Does Gold Disprove Marginal Utility?

by: John Overstreet


Looking on from Mars or from Omaha, it would seem that a vital commodity like water would be infinitely more valuable than a non-essential commodity like diamonds.

The classical labor theory of value and the now-standard neoclassical theory of marginal utility attempt to explain why non-essential commodities are typically more expensive than essential ones pound for pound.

The value of world gold supplies as determined by market prices tends to match or exceed the value of most other primary commodities, which suggests that utility plays no role.

If marginal utility were a sufficient account of prices, it could explain both the difference in unit prices and the parity of aggregate prices for gold and other commodities.

If prices are determined by simple supply and demand, then the size of the gold market suggests that humans collectively have a higher demand for gold than for essential goods.

"If you set out to construct a building with a crooked ruler, a faulty square that is set a little out of the straight and a level...slightly askew, there can only be one outcome...."


"Gold gets dug out of the ground in Africa, or someplace. Then we melt it down, dig another hole, bury it again and pay people to stand around guarding it. It has no utility. Anyone watching from Mars would be scratching their head."

--Warren Buffett

Orthodoxy and common sense suggest that prices, especially long-term prices, whether for gold or fried chicken or motorcycles or teddy bears, are determined by supply and demand. Why then is gold so expensive?

The classical explanation is that gold's rarity, its limited supply, or the difficulty in acquiring it, demands a premium. Even though there are not many vital uses for gold, it is so rare that chronically constricted demand for the metal does not appreciably suppress the price, at least the per-unit price relative to the per-unit price of other commodities.

This is the old water-diamond paradox, or the paradox of value. Robert Murphy, an Austrian School economist, explains it thusly:

"Why do diamonds have a higher exchange value than water, when diamonds are a mere frippery while water is essential to life?...The solution, of course, is that no individual is ever in the position of choosing between all of the diamonds in the world and all of the water….[T]here is so much water to go around that even if ten trillion gallons were to disappear, no one would care. On the other hand, if only a few pounds of diamonds were to vanish, some people would be very upset." (emphasis mine)

It should be noted that this a slightly circular argument at the end: the reason people would be upset over the missing diamonds is that they cost a lot, but the question is precisely why they cost so much. But, that is not what I am concerned about.

Elsewhere, he says:

"One of the most important advances in economic theory was the realization that people valued goods unit by unit, rather than comparing entire classes of goods against each other….Economists would say that diamonds are scarcer than water." (emphasis mine)

And, in an interview posted on YouTube a year ago, he said, "When you're valuing a good, what's important is the marginal utility, not the utility of the entire supply…."

I am going to attempt to quarrel with these statements and show that empirical evidence suggests that there is something wrong with what is an otherwise standard account of prices.

"Marginal utility" can be thought of as the utility of a given good relative to that of another good for a particular individual in a particular moment in time. In other words, it is easy to imagine conditions in which a person might value a cup of water more highly than all of the diamonds in the world, but in the modern world, the typical individual in a typical set of circumstances would opt for a small quantity of diamonds over a much larger quantity of water. Beyond a minimum requirement of water, the less likely you are to value each addition to that supply, and the more highly you will value less-vital commodities.

But, to what degree should we expect that effect to reduce the price of water and/or raise the price of diamonds? In the quote above, Warren Buffett seems to be saying, 'Not much at all.'

"Marginal utility" is a hybrid of the naïve utility theory of value (which would suggest that a good's relative price should be equivalent to its relative usefulness) and the naïve labor theory of value (which would suggest that the difficulty of obtaining something should determine its price). It was, apparently, a resuscitation of the utility theory of value in response to the labor theory of value's running amok in the 19th Century.

In other words, utility does determine price, but for historical reasons, our understanding of price determinants was thrown off by empirical observations of the unit prices of particular goods (e.g. water and diamonds). Because the unit prices of goods did not obviously reflect utility, the labor theory of value took root. This is interesting, because it appears that no one went about disproving the labor theory of value by producing data relating to supply, demand, and price. It was an intellectual exercise that restored the initial and seemingly discredited intuition about the critical role played by utility (which can be thought of as the most primitive form of demand).

