IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/124225.html

A complete characterization of equilibrium paths in a labour-less two-sector model of optimal growth

Author

Listed:
  • Guerrazzi, Marco

Abstract

In this paper, I develop a two-sector growth model in which the output of each industry is obtained only by means of capital. From a theoretical perspective, this setting reveals that the determinacy of the equilibrium path is possible even when the production technology available in the industry of consumption goods is not necessarily convex. Moreover, form a numerical point of view, I show that whenever the first-best solution of the model is tailored on the US economy, such a theoretical framework relaxes the complementarity between the propensities to consume and to save and it is also consistent with the observed countercyclical pattern of the relative price of capital goods.

Suggested Citation

  • Guerrazzi, Marco, 2025. "A complete characterization of equilibrium paths in a labour-less two-sector model of optimal growth," MPRA Paper 124225, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:124225
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/124225/1/MPRA_paper_124225.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Harrison, Sharon G. & Weder, Mark, 2002. "Tracing externalities as sources of indeterminacy," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 851-867, May.
    2. Collins, William J. & Williamson, Jeffrey G., 2001. "Capital-Goods Prices And Investment, 1870–1950," The Journal of Economic History, Cambridge University Press, vol. 61(1), pages 59-94, March.
    3. Alejandro Justiniano & Giorgio Primiceri & Andrea Tambalotti, 2011. "Investment Shocks and the Relative Price of Investment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 14(1), pages 101-121, January.
    4. Jonas D. M. Fisher, 2006. "The Dynamic Effects of Neutral and Investment-Specific Technology Shocks," Journal of Political Economy, University of Chicago Press, vol. 114(3), pages 413-451, June.
    5. Hergovich, Philipp & Merz, Monika, 2018. "The Price of Capital, Factor Substitutability, and Corporate Profits," IZA Discussion Papers 11791, IZA Network @ LISER.
    6. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    7. Hirofumi Uzawa, 1964. "Optimal Growth in a Two-Sector Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 31(1), pages 1-24.
    8. Miki Matsuo & Kazuo Nishimura & Tomoya Sakagami & Alain Venditti, 2009. "Characterization of Equilibrium Paths in a Two-Sector Economy with CES Production Functions and Sector-Specific Externality," Springer Books, in: Takashi Kamihigashi & Laixun Zhao (ed.), International Trade and Economic Dynamics, pages 421-431, Springer.
    9. F. H. Hahn, 1965. "On Two Sector Growth Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(4), pages 339-346.
    10. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    11. Benhabib, Jess & Farmer, Roger E. A., 1996. "Indeterminacy and sector-specific externalities," Journal of Monetary Economics, Elsevier, vol. 37(3), pages 421-443, June.
    12. David Cass, 1965. "Optimum Growth in an Aggregative Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(3), pages 233-240.
    13. Ferreira, Pedro Cavalcanti & Pessôa, Samuel de Abreu & Veloso, Fernando A., 2014. "Distortions in the investment goods sector and productivity decline," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 755, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    14. Mehdi Senouci, 2011. "Optimal growth and the golden rule in a two-sector model of capital accumulation," Working Papers halshs-00572510, HAL.
    15. Growiec, Jakub, 2022. "Automation, Partial And Full," Macroeconomic Dynamics, Cambridge University Press, vol. 26(7), pages 1731-1755, October.
    16. Hornstein, Andreas & Praschnik, Jack, 1997. "Intermediate inputs and sectoral comovement in the business cycle," Journal of Monetary Economics, Elsevier, vol. 40(3), pages 573-595, December.
    17. Jess Benhabib & Kazuo Nishimura, 2012. "Indeterminacy and Sunspots with Constant Returns," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 311-346, Springer.
    18. Marco Guerrazzi & Giuseppe Candido, 2025. "The determination of the price of capital goods: A differential game approach," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 46(1), pages 222-234, January.
    19. Restuccia, Diego & Urrutia, Carlos, 2001. "Relative prices and investment rates," Journal of Monetary Economics, Elsevier, vol. 47(1), pages 93-121, February.
    20. Venditti, Alain, 2005. "The two sector overlapping generations model: A simple formulation," Research in Economics, Elsevier, vol. 59(2), pages 164-188, June.
    21. Philipp Hergovich & Monika Merz, 2018. "The Price of Capital, Factor Substitutability and Corporate Profits," Vienna Economics Papers 1801, University of Vienna, Department of Economics.
    22. Weicheng Lian & Natalija Novta & Evgenia Pugacheva & Yannick Timmer & Petia Topalova, 2020. "The Price of Capital Goods: A Driver of Investment Under Threat," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 68(3), pages 509-549, September.
