## Wednesday, June 19, 2013

### Does multiplying the monetary base by 2 cut the value of cash by 2 or ... e?

A quick note on the idea seemingly accepted throughout economics that an instant doubling of all the cash would ceteris paribus decrease the value of that cash by half (and e.g. prices would double). See this diagram here; the curve is reproduced as a dashed gray curve above. It seems to derive from a particular marginal utility model of cash (where value is inversely proportional to the quantity).

If we use the information transfer framework, instead of ~ 1/x, we have ~ log 1/x behavior (shown in blue in the figure above, see Eq. 8a,b here). For small changes the 1/x scaling approximates the curve (log 1/x ~ -1 + 1/x near x = 1), but for larger shifts 1/x underestimates the decrease in value (and over estimates the increase in value)

The information transfer framework shows that under a doubling of the monetary base (ΔM/M = 1) the value of cash decreases to ~ 1/e ≈ 0.37 < 0.5.

Instead of an "inversely proportional fall in marginal utility", you would see a "logarithmic fall in relative bandwidth utilization". If I double the number of bits available to describe the economy, the quantity of states goes up by much more than a factor of two.

#### 1 comment:

1. I should note that the axes are transposed as is frequently done in economics -- "x" in the above is the vertical axis and "y = log 1/x" is the horizontal axis.