Tracing the history of left-digit bias research to its origins: Lessons from Ginzberg’s (1936) “Customary Prices”
Two recent influential field studies have endorsed the use of just-below prices by sellers. But Ginzberg's (1936) classic article reached a different conclusion and is worth revisiting.
“It is interesting that a strategy so widely used and accepted by merchants and academicians has so little proof behind it.” - Robert Holloway, 19731.
If we were to make a list of empirical generalizations that pricing practitioners believe in and use confidently, the left-digit bias, which also goes by other names like just below pricing, odd pricing, charm pricing, or earlier customary pricing, would be in the top five. While I am sure you know the effect and the logic behind it and have seen it on store shelves, catalogs, and web pages and used it yourself if you make pricing decisions, let me summarize it briefly first.
The Left-Digit Bias
The left-digit bias refers to the preference of sellers to use “just-below” prices because of the bias of buyers to focus on the left digits of a price. Instead of using round numbers like $50 or $100, sellers prefer to use prices that are just below them, such as $49 or $99. The conventional wisdom is that relative to round numbers, just-below prices convey a lower amount to the buyer because they focus on the left digits of the price (4 in 49 versus 5 in 50). This leads to an underestimation of the price, which in turn leads to a positive evaluation of the item and a great likelihood of choice and purchase. In the aggregate, a reliance on just-below prices leads to greater sales.
This effect is often used as a classic example of relatively small and inexpensive changes in price having relatively large and profitable impacts on buyer behavior. This is one reason why prices ending in 9 are so popular and ubiquitous. For instance, Snir and Levy (2021) reported that between 30% and 95% of all retail prices end with a 9 (although I could not find their frame or source for these values). Figure 6 in the recent Strulov-Shlain (2023) paper2 (discussed below) is consistent, showing that 41% of prices in grocery stores ended in 99, and 85% had 9 as the last digit.
A number of retailers like 99 Cents Only Stores (whose tagline is Where deals come true) have built a core value proposition and positioning strategy, indeed an entire business, around the left-digit bias. Many more retailers and other businesses use just-below prices extensively, so much so that it’s not unusual for virtually all their prices to end in 9 or 99. See a page from the Harbor Freight Tools catalog for an example.
The recent buzz about left-digit bias
The main purpose of this post is to trace the left-digit bias research to a 1936 article written by the economist Eli Ginzberg in the American Economic Review3 and draw lessons from it. But before we do that, two points about the left-digit bias are worth noting here.
First, as far as I know, a precise definition of the left-digit bias doesn’t exist. Some researchers equate it to 99-cent pricing and others to just-below prices (where what just-below means is unclear). Thus, using $49, $49.9, $49.99, $49.89, $49.8, or even $49.5 may qualify as just-below prices when compared to the $50 baseline price. But it is not clear (at least to me) how low we can go below the baseline and still call the price a “just-below price” or how high we can go above the round number and still consider it a baseline. The conventional wisdom, most of the time, is to stick to prices ending with 9 or 99, whole or in cents.
Second, two field studies have created a lot of buzz about the left-digit bias in pricing circles recently. At a time when behavioral science has gotten so many knocks from recent scandals, setbacks, and failures to replicate, it’s particularly reassuring to read field studies that report consequential levels of left-digit bias among two disparate consumer groups: Lyft riders and supermarket shoppers.
Starting with the Lyft study, List et al. (2023)4 analyzed observational data from around 1.7 million ride requests where Lyft, the ridesharing company, varied price offers, and additionally conducted a field experiment where they manipulated price offers to 21 million customers. The authors report their main finding like this:
“During the 7-month period we analyze, Lyft offered 1.7 million passengers a ride for a price somewhere between $10.96 and $11.03 (with prices approximately equally distributed across each cent value). What were the conversion rates for those price offers? The conversion rates for $10.96, $10.97, $10.98, and $10.99 were 50.2%, 50.4%, 50.2%, and 50.1%, respectively. In contrast, the conversion rates for $11.00, $11.01, $11.02, and $11.03 were 48.7%, 48.6%, 48.7%, and 48.8%, respectively. This is not an isolated incident, but rather a pattern of discontinuous drops in demand that we document graphically across every dollar threshold….[In the field experiment], passengers perceive a price that is lowered 1 cent below a dollar value as if the price was lowered by 50 cents. Put another way, the contribution of left-digit bias to the Law of Demand is such that roughly 50% of the decline in demand occurs discontinuously at dollar values.
