We study an infinite horizon economy with a representative agent whose utility function includes consumption, real balances and leisure. Real balances enter the utility function pre-multiplied by a parameter reflecting the inverse of the degree of financial market imperfection, i.e. the inverse of the transaction costs justifying a positively valued fiat money. Indeterminacy arises both through a transcritical and a flip bifurcation: somewhat paradoxically, the amplitude of the indeterminacy region improves as soon as the degree of market imperfection is set lower and lower. Such results are robust with respect to the choice for the elasticity of the labor supply, both when the latter is set close to zero and to infinite. We also provide conditions for the existence, uniqueness and multiplicity of the steady states and, finally, we asses the impact of the degree of market imperfection on the occurrence of such phenomena.