Multiple equilibria in a cash-in-advance two-sector economy

We consider a two-sector infinite horizon economy with a fractional cash-in-advance constraint on consumption expenditures. This formulation allows us to consider a steady-state velocity of money that is strictly greater than one and, therefore, provides a more plausible framework than the standard formulation in which all the consumption purchases are paid cash. We prove that the steady state is bound to be indeterminate and multiple equilibria occur when the share of the liquidity constraint is low enough and that a capital-intensive investment good or a strongly capital-intensive consumption good improve considerably the scope for indeterminacy. As a consequence, we show that without any restriction on the elasticity of intertemporal substitution in consumption, multiple equilibria might occur if the velocity of money is greater than a critical bound that is compatible with empirical estimates.