We develop a New Monetarist model with expenditure and unemployment risks that generates equilibria with non-degenerate distribution of money holdings. Distributional effects can overturn key insights of the model with degenerate distributions such that, e.g., the value of money depends on the income distribution, a one-time money injection raises aggregate real balances in the short run - price adjustments look sluggish; anticipated inflation can raise output and welfare; there can be a long-run trade-off between inflation and unemployment. Our model features an aggregate demand channel through which transfers to workers can raise employment and a new amplification mechanism of productivity shocks.
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