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Non-smooth dynamics and multiple equilibria in a Cournot–Ramsey model with endogenous markups

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  • Brito, Paulo B.
  • Costa, Luís F.
  • Dixon, Huw

Abstract

We consider a Ramsey model with a continuum of Cournotian industries where free entry generates an endogenous markup. The model produces two different regimes, monopolistic and Cournotian monopolistic competition, resulting in non-smooth dynamics. We analyze the global dynamics of the model, demonstrating it may exhibit heteroclinic orbits connecting multiple equilibria. Small transitory changes in parameters can lead to large permanent effects and there can be a poverty trap separating a low-capital and high-markup equilibrium from a high-capital low-markup equilibrium. We apply results from the mathematics of non-smooth dynamic systems, which provide a more general framework for understanding regime switching.

Suggested Citation

  • Brito, Paulo B. & Costa, Luís F. & Dixon, Huw, 2013. "Non-smooth dynamics and multiple equilibria in a Cournot–Ramsey model with endogenous markups," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2287-2306.
    • Handle: RePEc:eee:dyncon:v:37:y:2013:i:11:p:2287-2306
    DOI: 10.1016/j.jedc.2013.05.014
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    1. Ravn, Morten O. & Schmitt-Grohé, Stephanie & Uribe, Martín, 2008. "Macroeconomics Of Subsistence Points," Macroeconomic Dynamics, Cambridge University Press, vol. 12(S1), pages 136-147, April.
    2. Luis F Costa & Huw D Dixon, "undated". "A Simple Business-Cycle Model with Schumpeterian Features," Discussion Papers 05/30, Department of Economics, University of York.
    3. W. Davis Dechert & Kazuo Nishimura, 2012. "A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 237-257, Springer.
    4. Gali, Jordi, 1995. "Product diversity, endogenous markups, and development traps," Journal of Monetary Economics, Elsevier, vol. 36(1), pages 39-63, August.
    5. d'Aspremont, Claude & Dos Santos Ferreira, Rodolphe & Gerard-Varet, Louis-Andre, 1996. "On the Dixit-Stiglitz Model of Monopolistic Competition," American Economic Review, American Economic Association, vol. 86(3), pages 623-629, June.
    6. Marvin Goodfriend & Robert G. King, 1997. "The New Neoclassical Synthesis and the Role of Monetary Policy," NBER Chapters, in: NBER Macroeconomics Annual 1997, Volume 12, pages 231-296, National Bureau of Economic Research, Inc.
    7. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, November.
    8. d'Aspremont, Claude & Dos Santos Ferreira, Rodolphe & Gerard-Varet, Louis-Andre, 1997. "General Equilibrium Concepts under Imperfect Competition: A Cournotian Approach," Journal of Economic Theory, Elsevier, vol. 73(1), pages 199-230, March.
    9. Florin O. Bilbiie & Fabio Ghironi & Marc J. Melitz, 2012. "Endogenous Entry, Product Variety, and Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 120(2), pages 304-345.
    10. repec:adr:anecst:y:1995:i:37-38:p:10 is not listed on IDEAS
    11. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    12. Luís F. Costa, 2004. "Endogenous Markups and Fiscal Policy," Manchester School, University of Manchester, vol. 72(s1), pages 55-71, September.
    13. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    14. Joaquim Oliveira Martins & Stefano Scarpetta & Dirk Pilat, 1996. "Mark-Up Ratios in Manufacturing Industries: Estimates for 14 OECD Countries," OECD Economics Department Working Papers 162, OECD Publishing.
    15. Satyajit Chatterjee & Russell Cooper & B. Ravikumar, 1993. "Strategic Complementarity in Business Formation: Aggregate Fluctuations and Sunspot Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 795-811.
    16. Jaimovich, Nir, 2007. "Firm dynamics and markup variations: Implications for sunspot equilibria and endogenous economic fluctuations," Journal of Economic Theory, Elsevier, vol. 137(1), pages 300-325, November.
