Nominal rigidities equilibria in a non-Ricardian economy

I consider a cash-in-advance economy with nominal price rigidities. Nominal interest rates are the cost of liquidity and fiscal policy sets nominal transfers that affect the distribution of wealth. Under a fiscal policy associated with an unequal distribution of wealth and for policies of low or even zero interest rates, coordination failures exist, that is, involuntary unemployment persist even if prices are set at full employment levels. Coordination failures exist if and only if nominal rates are below a threshold. Moreover, I demonstrate the following result on welfare: full employment allocations at a nominal rate equal to the threshold (high liquidity costs) are better, in terms of welfare, from unemployment allocations at any non-negative interest rates below the threshold. On the other hand, under a sufficiently progressive fiscal system that reduces the inequality in the wealth distribution, coordination failures do not exist.