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Equilibrium Dynamics in a Two-Sector OLG Model with Liquidity Constraint

Author

Listed:
  • Antoine Le Riche

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - École Centrale de Marseille - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université)

  • Francesco Magris

    (CAC-IXXI, Complex Systems Institute, LEO - Laboratoire d'Économie d'Orleans [UMR7322] - CNRS - Centre National de la Recherche Scientifique - UT - Université de Tours - UO - Université d'Orléans)

Abstract

We study a two-sector OLG economy in which a share of old age consumption expenditures must be paid out of money balances and we appraise its dynamic features. We first show that competitive equilibrium is dynamically efficient if and only if the share of capital on total income is large enough while a steady state capital per capita above its Golden Rule level is not consistent with a binding liquidity constraint. We thus focus on the gross substitutability in consumption and on dynamic efficiency assumptions and show that, gathered together, they ensure the local determinacy of equilibrium and, as a consequence, rule out sunspot fluctuations. In addition, we prove that the unique steady state may change its stability from a saddle configuration to a source one (undergoing a flip bifurcation) for a capital intensive investment good as well as for a capital intensive consumption good, when the elasticity of the interest rate is set low enough. However, when the investment good is not too capital intensive, the flip bifurcation turns out to be compatible with high elasticities of the interest rate too. Analogous results within dynamic efficiency are found in the non-monetary model, the existence of a flip bifurcation requiring now a capital intensive investment good. Eventually, under dynamic inefficiency, in the non-monetary economy local indeterminacy may instead appear, either through a Hopf bifurcation or through a flip one, and its scope improves as soon as the consumption good becomes more and more capital intensive.

Suggested Citation

  • Antoine Le Riche & Francesco Magris, 2016. "Equilibrium Dynamics in a Two-Sector OLG Model with Liquidity Constraint," Working Papers halshs-01199654, HAL.
  • Handle: RePEc:hal:wpaper:halshs-01199654
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01199654v2
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    money demand; two-sector; overlapping generations; dynamic efficiency; equilibrium dynamics;
    All these keywords.

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E41 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Demand for Money
    • E50 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - General

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