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.