    17. Kiminori Matsuyama, 2004. "Financial Market Globalization, Symmetry-Breaking, and Endogenous Inequality of Nations," Econometrica, Econometric Society, vol. 72(3), pages 853-884, May.
    18. Tramontana, Fabio & Gardini, Laura & Agliari, Anna, 2011. "Endogenous cycles in discontinuous growth models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1625-1639.
    19. Santos, Manuel S., 2002. "On Non-existence of Markov Equilibria in Competitive-Market Economies," Journal of Economic Theory, Elsevier, vol. 105(1), pages 73-98, July.
    20. Luís Costa, 2001. "Can Fiscal Policy Improve Welfare in a Small Dependent Economy with Feedback Effects?," Manchester School, University of Manchester, vol. 69(4), pages 418-439, September.
    21. Rebelo, Sergio, 1991. "Long-Run Policy Analysis and Long-Run Growth," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 500-521, June.
    22. 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.
    23. Dos Santos Ferreira, Rodolphe & Dufourt, Frederic, 2006. "Free entry and business cycles under the influence of animal spirits," Journal of Monetary Economics, Elsevier, vol. 53(2), pages 311-328, March.
    24. Gali Jordi, 1994. "Monopolistic Competition, Business Cycles, and the Composition of Aggregate Demand," Journal of Economic Theory, Elsevier, vol. 63(1), pages 73-96, June.
    25. Benhabib, Jess & Gali, Jordi, 1995. "On growth and indeterminacy: some theory and evidence," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 43(1), pages 163-211, December.
    26. Jaimovich, Nir & Floetotto, Max, 2008. "Firm dynamics, markup variations, and the business cycle," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1238-1252, October.
    27. Julio J. Rotemberg & Michael Woodford, 1991. "Markups and the Business Cycle," NBER Chapters, in: NBER Macroeconomics Annual 1991, Volume 6, pages 63-140, National Bureau of Economic Research, Inc.
    28. Kaas, Leo & Madden, Paul, 2005. "Imperfectly competitive cycles with Keynesian and Walrasian features," European Economic Review, Elsevier, vol. 49(4), pages 861-886, May.
    29. Chevalier, Judith A & Scharfstein, David S, 1996. "Capital-Market Imperfections and Countercyclical Markups: Theory and Evidence," American Economic Review, American Economic Association, vol. 86(4), pages 703-725, September.
    30. Brito, Paulo B. & Costa, Luís F. & Dixon, Huw, 2013. "Non-smooth dynamics and multiple equilibria in a Cournot–Ramsey model with endogenous markups," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2287-2306.
    31. d’ASPREMONT, Cl. & DOS SANTOS FERREIRA, R. & GERARD-VARET, L.-A., 1988. "Unemployment in a Cournot oligopoly model with Ford effects," LIDAM Discussion Papers CORE 1988018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    32. Morten Ravn & Stephanie Schmitt-Grohé & Martín Uribe, 2006. "Deep Habits," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(1), pages 195-218.
    33. Peretto, Pietro F., 2007. "Corporate taxes, growth and welfare in a Schumpeterian economy," Journal of Economic Theory, Elsevier, vol. 137(1), pages 353-382, November.
    34. Costa, Luis F, 2001. "Can Fiscal Policy Improve Welfare in a Small Dependent Economy with Feedback Effects," Manchester School, University of Manchester, vol. 69(4), pages 418-439, September.
    35. d'Aspremont, C & Ferreira, R Dos Santos & Gerard-Varet, L-A, 1991. "Pricing Schemes and Cournotian Equilibria," American Economic Review, American Economic Association, vol. 81(3), pages 666-673, June.
    36. Paulo Brito & Huw Dixon, 2009. "Entry and the accumulation of capital: A two state variable extension to the Ramsey model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(4), pages 333-357, December.
    37. Wu, Yangru & Zhang, Junxi, 2000. "Endogenous markups and the effects of income taxation:: Theory and evidence from OECD countries," Journal of Public Economics, Elsevier, vol. 77(3), pages 383-406, September.
