Real Bills Doctrine - Bank Runs

Bank Runs

Suppose that the gambler’s IOU falls in value from $300 to $200, so that the market value of the dollar is now given by the equation: 100+400E=600E, or E=0.5 oz/$. If the bank tries to maintain convertibility at the original rate of E=1.0 oz/$, it will face a bank run. Customers see that a dollar will fetch only 0.5 ounces of silver on the market, and so they all rush to the bank for the chance of getting 1 ounce for that dollar. The bank, for its part, loses 0.5 ounces for every dollar redeemed at this rate, and this loss of assets causes the value of the dollar to fall still more. For example, if the bank redeems $40 for 40 ounces, then setting assets equal to liabilities yields 60+400E=560E, implying E=0.375 oz./$. If the bank pays out its last 60 ounces of silver for $60, then the equation becomes 0+400E=500E, or E=0.

At this point the bank will be out of business and the dollars it issued will have lost all value. But the worst problem is that the real value of the community’s money supply would have fallen. Originally, the total money supply consisted of $600, with an aggregate real value of 600 ounces. After the gambler’s IOU fell in value, the $600 in circulation had an aggregate real value of only 300 ounces. Money would be “tight”, and economic activity would be hampered. By the time the bank collapsed, the $500 still in the hands of the public would be worthless, and the only usable money left would be the 100 ounces of silver in the hands of the public. The resulting restriction of the money supply would be recessionary, since people would not have enough money to conduct their business conveniently.