A fashionable meme these days is the “questioning” of the Quantity Theory of Money. Evidently, one is considered naive who accepts that such a clear and transparent view of the economy could possibly be maintained.
pQ = mV
is a definitional tautology which defines mathematically the relationship between money and goods. It can be written dynamically by taking the natural logs of both sides of the equation and then differentiating with respect to time as,
p’/p +Q’/Q = m’/m + V’/V
We will demonstrate how application of this equation can give useful information. We will consider the plot of the Velocity between 1880 and 1966 shown above.
The smoothness of the velocity over this 86 year period suggests that the velocity can be expressed as a simple function of time. As the US was on the gold standard during this period, we know that p’/p = 0 This leaves
Q’/Q = m’/m + V’/V or, equivalently,
V’/V = Q’/Q – m’/m which is
V’/V = r – i The real interest r is K + E’/E where K is constant. Equilibrium is defined as E’/E = 0 which means that the employment percent is at a stable level. A reasonable value for
K is 0.045. K is the sum of the productivity growth rate, birth rate and capital depreciation constants.
It can be hypothesized that the interest rate i is a constant markup on r;
i = r + m so that
r – m = -m
so V’/V = -m giving ln V = -mt +ln V(0)
V/V(0) = exp(-mt) V(0) = 4.52 At (t – 1881) = 38, V = 2 (regression curve) so
ln(2/4.52) = – 38m –> -0.815 = -38m –> m = 0.02145
At t = -1 , V = 4.52*exp(-0.02145) = 4.62
From this we can conclude that banks in this period marked up the loans 2.1% over the real growth rate of 4.62% since V can be written in the alternative form V = i/(1-u). We assume that
- = 0.99 in 1880 so that V = 0.0462/(1-u) where (1-u) is the surplus value as previously defined. http://wp.me/P2kKxz-6g
From this, it can be concluded that
- credit was created 2.1%/year faster than the real growth of 4.62%
- the aggregate interest rate was 6.72%
- when V reached 1.5, the debt saturation (1-u) was 0.0462/1.5 = 0. 03075 around 1955
One wonders how many enterprises were not undertaken due to overly high interest rates, and what unproductive loans were made instead.