    23. Hiroyuki Hashimoto & Masaya Sakuragawa, 1999. "A Characterization of the Dynamical System in a Two-sector Overlapping-generations Model: The Case of Unbounded Growth," The Japanese Economic Review, Japanese Economic Association, vol. 50(2), pages 138-147, June.
    24. Lawrence J. Christiano & Jonas D. M. Fisher, 2003. "Stock Market and Investment Goods Prices: Implications for Macroeconomics," NBER Working Papers 10031, National Bureau of Economic Research, Inc.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guerrazzi, Marco, 2025. "A two-sector model of optimal growth in which labour is employed only in the industry of consumption goods: A complete characterization of equilibrium paths," MPRA Paper 126101, University Library of Munich, Germany.
    2. Guerrazzi, Marco, 2025. "A two-sector model of optimal growth in which labour is employed only in the industry of investment goods: A complete characterization of equilibrium paths," MPRA Paper 126299, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guerrazzi, Marco, 2025. "A two-sector model of optimal growth in which labour is employed only in the industry of consumption goods: A complete characterization of equilibrium paths," MPRA Paper 126101, University Library of Munich, Germany.
    2. Guerrazzi, Marco, 2025. "A two-sector model of optimal growth in which labour is employed only in the industry of investment goods: A complete characterization of equilibrium paths," MPRA Paper 126299, University Library of Munich, Germany.
    3. Marco Guerrazzi & Giuseppe Candido, 2025. "The determination of the price of capital goods: A differential game approach," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 46(1), pages 222-234, January.
    4. Frédéric Dufourt & Kazuo Nishimura & Alain Venditti, 2025. "Expectations, beliefs and the business cycle: tracing back to the deep economic drivers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(1), pages 89-149, February.
    5. José Luis Torres Chacon, 2015. "Introduction to Dynamic Macroeconomic General Equilibrium Models," Vernon Press Titles in Economics, Vernon Art and Science Inc, edition 2, number 54, March.
    6. Jaimovich, Nir, 2008. "Income effects and indeterminacy in a calibrated one-sector growth model," Journal of Economic Theory, Elsevier, vol. 143(1), pages 610-623, November.
    7. 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.
    8. Jean‐Philippe Garnier & Kazuo Nishimura & Alain Venditti, 2007. "Intertemporal substitution in consumption, labor supply elasticity and sunspot fluctuations in continuous‐time models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 3(4), pages 235-259, December.
    9. Tarek Coury & Yi Wen, 2007. "Global indeterminacy in locally determinate RBC models," Working Papers 2007-029, Federal Reserve Bank of St. Louis.
    10. Tarek Coury & Yi Wen, 2009. "Global indeterminacy in locally determinate real business cycle models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 49-60, March.
    11. Been‐Lon Chen & Shun‐Fa Lee, 2012. "Intersectoral Spillovers, Relative Prices and Development Traps," Review of Development Economics, Wiley Blackwell, vol. 16(2), pages 243-261, May.
    12. Nigar Hashimzade & Salvador Ortigueira, 2004. "Endogenous Business Cycle With Search In The Labour Market," Royal Economic Society Annual Conference 2004 161, Royal Economic Society.
    13. Mohanad Ismael & Francesco Magris, 2008. "Indeterminacy with Externalities and Capital Utilization," Documents de recherche 08-14, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    14. Kim, Jinill, 2005. "Does utility curvature matter for indeterminacy?," Journal of Economic Behavior & Organization, Elsevier, vol. 57(4), pages 421-429, August.
    15. Jean-Philippe Garnier, 2012. "Sunspots, cycles and adjustment costs in the two-sectors model," Working Papers hal-00991657, HAL.
    16. José Luis Torres Chacon, 2015. "Introduction to Dynamic Macroeconomic General Equilibrium Models [Second Edition, Paperback]," Vernon Press Titles in Economics, Vernon Art and Science Inc, edition 2, number 44.
    17. Jean-Philippe Garnier, 2014. "Endogenous fluctutations: a financial transmission Mechanism," Working Papers hal-01006946, HAL.
    18. Andrei Polbin & Sergey Drobyshevsky, 2014. "Developing a Dynamic Stochastic Model of General Equilibrium for the Russian Economy," Research Paper Series, Gaidar Institute for Economic Policy, issue 166P, pages 156-156.
    19. Frédéric Dufourt & Kazuo Nishimura & Alain Venditti, 2022. "Expectations, self-fulfilling prophecies and the business cycle," Working Papers hal-03923946, HAL.
    20. Escañuela Romana, Ignacio, 2016. "Azar, Determinismo e Indecidibilidad en la Teoría del Ciclo Económico [Randomness, Determinism and Undecidability in the Business Cycle Theory]," MPRA Paper 72978, University Library of Munich, Germany.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • O11 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Macroeconomic Analyses of Economic Development

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:124225. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.