Who bears the burden of auction house fees, buyers or sellers?

Blog neighbour Lee Rosenbaum writes today about increases in premiums Sotheby’s auction house, speculating that Christie’s will soon follow suit. She writes:

Here are Sotheby’s new charges (with old ones in parentheses), effective Feb. 1:

Buyers will be charged 25% of first $200,000 (previously $100,000) of the hammer price; 20% of amount above $200,000 to $3 million (previously above $100,000 to $2 million); 12% of excess over $3 million (previously $2 million).

Let’s look at a specific example of how this will work: If your winning bid on an object was $10 million, you would have previously paid $11,365,000 million, including the buyer’s premium. As of next month, it will cost you $11,450,000 million.

Bill Ruprecht, Sotheby’s soon-to-depart president and CEO, issued this statement about the hike:

This will improve Sotheby’s revenue, strengthen the company’s profit margins, fund innovation, help us continue to make interesting and exciting investments in the business, and support our growing online and traditional engagement with clients around the world.

The “clients around the world” who will not feel “supported” by this fee hike are the buyers. They may well declare: “Enough is enough! It’s the sellers [who, in some cases, are charged no commission and even get a cut of the buyer’s premium] who should be footing more of the bill.”

Not so fast.

Auction houses take a cut from sales, meaning that buyers pay more to acquire a work than sellers receive, with the auction house taking the difference. This is similar to what happens when the government taxes a good: buyers pay a higher price than sellers receive, and the state takes the difference. It is as if a ‘wedge’ has been driven between buyers’ and sellers’ effective prices. In auction premiums, as in tax policy analysis, the interesting question is ‘who bears the burden if the size of the wedge increases?’ And the answer does not lie in the side on whom the premium or tax is nominally levied. The allocation of the burden is more complicated that that, because prices adjust in response to changes in premiums (or taxes).

What is the evidence on who bears the burden of auction house premiums? In an economic study of the auction house price-fixing case (and in other papers as well) Orley Ashenfelter and Kathryn Graddy write:

To date, the theory upholds the initial reasoning that increased commissions should have a minimal effect on buyers, with the incidence falling primarily on the sellers.

They reason, and find evidence, that the burden of increases in buyers premiums falls upon sellers.

The reasoning is this: in auctions, the winning bid pays a price equal to the reservation price (the highest total price she is possibly willing to pay) of the second-highest bidder, plus a small increment. That reservation price does not change with changes in buyers premiums. If, for example, the reservation price of the second-highest bidder is $11,365,000 (consisting of a ‘price’ of $10 million and a auction house premium of $1,365,000), that amount does not change with an increase in the rate of the buyers premium. In other words, it doesn’t become $11,450,000 because of some change in auction house policy. Lee Rosenbaum is assuming the winning bid remains at $10 million with the change in buyers premium, but we have no reason to think it would.

The winning bids will fall with an increase in the buyers premium, and that cost is borne by sellers.

Ashenfelter and Graddy:

This analysis would be complete if the number of buyers and sellers in the auction were fixed, and if sellers did not set reserve prices. However, in practice, sellers set a secret reserve price, so that some items go unsold because the bidding does not reach this (seller’s) reserve price. To the extent that buyers are unconstrained by the reserve price, because the item sells for a price higher than the reserve, the analysis above is unaffected.

As Ginsburgh, Legros, and Sahuguet (2004) show, for the situation where the reserve price is binding, however, it is possible that the buyers will end up paying a higher price because of the existence of the buyer’s premium. However, if the reserve price is not binding, and the presence of a reserve price causes the number of bidders participating in the auction to decrease, then prices can be pushed down. This can occur if a buyer’s cost of participating is greater than his expected surplus.

Buyers who fail to purchase or participate in the auction because of the higher commission rates are worse off. In any case, however, this is a second order effect and any harm done to those who do not purchase is not capable of empirical identification. Overall, Ginsburgh, Legros, and Sahuguet (2004) conclude that ex ante, the welfare of all bidders is the same, regardless of the commission [emphasis mine].

So it is sellers who might declare that ‘enough is enough!’