by Keith Weiner, Sprott Money:

This question is no longer moot. As the world moves inexorably towards the use of metallic money, interest on gold and silver will return with it. This raises an important question.

Which interest rate will be higher?

The Wrong Approach

It’s instructive to explore a wrong, but popular, view. I call it the purchasing power paradigm. In this view, the value of money—its purchasing power —is 1/P (where P is the price level). Inflation is the rate of decline of purchasing power.

This view treats the quantity of goods you can buy as intrinsic to the money itself. This is a mistake, and it leads to a false theory of interest. Before I can present this wrong theory, let me define some terms.

The Nominal Interest Rate means the rate at which lenders lend and borrowers borrow in the market. The Real Interest Rate is the Nominal Interest Rate – inflation. Notice the switcheroo. The actual rate charged by actual lenders to actual borrowers is dismissed as merely nominal. A fictitious rate which is not used in any transactions is elevated to the status of real. Got that?

The theory asserts that interest is determined by inflation, that is, real interest > 0. With nominal rates below zero in Europe and elsewhere, this view is tempting and convenient.

According to this view, which metal has the higher interest rate comes down to which will have a faster-rising purchasing power. Most people would say silver, especially when silver is so cheap compared to gold by a long-term historical perspective.

Suppose silver’s purchasing power rises at 5% per annum (i.e. deflation) over the long run, then a nominal interest rate of 2% gives a real rate of 7%. If gold’s purchasing power is rising at only 3%, then its nominal rate must be 4%, if both metals have the same real rate .

First, and it should be obvious that, no one knows how prices will change in the future. Anyone who knew could make billions trading commodities futures. In any case, prices may change, but that is not the measure of the value of money. Consumer prices have many nonmonetary forces pushing them up (such as regulations and taxes) and down (such as improved manufacturing efficiency). At best, prices are a weak proxy for the value of a falling paper currency.

I don’t take the purchasing power approach.

Monetary Science

Instead, to determine which rate will be higher, let’s look at the incentives that encourage action. Everyone who owns metal will face the choice: to hoard it or to lend it.

In general, we know that if interest is greater than their time preference, people will lend. But that does not help us predict which metal will have the higher rate. For that, we must look at factors that differ between them.

For example, there is a cost to store precious metals. Since silver is about half as dense as gold, an ounce of silver is almost twice as bulky. And that ounce has about 1/75 as much value as an ounce of gold. This means to hold the same value in silver you need 150 times the volume of gold. An iPhone (the small size) made of gold is worth as much as two and half bread loaves made of silver. No wonder why storing silver is typically more expensive.

If silver storage costs you 0.75%, and gold is 0.5%, then there is a 0.25% spread in storage costs. Lending silver is a net gain for you, compared to lending gold at the same rate. This is an actionable spread (unlike the so called real rate)—an incentive to lend silver in preference to gold.

There are other differences between the metals, such as marginal utility. Economists had long struggled with a dilemma. Water is important to human life, but diamonds are not, so why is the price of a diamond much higher? If you are thirsty in a desert, the first gallon of water is worth a high price. The second is worth less. By the third or fourth, you are not willing to pay anything. The reason is that you use the first gallon for drinking. The second is a spare. The third is to wash yourself. The fourth is maybe to wash your clothes. Can you think of what to do with a fifth gallon?

Economist Carl Menger resolved the dilemma with his discovery of the principle of marginal utility . Marginal utility refers to the value of the next quantity of the good in relation to the previous. Marginal utility declines, because when the higher needs are satisfied, the next unit of the good goes to a lower need.

Water is so abundant, that at the margin its value is nearly zero. People use water to clean their driveways. Large, high-quality diamonds are not so abundant. They are used only for engagement rings and other important jewelry pieces.

Each kind of good has a different marginal utility. For food, it’s low because food perishes. For many durable goods, it’s higher because they can be stored until needed.

Over thousands of years, the market ranked all goods by marginal utility. It determined that the highest marginal utility belongs to gold. Gold is not consumed, and virtually all gold ever mined is still in human hands. Even today, gold mining continues and the market happily absorbs all that can be produced. Silver is second.

People value the last ounce of gold as much as the first (or nearly as much). Whereas wiith silver, the last ounce matters a bit less. People may be willing to part with some silver more easily. By this assessment, one might expect people to prefer to lend silver, and therefore gold should have the higher interest rate.

However, there are other factors to consider.

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