§ 7. Fiduciary coinage on governmental account. The fiduciary coinage problem may be presented also when coinage is not free, and the times and amount of coinage are determined by law or by legally authorized officials. In this case the bullion must be obtained by purchase in the open market (and paid for by some form of legal money, or by bonds). Coinage is then said to be "on governmental account."

Now, assuming that the normal money demand (the volume of business or sum of exchanges) remains unchanged, let us consider what will result if the government begins to issue money in this way when, as in the preceding case, 100,000 units of full-weight money are in circulation. This action might be taken most simply by recoining all the full-weight pieces that came into the treasury, making them contain one tenth less precious metal, and paying out 1111 pieces for every 1000 received. Every time this was done there would be an excess of 111 pieces above the normal money demand, and 111 full-weight pieces would be exported or melted (Gresham's law). The process (in strict theory) may be repeated 90 times, at which point 90,000 full-weight coins have been received, 100,000 light-weight coins have been issued to take their place, and 10,000 full-weight coins have gone out of circulation. The total seigniorage profit would be one-tenth of 90,000, or 9,000 units of bullion. No depreciation has taken place,4 the pieces, by reason of their limitation, bear a money value in excess of the bullion that is in them.

Now the government, with the next 1000 pieces collected by taxation, could buy enough bullion (in the open market) to make another 1111. The excess of 111 pieces could not now be promptly removed by the melting down or exporting of 111 coins, for all those remaining in circulation have a bullion value one tenth below their money value. As this process is repeated the number of coins must continue to grow from 100,000 to 111,111, and the value of the money piece in terms of bullion continue to fall from ten to nine. At this point the 111,111 pieces would contain just the same amount of bullion and have just the same value as the 100,000 pieces did before. Thereafter no further profit would accrue to the government from issuing coins of that weight. To make a further profit it must again reduce the amount of pure metal in the coin.

4 In this and following numerical examples no account is taken of the possibility that the standard metal may depreciate in the world market in terms of all other goods as a result of its diminished use as money in one or more countries. This properly belongs in a more complete theoretical treatment of the subject.

§ 8. Two stages of coinage debasement. It will be seen that, taking the number of full-weight coins at the saturation point as parity (when price is 100), then (a) price rises directly as the number of units of money; (b) the value of the monetary unit is the reciprocal of price (changes inversely with the number of units of money).

When a new seigniorage charge is imposed, the change in the physical content of the coin is called debasement. Two stages of this change may be distinguished (as is shown in the preceding description). The first stage is debasement without depreciation of the monetary unit; the second stage is debasement with depreciation. In the first stage the monetary unit, as a result of limitation, has an artificial value in excess of its bullion value; in the second stage its monetary value falls toward its bullion value, but may (depending on limitation) rest anywhere between the former full-weight bullion value and the new bullion-content value.

The process illustrated above was often repeated in the Middle Ages. A ruler, either by making a higher seigniorage charge or by coining on his own account, debased the quality or reduced the weight of the money of his realm. For a time the new coins, having the same monetary use, circulated at par with the old coins. The ruler, pleased with this almost magical power of getting a revenue with little trouble, continued to issue coins, until suddenly the heavier coins began to be exported or melted, and the value of the other money fell, to the mystification alike of the prince and of his people. The reason is now perfectly plain: the number of coins was not kept within the proper limits and they went down to their bullion value. The only way a further profit could be made in this way was to debase the coin again. By successive steps the coinage came to consist almost entirely of cheaper alloy.

§ 9. The gold-exchange standard. In a number of silver-using countries and colonial dependencies near the end of the nineteenth century, the fluctuations of the value of silver in terms of gold was a constant source of difficulty in the payment of foreign obligations to gold standard countries. Yet there were strong reasons in the habits of the people and in the industrial conditions of the country to prevent the adoption of gold and the disuse of silver as the actual money in circulation. The method adopted, that of the gold-exchange standard, in operation in India since 1893, in the Philippines since 1903, and in Mexico since 1904, involves these features:

(1)   Closing the mints of the country to the free coinage of silver.

(2)   Adoption of a fixed ratio of exchange between the silver coins in circulation and a gold coin which is made the standard of value in all transactions (as the dollar or the pound sterling), the money in circulation thus being all or nearly all of a fiduciary nature.

(3)   Regulation and limitation of the amount of silver money in circulation, so that a fixed parity between it and gold may be maintained, (a) by issuing coins in limited number and only on governmental account; (b) by the sale, at a fixed rate, of foreign exchange bills payable abroad in the standard unit, the money paid for the bills being withheld in a special reserve, thus reducing the total volume of money in circulation; (c) by the purchase of foreign bills of exchange at a fixed rate, thus paying out and putting again into circulation some of the fiduciary money in the special reserve.

These monetary changes furnish numerous illustrations and demonstrations of the quantity theory of money as applied to the entire circulating medium of the country.5 The silver coins which alone are in actual circulation become fiduciary by reason of the artificial limitation of their number, and their monetary value is made to conform to the value of gold 6 as used in international trade.

5 See "Modern Currency Reforms" (1916), by E. W. Kemmerer, professor of Economics and Finance in Princeton University, for a detailed rapt governments. Governmental paper money differs from bank-notes in that its value does not necessarily depend on the promise of redemption by the issuer. It differs from promissory notes and bonds in that its value is not based on the interest it yields, but mainly on its monetary uses. The issue of paper money may save the government the payment of interest on an equal amount of bonds. The promise to receive paper in payment for taxes or for public lands may help to maintain its value by reducing its quantity, but nothing short of its prompt redemption in standard coins makes it truly redeemable.