One Plus One Equals Two?

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Courtesy of Sandeep Jaitly @ Fekete Research:

Gold coins were offered in series by the various mints. Standard gold brought to the mint could be returned not only in the unit gold coin (for example, the Sovereign) but also any the fraction (Half-Sovereign) or multiples. Should there be a preference for one’s gold to be returned in half-unit gold coins, would it be as simple as opting for twice the number of half-unit gold coins, instead of the original number of unit
gold coins?

On a slightly closer inspection, it cannot be. The work expended in making two half-unit gold coins is greater than the work expended in making one gold unit coin. This much is obvious. On further inspection, two half- unit gold coins could obtain more goods than a unit gold coin could. What one is willing to do with two half- unit gold coins and not willing to do with one unit gold coin leads to the idea of change.

For example, imagine you need a pair of shoes. An acceptable pair is on offer for one unit gold coin and one half-unit gold coin. If you only had a double-unit gold coin about your person and the shopkeeper didn’t have the means to offer change for it, you wouldn’t walk out with a pair of shoes (unless you’re an exceptionally charitable tipper.) However, were you to walk into the shop with four half-unit gold coins, you would walk out with a pair of shoes (and one half-unit gold coin.) Continue reading