|Elijah and the Widow of Zarephath|
The phrase widow's cruse is defined as "an inexhaustible supply of something," which in turn is a reference to an obscure Bible story. Flip to I Kings 17:7–16 and there is a short passage in which the prophet Elijah asks a destitute widow to make him a loaf of bread. The Lord blesses the widow saying that the "jar of flour will not be used up and the jug of oil will not run dry until the day the Lord sends rain on the land."
What Tobin was referring to in his paper is that unlike the widow and her jug of oil, commercial banks aren't blessed with the ability to expand their liabilities indefinitely. When it comes to bank deposits, there is an "economic mechanism of extinction as well as creation, contraction as well as expansion."
Modern central bank's, on the other hand, do have such a cruse. Once central bank liabilities are created, there is no way for the economy to get rid of the excess. The hot potato analogy "truly applies", noted Tobin, because central bank money cannot be extinguished.
We know that the actions of any institution in possession of a widow's cruse will have major macroeconomic effects. With its cruse, a central bank can create excess media of exchange which, as it is passes from hand to hand, pushes up nominal income. An increase in quantities and/or prices is the only release valve for unwanted exchange media. A commercial bank, which has no cruse, might create an excess of deposits but this will not have any lasting influence on nominal income. After all, if the public doesn't desire new deposits, this excess will either quickly reflux back to the issuer, or it will displace competing deposits created by another bank and these deposits will reflux. To keep its deposits suspended in the economy will require a commitment of resources (say a superior interest rate). But resources are finite, unlike the widow's cruse.
Central banks didn't always have cruse. As David Glasner reminds us, when a central bank's liabilities, say those of the Bank of England, were convertible into gold, the Bank couldn't issue in excess of the public's desire for central bank notes. Unwanted notes would quickly return back to the Bank, inhibiting the Bank from having any macroeconomically important effects. The Bank of England, much like a modern commercial bank, could affect neither prices nor quantities via excess note issuance.
So what are the sufficient conditions for having a cruse? Consider that there are all sorts of financial instruments that can be expanded indefinitely. A company can continue issuing corporate stock, for instance, as long as it wants. To crib from Tobin, any expansion of corporate assets will generate a corresponding expansion of corporate liabilities, or in this case, equity. The mechanism for the creation of stock does not have an equivalent mechanism for the extinction and contraction of said stock. Without an instant-convertibility clause, stock is a perpetual instrument, much like modern central bank money. [For more along this line, see Money: is it immortal or does it die young?].
Despite its perpetual nature, I don't think that a stock-issuing company is blessed with a widow's cruse. An exogenous increase in the quantity of an individual company's stock will only affect relative asset prices; it won't change an economy's nominal income. To paraphrase Tobin, the burden of adaptation to an increase in the quantity of a corporate stock is not placed on the entire economy. This is because prices in an economy are not denominated in units of a given corporate stock, but in dollars, pounds, or whatever. Central bank money, on the other hand, is the economy's unit of account. The entire economy is burdened by the necessity of adapting to an increase in its supply.
So what does it take to have a widow's cruse? Two things. The liabilities of the issuer must be perpetual and non-convertible upon demand. Secondly, shops and markets must use those liabilities as a unit of account. Only when these two conditions will a widow's cruse have emerged. Commercial banks pass the latter but fail the former. Stock-issuing non-financial corporations pass the former but fail the latter. Only modern central bank money is both.