A model is constructed in which completely unbacked fiat money, issued by generic supplier implementing realistically specified monetary policy designed to obey certain sufficient conditions, is endogenously accepted by rational individuals at uniquely determined price level. The model generalizes Lucas (1978) to an economy with frictions and specialization in production, without imposing the cash-in-advance constraint. The uniqueness of equilibrium is the consequence of complete characterization of both the environment, and the equilibrium concept. The results challenge the doctrine that equilibria of monetary economies are inherently indeterminate, and that money can become worthless only due to self-fulfilling expectations. The paper shows that monetary policy canonically features two dimensions, one of which corresponds to nominal interest rate, and the other to continuous helicopter drop of net worth, which in the model takes the form of universal basic income.