## Wednesday, March 11, 2009

### How Many Significant Digits to Prices?

There is something funny about gas prices, and that's how exact they are. Gasoline seems to be the only common consumer commodity whose price is quoted in tenths of a cent. Of course, the last figure is invariably 9—on many signs, the little 9/10 figures don't even come off. The cent digit is usually 9, too, creating a charm price (e.g., \$2.299 a gallon). A charm price is one a little below a psychologically significant round figure. For many types of products, charm prices do seem to motivate buyers. So the little 9s make sense, and a price like \$2.299 basically means \$2.30, a number with two significant digits.
I mention this because a theme of my upcoming book is how fuzzy prices are. Many experiments have demonstrated that subjective valuations are much more fluid than we think. In bargaining experiments, "irrelevant" factors such as the genders of the participants or the number of offers on the table can change agreed-on prices by 10 percent or more. This might suggest that there is little point in quoting prices to more than 2 significant figures.
The imprecision of prices is recognized by the custom of rounding retail and asking prices. Imagine you're selling your home. You use a spreadsheet to compute the appropriate list price. Based on comps, square footage, taxes, and the plummeting market, you compute that the optimal asking price is \$562,118.83. You aren't likely to list it at that. You either round down to \$560,000, or round up to \$570,000, or opt for a charm price like \$569,000.
My point is, sellers mostly round to two significant digits (and then sometimes impose a charm price). A look at the prices in real estate listings, eBay, and Amazon confirms this. Prices like \$47.30 or \$274,200 are rarely encountered.

There are exceptions. One is cars. The 2009 Hyundai Elantra SE (pictured) has an MSRP of \$17,020 and an invoice price of \$16,334. That's four or five significant figures, and neither uses the old 9-ending trick. Is Hyundai so sure its customers will buy at \$17,020 and walk away at \$17,030?
No because Hyundai knows that list prices don't mean anything. Options, fees, and sales tax must be added; the total is negotiated; and then the salesman tries his darndest to sell you rust-proofing. There may not be much point in going psychological with a base list price because no one ever pays it and everyone knows they won't pay it.

I recently came across another case of weirdly exact pricing at Louis Vuitton's Beverly Hills store. Like most luxury retailers, LV uses contrast anchoring. They display a few items so outrageously priced that they rarely sell, and that's okay. These prices make everything else look reasonable in comparison. The most expensive item I saw was a diamond watch, priced at \$149,000 (in the midst of the grimmest recession since the 1930s). That's a charm price! Like they were worried it wouldn't sell at \$150,000.
LV has a lot of three-significant-digit prices that do not end in 9. I didn't note them, but I found these watch prices on the Louis Vuitton website: \$2,680.00, \$4,010.00, \$18,100.0, \$14,700.00. Pictured: the Emprise Paved Watch, large size, designed by Marc Jacobs, and retailing for \$134,000.
To the best of my knowledge, haggling is not part of the culture of Rodeo Drive, even in this economy. Does LV assume its customers have very exact reserve prices? Is it run by bean-counters who can't bear to round down?
I'd welcome from hearing from anyone who has encountered retail or list prices with four or more digit precision.

#### 1 comment:

1. I think using additional significant figures implies - or at least gives an unconscious perception - that a great deal of thought was put into the price.

If the watch was listed at \$4,000, you might offer \$3,000 or \$3,500, but if it's listed at \$4,132, maybe you'll just offer \$4,100. You wouldn't want to insult their diligence, would you?