I have to confess, however, that I am not sure I understand how this theory ought to work in the real world, because I cannot see how this precludes consideration of a comparison between the value of an "entire supply" of one good to that of another, as Murphy seemed to suggest. If we were to compare the utility of the entire supply of water to the utility of the entire supply of diamonds, the ratio of the former to the latter would be hard to calculate, but one could be fairly certain, as is Buffett, that it would be more than 1.0. Indeed, I would be tempted to say that it would be infinitely higher than 1.0. By that logic, water should be more valuable--incalculably more valuable--than diamonds, even on a per unit basis.

But, in the real world, both water and diamonds have prices, of course, which suggests that something like marginal utility is true. And, the fact that precious stones have been, for thousands of years, much pricier than water suggests that the price ratio for the total supply of water to the total supply of diamonds is closer to 1.0 than the Buffettesque utilitarian logic above would suggest.

It would seem that marginal utility can explain why water is not more expensive than diamonds on a per-unit basis, and perhaps it can accommodate diamonds being significantly more expensive than water, but can it account for the degree to which diamonds are more expensive than water? What would an "acceptable" or "reasonable" water-diamond ratio for total supplies at market prices be? 1000:1? 100:1? 10:1?

Perhaps I am mistaken, but even the most fanatical market "fundamentalist" would have a little trouble stomaching the notion that the water-diamond ratio at the aggregate level could reasonably be much below 10:1. If market prices say that the world's supply of diamonds are 20% as valuable as the world's water (that is, a 5:1 water-diamond ratio), that would seem to eliminate the need to hold the market mechanism in high regard. Right?

Can an economic order that values something as vital as the world's supply of water at only five times the world's supply of diamonds be rational or efficient?

Before working ourselves up into a lather over that kind of question, though, we should probably check what those ratios are in actual fact.

Unfortunately, though, I have no idea what the historical prices and production levels for water or diamonds are. But, it probably doesn't matter. Water and diamonds are merely examples from the extremes of the commodity spectrum, from the most to least useful. And, fortunately, we do have data on a lot of commodities that fall in between those two poles, like precious metals (e.g., gold and silver), agricultural staples (wheat, corn, and rice), and basic minerals (iron, copper, and bauxite).

The USGS, in particular, provides a whole pile of data on global prices and production for different mineral commodities (including precious metals) going back to 1900. If we compare the total values of 11 of these commodities (gold, silver, copper, zinc, iron ore, bauxite, aluminum, lead, nickel, phosphate rock, and tin) over the last 100+ years, we find a number of interesting things, but for the purposes of this discussion, it suggests that over the long term the total supply of gold is as valuable as that for nearly every other commodity.

In the following chart, I calculated the world "GDP" for these eleven major minerals at market prices going back to 1906 and then calculated what percentage of that total was taken up by each commodity individually. Gold has almost always been one of the top three or four mineral commodities in terms of "market share," even though, like diamonds, it is relatively useless. Only iron ore, aluminum, and copper are comparable. The only time this was not true was during the Bretton Woods period when the US was effectively holding the price of gold down. Once gold was set free, it rose (again, in terms of total relative production value) to a position slightly below its pre-Depression levels. Before World War I and the Federal Reserve, the ratio of every other mineral commodity to gold was below 1.0, and in the interwar years, it remained low. In 1932, gold was nearly as valuable as the other mineral commodities combined. Gold held a similarly commanding position until the end of World War II, it seems.

market share of each commodity relative to the total 1900-2012

(Source: Calculations from USGS data)

The following chart demonstrates the same relationships, although this shows each commodity's ratio relative to gold rather than to the combined totals for all commodities. In a fair fight, few commodities get much above 1.0 against gold.

The reason for this is at least partly due, as I demonstrated in a previous article, to the long-term inverse correlation between relative prices and relative supply. This was true over the century of mineral commodity prices we just looked at, as well as the agricultural data for 2012. The implication is, therefore, that there is a centripetal force that tends to pull the ratio for the total value of any two commodities towards 1.0.

ratio of world commodity output to world gold output by market prices 1900-2012

In short, the relationship between supply and price across commodities makes it seem as if utility is virtually inconsequential. Was Adam Smith's rather odd labor theory of value right after all?

