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Monetary Equilibrium and Relative Prices

February 13, 2012
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There’s long been debate on the role of an elastic money supply in achieving monetary equilibrium in a free market. Namely, should the money supply follow a 100-percent reserve requirement on banks or should banks be allowed to make use of fractional reserves. The debate offers two lines of reasoning. An ethical argument in favor (and against) of the 100-percent rule, and an economic argument in favor (and against) the 100-percent rule. The 100-percent argument maintains, in the former line of argumentation, that fractional reserves represent a fraudulent practice, and in the latter that fractional reserves produce economic imbalances and, therefore, should be avoided. This debate has been long standing, and sometime seems to have become untidy or disorganized. Such is the situation, that key terms like ‘savings’ and ‘inflation’ have a different meaning in the 100-percent and free banking literature. The debate has a terminological barrier that sometimes results in arguments passing one over the other.

A recent working paper by Will Luther and Alexander W. Salter (2011), however, contributes in re-phrasing the argument into the key points, and in doing so they point to the key issue of the role of the money supply in monetary equilibrium and relative prices. The question that requires an answer is, “How should the money supply react when there is a change in money demand?” Should the money supply increase so that the price level remains stable, or should money supply be fixed (in the extreme case, a vertical line) and let the price level fall? [in the case of 100-percent rule, changes in money supply would equal changes in the supply of the commodity used as money, namely, money multiplier will be equal to 1].

Luther and Salter point to two problems: (1) the cost of adjustment in relative prices and (2) Cantillon effects (wealth transfers through non-neutral effects brought by changes in money supply). Both, of course, are closely related.

For the sake of argument, let as assume that whether or not there is a change in money supply, the final relative prices that will prevail are the same. Namely, we’ll assume long-run neutrality for the money supply. I am not arguing that money is neutral in the long-run, but that for the sake of simplicity I will assume that that is the case. Namely, that the only difference in the vector of prices is the nominal level, not the relative prices. An illustration of this can be two straight lines with different intercept but the same slope. What differs between these two lines is their level, not their slope. Therefore, if there is an increase in money demand, should the money supply change so that the line remains at the same level, or should it be fixed, and let the straight line change its level? Even though any quantity of money can be optimal, and produce the correct vector of relative prices, that does not mean that any quantity of money supply is optimal at any given point in time; any quantity of money can be optimal once the adjustment process has taken place. The problem is what is the less costly means of adjustment?

As Luther and Salter point out, the answer to this question depends on which case is less costly. It is at this point that the Cantillon effects kick in. Do the Cantillon effects, or the changes in relative prices (different to those that the market would have produced by itself), provoke more distortions when the money supply is elastic or when it is inelastic? If the money supply does not change, then our straight line needs to change its intercept; but in the process of moving vertically, the slope that is formed by relative prices is affected, until finally the new level with the same relative prices as before is attained. If the money supply changes, then our straight line remains at the same level, but in the process of changing money the slope is affected. In other words: either the line moves and the slope trembles, or the line does not change its level but the slope trembles as well. Given that what is important for the economy is the relative prices, the question is which of the two cases represent a less trembling scenario. Strictly speaking, the answer to this question may depend on the empirical results, and it may not be a corner solution (money supply perfectly elastic or perfectly inelastic), but there is a reason why an elastic money supply can contribute to reduce noise on the relative prices and, at the same time, keep the price level “stable.”

If money demand increases and this is also translated into savings into banks accounts (from having sold assets for cash, which is then deposited –ed.), then bank reserves increase. This means that banks do not need to spot, or discover, changes in money demand; they get reflected in the behavior of monetary reserves. Banks play a role in changing the money supply once money demand has changed. How, then, are changes in the money supply going to be channeled through the market? A bank does not randomly allocate changes in its money supply, but new banknotes are issued to the most promising entrepreneurial projects. Namely, to those investments and ventures that seem to be better aligned with individuals valuations through market prices, and offer higher rates of return. Therefore, as long as banks continue to channel changes in money supply to those projects that better reflect consumer needs, changes in relative prices that occur due to changes in money supply may well be toward equilibrium, rather than disequilibrium, prices. In other words, banks under free banking do not issue banknotes randomly, but to specific promising ventures once an increase in money demand has been channeled into bank accounts in the form of savings.

Let us illustrate the situation the following equation: MV = PQ.

Where M = money supply; V = velocity of circulation (inverse of money demand), P = price level (of consumer goods) and Q = output.

Let M = Gm, where G = gold and m = money multiplier. Then: GmV = PQ. (note: under a 100-percent rule, m = 1)

If there is an increase in money demand, then V decreases. There are two ways to keep the relationship: by a fall in P or by an increase in M (of course, there can also be changes in Q, but that’s not the main point of dispute in the debate and I will not consider this case). If prices are sticky, then changes in M can contribute to stabilize the relationship in a less costly way than a change in the level of P would do by a change in m. The more sticky prices are, the less we want the price level to change, since more distortions will be manifested in relative prices changing. Stickiness is a relative term; some prices are more sticky than others. If all price are equally sticky, than all prices change at the same rate and there are no effects on the relative prices, and therefore there is no clear economic sense for “sticky prices.” But if banks can play the role of channeling changes in M to those specific activities that are considered more valuable in the market, than changes in M that offset changes in P play at the same time a role in minimizing the Cantillon effects by extending credit in the form of banknotes to those entrepreneurs with a higher marginal degree of entrepreneurial alertness.

Different is the case when fractional reserves are outlawed. An increase in money demand must result in a decrease in the price level, and with it in Cantillon effects as well since banks cannot play the role of channeling changes in money supply to profitable investments. Changes in the relative prices will depend on two drivers: (1) relative stickiness and (2) how monetary shortage spreads through the market. The difference is that in this case banks do not have the flexibility to channel changes in monetary demand to promising entrepreneurial projects. On the contrary, the Cantillon effects when money supply falls short to money demand are the same as the ones when money supply exceeds money demand. All the adjustment falls in the side of prices. If prices were perfectly elastic, there will be no need for changes in M. Changes in M, actually, help to reduce the cost of changes in the level of P.

Luther and Salter do well in re-focusing the debate on what is important. By doing this, the unintended role of banks as minimizers of Cantillon effects come to surface. And even if this role may not be very explicit on their article, it does bring this role of banks closer to surface. Despite the fact that the final answer of how much M and P should change becomes an empirical problem of time and circumstances (how fast do prices adjust), the fact that banks under free banking do not randomly change the supply of money, but strategically allocate it as credit helps to minimize the wealth effects of monetary changes, a situation that is absent in the presence of 100-percentr rule.

PS: When thinking in terms of a vector of relative prices, usually a numeraire is used as a reference. For convenience, this is usually the monetary unit, like one dollar (models without money may use, for instance, a unit of labor). But money, as an economic good, also has a price, the inverse of the price level as a manifestation of its purchasing power. To keep the price level constant, therefore, means that there is no change in the relative price of money versus goods. But to let the price level fall requires a change in the relative price between money and goods in the market. In the case of a commodity money, as it may be the case of a gold standard regime, an increase in the relative price of money results in an increase in the supply of money until the original price level is reached once again. A change in the price level can be seen as a short-run effect, and to force a 100-percent rule as a way to cut short, or increase the cost, of going from the short-run to the long-run.

Nicolas Cachanosky is a doctoral student in economics at Suffolk University, as well as a previous Sound Money Essay Contest winner.

image: www.flickr.com/dnnya17