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

Antoine Le Riche and Francesco Magris

Chapter Chapter 7 in Sunspots and Non-Linear Dynamics, 2017, pp 147-174 from Springer

Abstract: Abstract We study a two-sector $$\textit{OLG}$$ 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.

Keywords: Overlapping generations; Two-sector; Money demand; Dynamic efficiency; Equilibrium dynamics (search for similar items in EconPapers)
JEL-codes: D24 E30 E32 E41 E50 (search for similar items in EconPapers)
Date: 2017
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Related works:
Working Paper: Equilibrium dynamics in a two-sector OLG model with liquidity constraint (2017)
Working Paper: Equilibrium Dynamics in a Two-Sector OLG Model with Liquidity Constraint (2016)
Working Paper: Equilibrium Dynamics in a Two-Sector OLG Model with Liquidity Constraint (2015)
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DOI: 10.1007/978-3-319-44076-7_7

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