Abstract

We study a two-sector OLG growth model in which a share of old age consumption expenditures must be paid out of money balances and 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 per capita capital above its Golden Rule level is not consistent with a binding liquidity constraint. We thus focus on the gross substitutability assumption in consumption and on dynamic efficiency and show that, gathered together, such assumptions 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 much 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 the 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.