Unlendable Money Fallacy

The Fisher Equation must be used for combining a rate of growth in a money that is itself subject to inflation, as depreciation occurs in the future money. This adjusts the nominal interest rate to obtain the real interest rate. Presentation is simplified by using ratios in place of rates. As shown in Depreciation Principle, the commodity money growth rate is 0%, or a growth ratio of 100%.

Monopoly money exhibits depreciation due to seigniorage.

monopoly-money-growth-ratio = commodity-money-growth-ratio / seigniorage-ratio.
100% / 103% = ~97%

Fixed supply money may appreciate due to price deflation.

fixed-supply-money-growth-ratio = commodity-money-growth-ratio / inflation-ratio.
100% / 97% = ~103%

A fixed-supply money is often presumed to change in purchasing power in proportion to the products it represents (i.e. demand). In other words, with twice the amount of products each unit of the money will trade for twice its previous amount of products.

purchasing-power-this-year = purchasing-power-last-year * annual-growth-ratio
103 = 100 * 103%

The presumption of fixed-supply money price deflation also rests on the assumption of positive economic growth. In the case of economic contraction the money exhibits price inflation. The case of economic growth (increasing wealth) implies interest exceeds depreciation. Both interest and depreciation must always be positive as implied by time preference.

interest-ratio > depreciation-ratio > 100%
interest-ratio / growth-ratio = depreciation-ratio
interest-ratio / growth-ratio > 100%
interest-ratio > growth-ratio

Economic contraction (decreasing wealth) implies an increasing rate of interest, as implied by the theory of marginal utility, until positive growth is restored. As such contraction is a self-correcting condition.

depreciation-ratio > interest-ratio > 100%
interest-ratio / growth-ratio = depreciation-ratio
interest-ratio / growth-ratio > 100%
interest-ratio > growth-ratio

Notice that in both cases of economic growth and contraction, interest must exceed growth, as lending is the only source of growth. Given that growth is the sole basis of deflation in a deflationary money, hoarding the money represents monetary depreciation (consumption).

There is a theory that it is economically irrational to lend a deflationary money. As has been shown, it is rational to lend any money, including one that is deflationary, invalidating the theory. Any contrary behavior implies a purely speculative condition, not supported by the fact of fixed supply.