ABSTRACT
The original meaning of seigniorage, the difference between the circulating value of a coin and the cost of the bullion and minting, involves a once-for-all gain to the issuer on the issue of money. Owing to the durability of the precious metals, especially gold, one can reasonably assume that this gain is realized only once per unit of money in existence, though, presumably, worn, clipped or sweated coins would come back eventually for melting down and reissue. If one wished to take account of that, one would regard the money supply as yielding a flow of seigniorage (v − c)1, (v − c)2, …, (v − c)∞, which could in turn be summed into a capital value of the right to issue money: https://www.w3.org/1998/Math/MathML"> ∑ t = 0 ∞ v − c ( 1 + i ) t = ( v − c ) 1 + i i https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203482155/a9cd2c86-eff4-4b5f-9891-4f8828198142/content/math111_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where v is circulating value, c cost, and i the interest rate ruling over the period between recoinages. This expression differs from the usual formula for the capitalized value of an income flow because the first yield accrues immediately.
