A note on Bitcoin’s monetary disequilibrium

After the two interviews that Adrian and I did for Semanario Virtud (here and here), the problem of monetary equilibrium became an issue of interest in the comments section. This is a point that we both think it deserved a more specific discussion. Can Bitcoin guarantee monetary equilibrium? And if not, can this problem be solved?

Like in any other market, monetary equilibrium is achieved when money demand equals money supply. Also, in this market, equilibrium is more efficiently achieved when changes in money demand are matched by changes in money supply (not too different to many other markets that see supply increase when demand does.) Therefore, the price of money (1/P) remains stable unless there are changes in productivity. A change in productivity changes the relative quantities of goods and services to money supply, therefore a change in the relative price of money with respect to goods and services (1/P). This, also, is the reason why this is referred as the productivity norm: the price level should change inversely with respect to changes in productivity.

We know, then, that the monetary equilibrium condition can be approximated by stating that MV = Py = constant per unit of factor of production (where V is the inverse of money demand.) Therefore, changes in V are compensated by changes in M (money supply.)

There are two reasons of interest why P may fall: 1) an increase in y (real output) and 2) a fall in V that is not compensated by an increase in M.

In the first case, the increase in output is the result of an increase in productivity. This means that with the same amount of inputs more goods can be produced (lower average cost of production.) This means that in a competitive market prices of final goods and services will fall until there are no more economic profits. Because factors of production keep earning the same nominal income (W), real income (W/P) increases. In this case, any change in relative prices inside P captures the change in productivity of particular industries. This is the case of “good deflation.”

In the second case, an increase in money demand (hoarding) means that there is less money in circulation buying goods. Therefore, the demand of certain goods will fall and so will prices. However, in this case, the change in relative prices will not capture changes in productivity. Some good see their demand fall before, and some good see their demand fall later. If money demand increases, the first buyer faces the same old prices with less money ready to be spent, which means he has to cut down consumption of some goods. The last buyer (who may have not changed his money demand) can go into the market with the prices updated. This is no other thing that the Cantillon effects that occur during inflation with the caveat that the price level is going downwards rather than upward. This is the case of “bad deflation.” It requires an heroic, and I would say wrong, assumption to sustain that too much money affects relative prices but a shortage of money supply that pushes the prices down somehow affects all prices at the same time. This problem is not solved by dividing bitcoins into very small units any more than a rules that is too short for our needs does not become larger by measuring in millimeters rather than centimeters. It is the change in units of account what becomes a problem.

This case, also, requires an adjustment in the price of factors of production. Because there has been no change in productivity, the ratio of final prices (IPC) to producer prices (PPI) should remain the same (IPC/PPI). How will the pattern of reduction in the payment to factors of production (W) match the pattern of reduction the price of final goods and services (P) occur without affecting relative prices? What if wages and other intermediate goods prices are downward inflexible?

Assume a gold standard, a fiat money regime, and bitcoin money regime, then:

  1. GmV = Py
  2. FmV = Py
  3. BV = Py

where G: gold, F: fiat money, B: bitcoins, m: money multiplier.

In a free banking with gold standard changes in V can be compensated with changes in either G or m. Namely, an increase in money demand (V falls) increases the reserves held in bank accounts. Banks, then, increase the circulation of banknotes increasing M (Gm). The role of “m” is to make Gm neither too inelastic nor too elastic (the problem with Fm).

In the case of Bitcoins, however, there is no money multiplier because there is no banking system developed. This is a similar case to that of a gold standard without banks (or, what is very similar, a 100-percent reserve requirement). In such case m = 1.

This means that changes in the demand for base money (bitcoin or gold) have to be compensated by changes in base money. If this is not possible, then the result is the “bad deflation” scenario. It produces a similar result to say that all of a sudden money supply is contracted by a 10% than to say that all of a sudden money demand increases by 10% but money supply remains fixed. Both scenarios offer the same type of disequilibrium, money shortage.

It should not be a matter of confusion the fact that any money supply can be efficient at equilibrium is quite different to the statement that that any money demand is efficient at any point in time. If this where the case, then inflation wouldn’t be a problem either.

The bitcoin rule, then, faces a challenge. The more successful it becomes, the higher the increase in demand. But the evolution of bitcoin supply is predefined. This means than an excess in bitcoin demand cannot be compensated by an increase in bitcoin supply. In this sense, the bitcoin rule is inefficient in the same way that a 100-percent reserve requirements would be in a free banking regime is inefficient. The bitcoin protocol is focus on limiting money supply instead of the focus being on monetary equilibrium.

This inelasticity of bitcoin supply may be solved with the presence of issuer banks similar to the case of free banking. A bank that issues convertible banknotes to bitcoins instead of gold. Then the monetary equilibrium equation for Bitcoin becomes: BmV = Py.

This, however, may be a necessary but not a sufficient change in the bitcoin world. It is possible that the amount of base money (bitcoins) is too low to support the reserves of the system. This wouldn’t be the case if we are already at equilibrium and the price level can be any level we need it to be. But the bitcoin is that of transition, not that of being in equilibrium. Can gold standard work with only one ounce of gold in the whole world (assuming we can divide the gold in pieces as small as we want)? One ounce of gold won’t be enough gold for the banks to have a safe level of reserves unless the prices are low enough. The transition problem from today prices to the prices required for one ounce of gold to be enough cannot be ignored.