The Small-Change Problem: The Three Options--Strike All Coins from the Standard Metal, Use Bimetallism, or Issue Fiduciary (Token) Coins--All Had Drawbacks

How might the eighteenth-century British government have tried to supply its citizens with small change? Having defined its basic monetary unit in terms of one precious metal, the government faced three options. It could

1. strike both large- and small-denomination coins from the standard metal, with the coins' weights corresponding to their face values;
2. resort to bimetallism, with low-denomination coins made from the less valuable metal, and large-denomination coins made from the more valuable one; or 
3. issue avowedly fiduciary or token small-denomination coins, on government account. 

Each option had its drawbacks. [What follows is a much-simplified analysis of the small-change problem.]

Under the first option, if the standard metal was sufficiently valuable, coins of lower denominations would be too small to be practical, as happened with Great Britain's quarter guineas. A still more egregious case was that of the silver farthings the Royal Mint issued in 1464. Weighing only three troy grains each, these were "lost almost as fast as they were coined." The standard metal could, of course, be one from which convenient small-denomination coins might be made; but then large-denomination coins of the same metal would end up being too bulky. 

A bimetallic system might have avoided the problem of undersized or oversized coins. But it suffered from its tendency to give effect to Gresham's law, with one metal alone being taken to the mint for coining and with coins of the other metal being clipped, filed, sweated, or melted. The nation would then be exposed to shortages of decent small or large change, depending on which metal was overvalued. The situation might not be much better, in other words, than if the mint stuck to a single metal. 

The token coinage alternative, finally, had its own peculiar drawback: the large difference between token coins' nominal, or face, value and their "intrinsic worth" would tempt counterfeiters. Unless legitimate coins could be distinguished from fake ones (by mint authorities, if not by the general public), false coiners would foil the mint's attempts to keep the supply of token coins in line with the demand for them, causing both real and fake token coins to be discounted. If the mint tried to limit the supply and prop up the value of its token coins by offering to redeem them in full-bodied (silver or gold) coin, counterfeiters might take the mint to the cleaners. If, on the other hand, it avoided losses by refusing to take back unwanted coins, counterfeiting might give rise to a glut, eventually driving the tokens' value down to a level no greater than their "intrinsic worth," and making them no more fit to serve as money than matches, nails, or . . . buttons. 

--George Selgin, Good Money: Birmingham Button Makers, the Royal Mint, and the Beginnings of Modern Coinage, 1775-1821; Private Enterprise and Popular Coinage (Oakland, CA: The Independent Institute, 2011), 13-15.

Under Gold/Silver Bimetallism, Silver Is "Overvalued" and Gold "Undervalued" at the Mint if the Gold/Silver Mint Ratio Falls Short of the Market Prices Ratio

The mint price of bullion is the nominal or "face" value of coins given in exchange for bullion brought to the mint, while the mint equivalent is the nominal value of coins actually made from the bullion. When coinage is gratuitous, as it was in Great Britain, the two values are equal. Otherwise, the mint price will fall short of the mint equivalent by the charge for coinage, which may include a profit to the mint or government. That profit is known as seigniorage, after the lords, or seigneurs, who exercised the right of coinage in medieval France. . . . 

Under bimetallism, the government allows free coinage, usually with little or no seigniorage, of two metals, assigning a mint equivalent and corresponding mint price to each. The mint ratio is the ratio of mint prices for the two metals, which represents the relative values assigned to them by the mint. For example, if the mint pays £44 10s (or 890 shillings) in gold coin for each troy pound of gold brought to it, while paying £3 2s (or 62 shillings) in silver coin for each troy pound of silver, the gold/silver mint ratio is 890 ÷ 62 = 14.355. A pound of gold is, in other words, officially worth 14.355 times as much as a pound of silver.

In a gold and silver bimetallic arrangement, silver is said to be overvalued and gold undervalued at the mint if the gold/silver mint ratio falls short of the ratio of the metals' market prices. Suppose, for example, that a pound of gold is worth thirteen times as much as a pound of silver in the open market. In that case, a mint ratio of 14.355 overvalues gold while undervaluing silver. Even if some mint ratio is initially consistent with market prices, changes in the metals' relative scarcity are likely eventually to cause one to become officially undervalued relative to the other.

--George Selgin, Good Money: Birmingham Button Makers, the Royal Mint, and the Beginnings of Modern Coinage, 1775-1821; Private Enterprise and Popular Coinage (Oakland, CA: The Independent Institute, 2011), 10-11.