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On indeterminacy in one-sector models of the business cycle with factor-generated externalities

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  • Meng, Qinglai
  • Yip, Chong Kee

Abstract

By relaxing the restrictions commonly imposed on the magnitude of capital externalities in one-sector models with Cobb-Douglas technology, we find that indeterminacy can arise in the following two cases: (i) the felicity function is separable in consumption and leisure and there are negative capital externalities; (ii) the felicity function is non-separable and the social elasticity of production with respect to capital is greater than one. In both cases indeterminacy happens when the aggregate labor-demand curve is downward-sloping. In addition, with Cobb-Douglas technology we show that the presence of income effects on the demand for leisure is a necessary condition for indeterminacy to occur, and that therefore for certain felicity functions characterized by the presence of no income effects indeterminacy can never occur regardless of the signs and magnitudes of capital and labor externalities.

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  • Meng, Qinglai & Yip, Chong Kee, 2008. "On indeterminacy in one-sector models of the business cycle with factor-generated externalities," Journal of Macroeconomics, Elsevier, vol. 30(1), pages 97-110, March.
    • Handle: RePEc:eee:jmacro:v:30:y:2008:i:1:p:97-110
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    1. Sunspots and Credit Frictions
      by Christian Zimmermann in NEP-DGE blog on 2010-01-25 09:20:38

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    2. Long Xin & Pelloni Alessandra, 2011. "Welfare improving taxation on savings in a growth model," wp.comunite 0091, Department of Communication, University of Teramo.
    3. Guo, Jang-Ting & Harrison, Sharon G., 2010. "Indeterminacy with no-income-effect preferences and sector-specific externalities," Journal of Economic Theory, Elsevier, vol. 145(1), pages 287-300, January.
    4. Long, Xin & Pelloni, Alessandra, 2017. "Factor income taxation in a horizontal innovation model," Journal of Public Economics, Elsevier, vol. 154(C), pages 137-159.
    5. Jang-Ting Guo & Sharon G. Harrison, 2015. "Indeterminacy with Progressive Taxation and Sector-Specific Externalities," Pacific Economic Review, Wiley Blackwell, vol. 20(2), pages 268-281, May.
    6. Frédéric Dufourt & Kazuo Nishimura & Alain Venditti, 2013. "Indeterminacy and Sunspot Fluctuations in Two-Sector RBC models: Theory and Calibration," AMSE Working Papers 1315, Aix-Marseille School of Economics, France, revised Nov 2009.
    7. Wong, Tsz-Nga & Yip, Chong K., 2010. "Indeterminacy and the elasticity of substitution in one-sector models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 623-635, April.
    8. Yoichi Gokan, 2017. "Do Consumption Externalities Correspond to the Indivisible Tax Rates on Consumpiton?," CIRJE F-Series CIRJE-F-1041, CIRJE, Faculty of Economics, University of Tokyo.
    9. Jang‐Ting Guo & Yan Zhang, 2022. "Macroeconomic stability under balanced‐budget rules and no‐income‐effect preferences," Pacific Economic Review, Wiley Blackwell, vol. 27(1), pages 3-17, February.
    10. McGough, Bruce & Meng, Qinglai & Xue, Jianpo, 2013. "Expectational stability of sunspot equilibria in non-convex economies," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1126-1141.
    11. Antoci, Angelo & Galeotti, Marcello & Russu, Paolo, 2011. "Poverty trap and global indeterminacy in a growth model with open-access natural resources," Journal of Economic Theory, Elsevier, vol. 146(2), pages 569-591, March.
    12. Magris, Francesco, 2012. "Indeterminacy and multiple steady states with sector-specific externalities," Economic Modelling, Elsevier, vol. 29(6), pages 2664-2672.
    13. Been‐Lon Chen & Shun‐Fa Lee & Xavier Raurich, 2020. "Non‐separable utilities and aggregate instability," International Journal of Economic Theory, The International Society for Economic Theory, vol. 16(2), pages 222-237, June.
    14. Yoichi Gokan, 2017. "Do Consumption Externalities Correspond to the Indivisible Tax Rates on Consumpiton?," CIRJE F-Series CIRJE-F-1040, CIRJE, Faculty of Economics, University of Tokyo.
    15. Nishimura, Kazuo & Venditti, Alain, 2010. "Indeterminacy and expectation-driven fluctuations with non-separable preferences," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 46-56, July.
    16. Chang Cheng-Wei & Lai Ching-Chong, 2017. "Macroeconomic (in)stability and endogenous market structure with productive government expenditure," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(2), pages 1-16, April.
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    18. Carboni, Oliviero A. & Russu, Paolo, 2013. "Linear production function, externalities and indeterminacy in a capital-resource growth model," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 422-428.

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