That is too much to consider at the moment. Rather, I want to shift for a moment to consideration of changes in the value of the global supply of gold and to the narrower question of the suppression of the gold price. Conspiracy-minded gold bugs often accuse shadowy forces of manipulating the gold market, and, if we refer to total production values, it is true that the metal does not have quite the market weight it had before Bretton Woods. But what does that mean?

One can only be sure that gold is being manipulated if one has some way of guessing at the "correct" price. But, we only have two eras to compare the post-Bretton Woods (1971-present) price levels to: Bretton Woods (1944-1971) and pre-Bretton Woods (pre-1944). It seems pretty clear that the price of gold during Bretton Woods was suppressed. We are left, therefore, with gold prices in the decades and centuries before the end of World War II. Since the dollar was pegged to gold at the time, however, how do we know if gold was not artificially high then?

If you are an Austrian and you believe that we should return to the old gold standard, then presumably you think gold should be even higher than it currently is (again, we're talking about long-term relative values, not just the fall in gold's unit price over the last three years). Alternatively, adjustment could come through a decline through prices and/or production levels among the other commodities.

If we can use minerals as a proxy for global commodity production and use the pre-Fed years as a target for a return to the old gold standard, this would suggest a "need" to reduce global commodity GDP by something like 50% or to raise gold's global GDP by 100%, or something in between. I determined this by comparing the average 1906-1913 mineral-gold ratio in the chart above, which is about 2.3, to the average 1980-2012 ratio, which is about 5.2. No matter what you believe about the proper value or role of gold, a return to the old gold standard would most likely be economically traumatic.

Whether the value of gold production since 1971 is more or less correct than its value before 1944 is not insignificant, but in either instance, one first has to ask why it has been so high in both periods. Does marginal utility account for that strength? Can it? If we translate marginal utility into the simpler terms of supply and demand, how is it possible that the demand for such a useless metal could be so strong as to give it more market weight than most other commodities? On what basis can a useless commodity achieve parity with essential commodities in terms of global production value?

It seems to me, as I write this, that there are a few solutions to this problem:

1. I have misunderstood the theory of marginal utility and the relationship between supply and demand as it relates to price.

2. The data, in particular those on production, are wrong.

3. Marginal utility does not explain price levels, either because it is wrong or, what amounts to much the same thing, it is only a partial solution.

If it is number one, then I am sure someone can explain it, since it is a bedrock principle of economic theory. Number two seems unlikely, because the data just seem too consistent across time, and even if they underestimate non-precious metals production levels by 50%, that would not be of sufficient magnitude to resolve the strength of gold.

If it is number three, then that leads to a more complex set of problems. If marginal utility is rational but does not explain prices, then the markets are irrational. That would not be news, of course, but this would be a whole different order of irrationality than the relatively brief flurries of speculation we supposedly find in discrete markets. This would be a pervasive, persistent sort of irrationality that would damage any pretense of market efficiency. Perhaps the state or some international organization could correct the situation by setting proper prices and/or production levels for goods.

Or, perhaps marginal utility is just bad theory and only appears to be rational to us when we consider prices abstractly and without reference to a wider spectrum of data. It seems to me that the harder a science is--that is, the more a given discipline's theories are exposed to the onslaught of data--the more unlikely and counterintuitive the relationships that emerge in the long run, which fundamentally alters or expands our perception of what is "rational" and "irrational."

The theory of marginal utility does not explain how the value of the world's supply of an essential commodity, like water, could be brought to such low levels relative to the value of a useless one, like diamonds, never mind how the former could be brought to a level below that of the latter. Shouldn't economists be able to explain, not only the reason for gaps in per-unit prices, but a) the stability and size of that gap and b) the absence of a gap at the aggregate level? The tendency of values for the respective world supplies of commodities to approximate one another suggests a need for something more comprehensive and precise than marginal utility as it is currently constructed, and gold stands as a shining example of this problem.

Disclosure: The author has no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it. The author has no business relationship with any company whose stock is mentioned in this article.