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An exact consumption rule with liquidity constraints and stochastic income


  • Travaglini Giuseppe

    () (Università di Urbino Carlo Bo, Facoltà di Economia)


This model provides a closed form solution to the problem of liquidity constrained consumption with stochastic income. To keep the model tractable we employ a quadratic utility function. Income follows a geometric Brownian motion. The analytical solution exhibits a smooth, non linear, relation between consumption and income along the optimizing path even when the constraint binds. This outcome confirms the assertions in the literature that even liquidity constrained consumers may satisfy the standard Euler equation. But, in our model this result emerges from the analytical solution.

Suggested Citation

  • Travaglini Giuseppe, 2008. "An exact consumption rule with liquidity constraints and stochastic income," Economics Bulletin, AccessEcon, vol. 5(6), pages 1-9.
  • Handle: RePEc:ebl:ecbull:eb-08e20001

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    References listed on IDEAS

    1. Zeldes, Stephen P, 1989. "Consumption and Liquidity Constraints: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 97(2), pages 305-346, April.
    2. Stephen P. Zeldes, 1989. "Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," The Quarterly Journal of Economics, Oxford University Press, vol. 104(2), pages 275-298.
    3. Saltari, Enrico & Travaglini, Giuseppe, 2006. "The effects of future financing constraints on capital accumulation: Some new results on the constrained investment problem," Research in Economics, Elsevier, vol. 60(2), pages 85-96, June.
    4. Park, Myung-Ho, 2006. "An analytical solution to the inverse consumption function with liquidity constraints," Economics Letters, Elsevier, vol. 92(3), pages 389-394, September.
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    Cited by:

    1. Travaglini, Giuseppe, 2012. "Note sulla teoria del consumo
      [Notes on consumption theory]
      ," MPRA Paper 36146, University Library of Munich, Germany.
    2. Giuseppe Travaglini, 2012. "Pollution control: targets and dynamics," Working Papers 1201, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
    3. Tuomas Malinen, 2011. "Income Inequality and Savings: A Reassessment of the Relationship in Cointegrated Panels," DEGIT Conference Papers c016_076, DEGIT, Dynamics, Economic Growth, and International Trade.
    4. Saltari, Enrico & Travaglini, Giuseppe, 2011. "Optimal abatement investment and environmental policies under pollution uncertainty," MPRA Paper 35072, University Library of Munich, Germany.
    5. Tuomas, Malinen, 2011. "Inequality and savings: a reassesment of the relationship in cointegrated panels," MPRA Paper 33350, University Library of Munich, Germany.

    More about this item


    Optimal control Stochastic income Liquidity constraints Consumption;

    JEL classification:

    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling


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