Untitled Document
Coins & bullion since 1973


Uses and Abuses of Gresham's Law
in the History of Money

by Robert Mundell
Nobel Prize for Economics, 1999


6. The Theory of the Breaking Point

The ancients recognized the attraction and succumbed to the fiscal temptations of replacing 'intrinsic' money with overvalued currency. But they did not know when to stop. How far could the precious metals be replaced without running the risk of inconvertibility, depreciation and inflation? What is the relation between the seigniorage benefit and the money supply or GDP?

John Stuart Mill had studied carefully the works of Hume and Smith and gave the following answer:

"Suppose that, in a country of which the currency is wholly metallic, a paper currency is suddenly issued, to the amount of half the metallic circulation. . .[There] will be nothing changed except that a paper currency has been substituted for half the metallic currency which existed before. Suppose, now, a second emission of paper; the same series of effects will be renewed; and son on, until the whole of the metallic money has disappeared. . .

Up to this point, the effects of a paper currency are substantially the same, whether it is convertible into specie or not. It is when the metals have been completely superseded and driven from circulation, that the difference between convertible and inconvertible paper becomes operative. When the gold or silver has all gone from circulation, and an equal quantity of paper has taken its place, suppose that a still further issue is superadded. . .The issuers may add to it indefinitely, lowering its value and raising prices in proportion; they may, in other words, depreciate the currency without limit."(27)

Mill concludes that:

"The substitution of paper for metallic currency is a national gain: any further increase of paper beyond this is a form of robbery."(28)

According to Mill, the "breaking point" at which the benign process of replacing 'intrinsic' currency for paper or overvalued coin is reached when the "cheap" or "bad" money has driven out all the "dear" or "good" money. To put the point arithmetically, suppose M is the total demand for money at existing prices and incomes. The money can be in either of two forms, gold or foreign exchange, R, or domestic paper money, D. Then M = R + D. If, with Mill, we start off with a purely metallic circulation, then D = 0 and R = M. Now suppose D is increased by half of M. Then R will be lowered by an equal amount. The process of substitution reaches its theoretical end point when R = 0 and D = M. After this point a further increase in D will increase M and lead to inflation along the lines of the quantity theory of money.

In practice, however, the limit is reached long before. As the public sees the process going on, it starts to anticipate the direction in which the government is proceeding and will sooner rather than later start to hoard the good money. The possibility of speculation therefore sharply reduces the extent to which the "good" money can be replaced. In the arithmetic example, we may suppose that confidence requires that a fraction, say , of the money supply is kept in the form of gold or foreign exchange. Then R = M, so that M = R+ D = M + D, and so D/M = 1-, which sets the feasible and safe limit of the substitution. If for example, equals one-third, the limit of the substitution would be two-thirds of the money supply. To translate this into a relation to GDP, we can assume that the money supply must be in equilibrium proportionate to money income, Y, so that M = kY, where k is the desired ratio of money to GDP. It follows that D/Y = (1 - )k. Further qualifications are needed to take account of banking systems.(29)

The opportunity for currency overvaluation and the exploitation of the monetary system as a fiscal device is not open to all countries. A sine qua non is the power to monopolize the coinage and to mandate its use as legal tender, two characteristics that require a strong central state. However, as already noted, the ancients were not very aware of the limits to the policy. A good example is Dionysius of Syracuse, who may have been influenced by Plato.

Syracuse was a Greek colony founded in 734 BC--in legend by Archias, from Corinth. After its government proceeded through the usual phases of feudal oligarchy, and monarchy, it succumbed, during the later stages of the Peloponnesian War, to a tyranny in the wake of invasions first by the Athenians and then Carthage. The new leader was Dionysius I, who ruled from 405 to 367 BC, "the strongest and longest tyranny of any recorded by history," says Diodorus.(30) What interest us is his coinage policy and his relationship with Plato, the philosopher who championed overvaluation and exchange control in his ideal Republic.(31)

In 388 or 387 BC Plato made the first of his three visits to Syracuse. Whether the idea derived from Plato, or from frequent earlier trials with overvalued money in the Greek states, Dionysius issued tin coins around this time overvalued four times.(32) The idea would be consistent with Plato -- at least the later Plato -- who held in The Laws that domestic money should be non-exportable, restricted in supply, and exchangeable with "Hellenic" money at what amounts to an exchange control authority. Dionysius' first issue must have been accepted because he tried it again, on the second occasion by overvaluing silver coins twice. Nevertheless, although he compelled these coins to be accepted under penalty of death,(33) the penalty was insufficient to keep these coins in circulation at their nominal value and they soon fell to their commodity value. Whether the story told by Plutarch, that Dionysius got rid of Plato by sending him to the slave market at Corinth, where several philosophers were present by a happy chance so they could buy his freedom, is true or not, Plato's intervention into the practical game of power politics proved to be a dismal failure.(34)

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