The Federal Reserve Act calls upon the newly created Banks "... to furnish an elastic currency..." since such action was thought to be welfare improving during times of high currency demand. This paper considers the welfare implications of an "elastic currency" regime within the context of an overlapping generations model of fiat money that includes banks that face aggregate risk. Although in the economy's stationary equilibrium the bank chooses to hold both fiat currency and illiquid capital in its portfolio, it would prefer to hold additional amounts of currency (were they available) during periods of high withdrawal demand. To remedy this problem, a central bank is introduced that offers zero-interest, intraperiod loans of currency via a discount window. When the central bank optimally chooses the size of the loan, it is shown that the resulting stationary equilibrium supports the economy's "golden rule" allocation.