We don’t know the identities of most of the buyers who made this a blockbuster week for art auctions, bidding up works by Rothko, Giacometti and Lichtenstein, among others, to eight and nine figures. "Les Femmes d’Alger (Version O)," a 1955 painting by Picasso, sold for $179.4 million.

We don’t know exactly where their money came from, or why they chose to spend vast amounts of it at auctions held by Christie’s and Sotheby’s.

But this much we do know: The astronomical rise in prices for the most-sought-after works of art over the last generation is in large part the story of rising global inequality.

At its core, this is the simplest of economic math. The supply of Picasso paintings or Giacometti sculptures (one of which sold for $141 million at the same auction this week) is fixed. But the number of people with the will and the resources to buy top-end art is rising, thanks to the distribution of extreme wealth.

One of the most important findings of the leading economists who study inequality is that wealth and incomes at the very top are "fractal." What they mean is that when you zoom in on the upper end of wealth distribution, patterns repeat themselves in an ever more finely grained pattern.

Partners at law firms who are in the top 1 percent of all earners have seen their incomes rise faster than dentists who are in the top 10 percent. But by a similar margin, chief executives of large companies who are in the top 0.1 percent are seeing their incomes rise faster than those law firm partners. Hedge fund managers in the top 0.01 percent are similarly outperforming the CEOs.

And the kind of people who can comfortably afford to pay a nine-figure sum for a Picasso, the top 0.001 percent, say, are doing still better than that. You can draw that conclusion by reading the work of the French economists Thomas Piketty and Emmanuel Saez. Or you can form it by looking carefully at the market for the work of a certain Spanish painter.

Let’s assume, for a minute, that no one would spend more than 1 percent of his total net worth on a single painting. By that reckoning, the buyer of "Les Femmes d’Alger (Version O)" on Monday would need to have at least $17.9 billion in total wealth. That would imply, based on the Forbes Billionaires list, that there are 50 plausible buyers of the painting worldwide.

This is meant to be illustrative, not literal. Some people are willing to spend more than 1 percent of their wealth on a painting; the casino magnate Steve Wynn told Bloomberg he bid $125 million on the Picasso this week, which amounts to 3.7 percent of his estimated net worth. The Forbes list may also have inaccuracies or be missing ultra-wealthy families that have succeeded in keeping their holdings secret.

But this crude metric does show how much the pool of potential mega-wealthy art buyers has expanded since, for example, the last time this particular Picasso was auctioned, in 1997.

After adjusting for inflation and using our 1 percent of net worth premise, a person would have needed $12.3 billion of wealth in 1997 dollars to afford the painting. Look to the Forbes list for that year, and only a dozen people or families worldwide cleared that bar.

In other words, the number of people who, by this metric, could easily afford to pay $179 million for a Picasso has increased more than fourfold since the painting was last on the market. That helps explain the actual price the painting sold for in 1997: a mere $31.9 million, which in inflation-adjusted terms is $46.7 million. There were, quite simply, fewer people who could bid against one another to get the price up to its 2015 level.

More people with more money bidding on a more or less fixed supply of something can only drive the price upward. On Monday, the auction was for fine art. But the same dynamic applies for real estate in central London or for bottles of 1982 Bordeaux.

That helps explain why the recent Picasso sale represented a 462 percent gain since its previous auction in 1997, a span in which the Standard & Poor’s 500 index returned 215 percent, including reinvested dividends. (The comparison isn’t entirely apt, in that the painting would have required spending each year on security, storage and insurance, lowering returns. On the other hand, the Picasso looks better on one’s living room wall than a mutual fund prospectus.)

What does that mean for the future? There is no free lunch, even for people paying millions of dollars for a painted canvas. Art prices are vulnerable to fashion, of course. Picassos could go out of favor, relatively speaking, in which case the anonymous buyer this week may not see the same type of financial return the previous owner enjoyed.

There are legal risks. China is cracking down on official corruption and particularly on showy displays of wealth, which could crimp Chinese demand for fine art in the years ahead. U.S. and European authorities may wish to put further effort into preventing art transactions from being used to launder money or evade taxes, as two practices the economist Nouriel Roubini has argued are commonplace.

But any billionaire spending astronomical sums for a painting or sculpture should hope most of all that this basic inequality trend — of the ultrarich faster than everyone else — remains intact. Because as long as it does, there will always be another potential buyer out there to fuel a bidding war like the one that took place this week.

© 2015 The New York Times Company