The introduction of banks that issue money and supply balances and pay out their profits as dividends is the natural modification of the model of general competitive equilibrium that encompasses monetary economies. Competitive equilibria exist. Nevertheless, eventhough there is a well defined money market, competitive equilibrium allocations are indeterminate. On an event tree with N nodes, of which S terminal, there are N + S degrees of nominal and, possibly real, indeterminacy. Monetary policy removes some degrees of indeterminacy through a choice of instruments, set according to a state-contingent rule. Interest rates are suitable instruments for the control of expected inflation but not of the variability of inflation. Monetary policy is also effective due to redistributive effects and nominal rigidities.
Dreze, J., & Polemarchakis, H. M. (1998). Intertemporal general equilibrium and monetary theory (CORE Discussion Papers 1998/53). https://hdl.handle.net/2078.5/128111