 2017. "Unique Tarski Fixed Points," Working Papers 604, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
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    Cited by:

    1. Kikuchi, Tomoo & Nishimura, Kazuo & Stachurski, John & Zhang, Junnan, 2021. "Coase meets Bellman: Dynamic programming for production networks," Journal of Economic Theory, Elsevier, vol. 196(C).

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