Sec. 7. #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 1/10 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 charge would be 1-10 of 90,000, or 9000 units.  No depreciation has taken place, and 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 1/10 below their money value.  As this process is repeated the excess 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 10 to 9.  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.

This process 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.