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Market Pricing of a Single Item

(Part of a series of articles on pricing.)

Last time I discussed marginal utility as the cornerstone of pricing. People will only trade when they perceive the thing they obtain has a greater marginal utility than the thing they give up. This fact delimits a range of prices acceptable to both buyer and seller.

Here I consider the simple case of a single item to be traded. This may occur when the item is inherently unique (e.g. a work of art), when there is only one buyer who only desires a single unit, or when there is only one seller who only offers a single unit.

When there are multiple buyers for the single item, sale by auction is most natural. The item will be sold to the highest bidder, the person who judged it to have the highest marginal utility. In order to exclude all other bidders, and thereby to win the auction, the price will fall within the range between the second-highest bidder's marginal utility and the highest bidder's marginal utility.

For completeness, the seller's marginal utility must also be considered. The price must at least equal the greater of the seller's marginal utility and the second-highest bidder's marginal utility, and must not exceed the highest bidder's marginal utility.

When there are multiple sellers but only one buyer interested in only one unit, the situation is the mirror image. In that auction sellers would offer progressively lower prices until the lowest bidder emerged. The range of possible prices is again constricted — it must at most equal the lesser of the buyer's marginal utility and the second-lowest bidder's marginal utility, and must at least equal the lowest bidder's marginal utility.

The operation of these principles can be directly seen at auctions such as on eBay. The proxy bidding system encourages buyers to bid at their marginal utility, and the starting price or reserve price represents the seller's marginal utility.

The case of multiple sellers but only a single buyer is not directly supported at eBay, but it can roughly be seen to occur when a seller (or competing sellers) offers many items in separate auctions that are not popular enough to attract bids for each item. The starting or reserve price again represents the seller's marginal utility. If the items do not sell, the seller (or competing sellers) are likely to relist them at a lower price.

The competition among agents, whether they be buyers or sellers, operates to narrow the range of possible prices, shifting it in favor of the side that has less competition.

A possible objection to the foregoing is that the price range is actually being fixed by the amount of money the bidders have available, not by their marginal utilities. A super-rich buyer could win any auction with a negligible portion of his wealth and may not actually value the item very highly. What may be an amusing trifle to the rich bidder may be of great importance to a poorer person who was outbid.

There is some truth in this objection. Marginal utility determines the willingness to pay, but wealth determines the ability to pay. To succeed in an auction, both willingness and ability must be present.

To resolve the objection, it is important to understand that the law of diminishing marginal utility applies to money as well. A poor person values their money very highly, while it is easy (and popular) to imagine the super-rich lighting their cigars with hundred-dollar bills. The higher bid of the super-rich buyer is still reflective of the marginal utility they place on the item — they're willing to bid a lot for a trifle, because the money is also a trifle to them.

Even when the poor bid against the rich, the amount of their bids are still connected to their respective marginal utilities, and incorporate the fact of the rich person's lower valuation of money.

The bids are established by the varying marginal utilities of the agents involved, and therefore so is the resulting price range.

The ethical matter of the disadvantage of the poor when bidding against the rich is outside the scope of this discussion. My belief (which I consider off-topic here and state without argument) is that this circumstance is fully morally correct and I would vigorously defend the rich person's ability to outbid the poor person. (Any other proposed resolution of the "injustice" must confront the injury done to the seller who would presumably be forbidden from accepting the rich person's higher bid.)

Tiny Island