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Stochastic Growth When Utility Depends on Both Consumption and the Stock Level


  • Nyarko, Yaw
  • Olson, Lars J


This paper examines the dynamic behavior of optimal consumption and investment policies in the aggregate stochastic growth model when utility depends on both consumption and the stock level. Such models arise in the study of renewable resources, monetary growth, and growth with public capital. The paper shows that there is a global convergence of optimal policies to a unique stationary distribution if (a) there is sufficient complementarity in the model, or (b) if there is sufficient randomness in production. Two examples illustrate the possibility of multiple stationary distributions. In one, multiple stochastic steady states exist for a generic class of production and utility functions.

Suggested Citation

  • Nyarko, Yaw & Olson, Lars J, 1994. "Stochastic Growth When Utility Depends on Both Consumption and the Stock Level," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(5), pages 791-797, August.
  • Handle: RePEc:spr:joecth:v:4:y:1994:i:5:p:791-97

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    References listed on IDEAS

    1. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66, pages 467-467.
    2. Magill, M. & Quinzii, M., 1992. "Real effects of money in general equilibrium," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 301-342.
    3. Magill, Michael & Quinzii, Martine, 1994. "Infinite Horizon Incomplete Markets," Econometrica, Econometric Society, vol. 62(4), pages 853-880, July.
    4. BLOISE, Gaetano & DRÈZE, Jacques & POLEMARCHAKIS, Heracles, 2002. "Money and indeterminacy over an infinite horizon," CORE Discussion Papers 2002021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Olson, Lars J., 1995. "Dynamic Economic Models with Uncertainty and Irreversibility: Methods and Applications," Working Papers 197822, University of Maryland, Department of Agricultural and Resource Economics.
    2. Olson, Lars J. & Roy, Santanu, 1996. "On Conservation of Renewable Resources with Stock-Dependent Return and Nonconcave Production," Journal of Economic Theory, Elsevier, vol. 70(1), pages 133-157, July.
    3. Lars Olson & Santanu Roy, 2008. "Controlling a biological invasion: a non-classical dynamic economic model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(3), pages 453-469, September.
    4. Santanu Roy, 2010. "On sustained economic growth with wealth effects," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 29-45.
    5. Olson, Lars J. & Roy, Santanu, 2005. "Theory of Stochastic Optimal Economic Growth," Working Papers 28601, University of Maryland, Department of Agricultural and Resource Economics.

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