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Strict Concavity of the Value Function for a Family of Dynamic Accumulation Models

Author

Listed:
  • Bobenrieth Eugenio S.A.

    (Pontificia Universidad Católica de Chile, ebobenrieth@uc.cl)

  • Bobenrieth Juan R.A.

    (Universidad del Bío-Bío, jbobenri@ubiobio.cl)

  • Wright Brian D.

    (University of California, Berkeley, bwright@berkeley.edu)

Abstract

We prove strict concavity of the value function for liquidity constrained dynamic accumulation models without adopting at least one of the following restrictive assumptions: zero response of productive effort, bounded marginal value of accumulated balances, or strictly convex cost of holding accumulated balances. Thus we extend well known theoretical results to more general models of saving with liquidity constraints and of commodity storage with non-negativity constraints on stocks. Our results provide a foundation for estimation of a homogeneous markovian process for consumption in models of saving, or for price in commodity storage models, under more realistic assumptions.

Suggested Citation

  • Bobenrieth Eugenio S.A. & Bobenrieth Juan R.A. & Wright Brian D., 2012. "Strict Concavity of the Value Function for a Family of Dynamic Accumulation Models," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-11, April.
    • Handle: RePEc:bpj:bejtec:v:12:y:2012:i:1:n:9
    DOI: 10.1515/1935-1704.1838
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    References listed on IDEAS

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    1. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, vol. 59(5), pages 1221-1248, September.
    2. Deaton, Angus & Laroque, Guy, 1996. "Competitive Storage and Commodity Price Dynamics," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 896-923, October.
    3. Allen B. Paul, 1970. "The Pricing of Binspace—A Contribution to the Theory of Storage," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 52(1), pages 1-12.
    4. Eugenio S. A. Bobenrieth H. & Juan R. A. Bobenrieth H. & Brian D. Wright, 2002. "A Commodity Price Process with a Unique Continuous Invariant Distribution Having Infinite Mean," Econometrica, Econometric Society, vol. 70(3), pages 1213-1219, May.
    5. José A. Scheinkman & Jack Schechtman, 1983. "A Simple Competitive Model with Production and Storage," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(3), pages 427-441.
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    Cited by:

    1. Bobenrieth H., Eugenio S.A. & Bobenrieth H., Juan R.A. & Wright, Brian D., 2008. "A foundation for the solution of consumption-saving behavior with a borrowing constraint and unbounded marginal utility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 695-708, March.
    2. Juan R. A. Bobenrieth & Eugenio S. A. Bobenrieth & Andrés F. Villegas & Brian D. Wright, 2022. "Estimation of Endogenous Volatility Models with Exponential Trends," Mathematics, MDPI, vol. 10(15), pages 1-27, July.
    3. He, Zhechun & Simmons, Peter, 2022. "The impact of the minimum housing scale constraint on life-cycle risky asset and housing investment," Journal of Housing Economics, Elsevier, vol. 55(C).
    4. Zhechun He & Peter Simmons, 2018. "A Life Cycle Model with Housing Tenure, Constrained Mortgage Finance and a Risky Asset under Uncertainty," Discussion Papers 18/18, Department of Economics, University of York.

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    More about this item

    Keywords

    consumption; savings; strict concavity; value function;
    All these 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
    • Q11 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Aggregate Supply and Demand Analysis; Prices

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