Crises in competitive versus monopolistic banking systems

We study a monetary, general equilibrium economy in which banks exist because they provide inter-temporal insurance to risk-averse depositors. A "banking crisis" is defined as a case in which banks exhaust their reserve assets. This may (but need not) be associated with liquidation of a storage asset. When such liquidation does occur, the result is a real resource loss to the economy and we label this a "costly banking crisis." There is a monetary authority whose only policy choice is the long-run, constant rate of growth of the money supply, and thus the rate of inflation. Under different model specifications, the banking industry is either a monopoly bank or a competitive banking industry. It is shown that the probability of a banking crisis may be higher either under competition or under monopoly. This is shown to depend on the rate of inflation.