    38. Franck Portier, 1995. "Business Formation and Cyclical Markups in the French Business Cycle," Annals of Economics and Statistics, GENES, issue 37-38, pages 411-440.
    39. Zilibotti, Fabrizio, 1994. "Endogenous Growth and Intermediation in an 'Archipelago' Economy," Economic Journal, Royal Economic Society, vol. 104(423), pages 462-473, March.
    40. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448, Elsevier.
    41. Luís Costa, 2006. "Entry and fiscal policy effectiveness in a small open economy within a Monetary Union," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 5(1), pages 45-65, May.
    42. Mark Bils & Peter J. Klenow, 2001. "The Acceleration of Variety Growth," American Economic Review, American Economic Association, vol. 91(2), pages 274-280, May.
    43. Yang, Xiaokai & Heijdra, Ben J, 1993. "Monopolistic Competition and Optimum Product Diversity: Comment," American Economic Review, American Economic Association, vol. 83(1), pages 295-301, March.
    44. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
    45. Dos Santos Ferreira, Rodolphe & Lloyd-Braga, Teresa, 2005. "Non-linear endogenous fluctuations with free entry and variable markups," Journal of Economic Dynamics and Control, Elsevier, vol. 29(5), pages 847-871, May.
    46. Rotemberg, Julio J & Woodford, Michael, 1992. "Oligopolistic Pricing and the Effects of Aggregate Demand on Economic Activity," Journal of Political Economy, University of Chicago Press, vol. 100(6), pages 1153-1207, December.
    47. Dixit, Avinash K & Stiglitz, Joseph E, 1993. "Monopolistic Competition and Optimum Product Diversity: Reply," American Economic Review, American Economic Association, vol. 83(1), pages 302-304, March.
    48. Rotemberg, Julio J. & Woodford, Michael, 1999. "The cyclical behavior of prices and costs," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 16, pages 1051-1135, Elsevier.
    49. Joaquim Oliveira Martins & Stefano Scarpetta, 2003. "Estimation of the Cyclical Behaviour of Mark-ups: A Technical Note," OECD Economic Studies, OECD Publishing, vol. 2002(1), pages 173-188.
    50. Dixon,Huw David & Rankin,Neil, 1995. "The New Macroeconomics," Cambridge Books, Cambridge University Press, number 9780521479479.
    51. Gali, Jordi, 1994. "Monopolistic competition, endogenous markups, and growth," European Economic Review, Elsevier, vol. 38(3-4), pages 748-756, April.
    52. d ASPREMONT, Claude, & DOS SANTOS FERREIRA , Rodolphe & GERARD-VARET , Louis-André, 1994. "Market Power, Coordination Failures and Endogenous Fluctuations," LIDAM Discussion Papers CORE 1994068, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    53. repec:adr:anecst:y:1995:i:37-38:p:17 is not listed on IDEAS
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    Cited by:

    1. Savagar, Anthony, 2021. "Measured productivity with endogenous markups and economic profits," Journal of Economic Dynamics and Control, Elsevier, vol. 133(C).
    2. Brito, Paulo B. & Costa, Luís F. & Dixon, Huw, 2013. "Non-smooth dynamics and multiple equilibria in a Cournot–Ramsey model with endogenous markups," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2287-2306.
    3. d’Aspremont, Claude & Dos Santos Ferreira, Rodolphe, 2020. "Exploiting separability in a multisectoral model of oligopolistic competition," Mathematical Social Sciences, Elsevier, vol. 106(C), pages 51-59.
    4. Francesco Carli & Leonor Modesto, 2022. "Sovereign debt, fiscal policy, and macroeconomic instability," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(6), pages 1386-1412, December.
    5. Anton Bondarev, 2021. "Games Without Winners: Catching-up with Asymmetric Spillovers," Dynamic Games and Applications, Springer, vol. 11(4), pages 670-703, December.

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    More about this item

    Keywords

    Endogenous markups; Regime switch; Discontinuity-induced bifurcations;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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