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.)

How is this potential problem solved? How was it solved in the past? Was it solved in the past? Sadly, the problem wasn’t solved in the past and was brushed over with a bit of positivism with numbers. When the mints were open and ‘free’ (including the cost of assaying, refining and manufacturing which was covered by the state) to the coinage of gold coins, gold could be returned in unit gold coins or twice the number of half- unit gold coins at no visible cost. The extra work expended in creating half-unit gold coins was somehow brushed over. In the absence of a taxing authority, this apparently equivalent offer would not be available. A variation on this can also be observed with the ‘tolerance and abrasion standards.’ Legally, a gold Sovereign coin of 7.98805g fine gold can be accepted as a ‘gold Sovereign coin’ as long as it weighs more than 7.93787g (0.63% of the actual definition †.) Accordingly, a ‘gold Sovereign coin’ can be one of two things in extremum and it tended to the inferior. Freshly minted gold Sovereigns would have been ‘sweated’ (shaken in a bag to obtain gold residue) to get as close as possible to the minimum legal weight before being circulated because of this positivist muddling. Gresham’s ‘law’ is a consequence of this dichotomy…

This problem could be solved without the ‘aide’ of the state in a number of ways. The difference in cost between minting and receiving one unit gold coin versus two half-unit gold coins should be borne by the person directly depending on their preference, not indirectly through total subsidization. Retailers offering ‘change’ to customers expensing this likely minute cost differential themselves would be more likely to get business compared to those not offering ‘change’ without a cost.

We have defined ‘one plus one’ is ‘two’ but we must not make the mistake of thinking ‘one plus one’ as being ‘two.’

Sandeep Jaitly, Fekete Research, 18th August 2014.

(†) Coinage Act 1971, http://www.legislation.gov.uk/ukpga/1971/24/pdfs/ukpga_19710024_en.pdf

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