Based on these impressive findings, it is clear that Lyft customers are subject to a significant left-digit bias when they are assessing offers from Lyft and deciding whether to accept the ride (or use Uber instead). The authors summarized their recommendation in this way:
“to maximize profits all prices should be raised or lowered to a 99-cent mark, ceteris paribus. If this were to be done and assuming the effects we estimate hold in the long run, we estimate that Lyft could increase profits by $.25 per ride. Given ridership in 2019, a left-digit pricing strategy could increase profits by approximately $160M per year.”
This is a large impact and a strong recommendation indeed! The other paper is Shrulov-Shlain (2023), which reported an analysis of sales data of 3,500 CPG products sold in US supermarket chains. The author’s main goal was to study how grocery store managers respond to left-digit bias in their pricing strategy. (He found that they “respond coarsely”, underestimating the extent of to which shoppers are susceptible to the left-digit bias and using simple rules-of-thumb for setting prices instead of optimizing the price by estimating the degree of the bias for each item). Important for our purposes, he found a robust left-digit bias among supermarket shoppers, as shown in Figure 2 in his paper, where the demand for various coffee SKUs rises at each just-below price and drops off at each round price.
The Lyft and the supermarket studies are impressive, and both support the argument that pricing practitioners should liberally, or even exclusively, use 9-ending prices and abandon all other endings. There’s a lot to be optimistic about here. However, now let’s trace the history and look at the other side of the coin to see how much optimism is really warranted.
What does Ginzberg (1936) say?
The earliest citation in any paper on the left-digit bias is usually Ginzberg (1936), so it is worth going back to where this research started. The cite is not a paper but a super-interesting one-page “Communication” (similar to a Letter to the Editor today) in a 1936 volume of American Economic Review. Let’s go through it in detail. It begins like this.
For many years, retail prices in this country have been quoted at one or two cents below the decimal unit — $.49, $.79, $.98, $1.49, $1.98, tell the tale. Several years ago, one of the large mail-order houses undertook an experiment to discover the significance of these customary prices. If they proved to be of no particular importance, substantial economies in accounting were in the offing. The merchandising executives suspected that the pricing tradition survived because of universal indulgence: they believed that, if attacked, it would soon give up the ghost. But this was only a suspicion; hence, they proceeded.
By 1936, then, just-below prices were already considered customary and were seen by many skeptical managers as a “universal indulgence,” an unnecessary, expensive complication to deal with when they would’ve liked to use simple, round prices instead. This matches the perspectives of today’s managers. I’ve met pricing managers who swear by just-below pricing and others who can’t stand it.
Excellent opportunities were afforded to control the experiment. The concern issued annually two large catalogues, in the Spring and in the Fall; also two small ones, known to the trade as flyers, aimed at stimulating trade during the dull months. Its principal competitor followed suit. The test was undertaken one Spring. The total edition of the catalogue numbered approximately 6,000,000. Variations in merchandise offered and featured—a recognition of economic and climatic differences—resulted in the production of regional catalogs. However, identity rather than dissimilarity was their outstanding characteristic. A group of representative items was selected and priced in several regional catalogues at: $.50, $.80, $1, $1.50, $2; in the remainder of the edition, these identical commodities were presented at customary prices: $.49. $.79, $.98, $1.49, $1.98.
Professor Ginzberg is reporting an impressive field experiment run by a retailer almost 90 years ago, but one that would make anyone proud to run today. Because of the passive voice, it’s not clear if he orchestrated and designed the study or simply reported something the mail-order retailer had done, but either way, it sounds solid. Now, this is where it gets interesting.
The results of the experiment were as interesting as they were perplexing. For certain items, the change from the customary to the rounded price indicated that sales were halved; for others, no appreciable effect was noticeable; for still others, sales were disproportionately large. Throughout the trial the prices of the leading competitor had, of course, remained unchanged. Detailed records of sales in the preceding and present period by classes and by regions permitted the company to account, with a fair degree of certainty, for all variables influencing demand, other than the departure from customary prices. Although considerable effort was devoted to interpreting the results, the data would not lend themselves to generalizations. The vice-president in charge of merchandising ventured to guess that the losses were balanced by the gains. He realized full well that a repetition of the experiment might yield sufficient additional data to permit of more definite conclusions. But when a change of one cent a yard led to a loss of $50,000, the experimental zeal, even of a daring business man, was likely to be held in check. Next time the losses might not be offset. One thing was clear: competition was itself a custom limited by the history of institutions, by the psychology of the competitors. The searcher after profits would continue to pay his respects to both.
What a dramatic way to end the letter! Unlike the two recent 2023 field studies, Ginzberg’s study in 1936 did not end with a resounding endorsement for the left-digit bias. We can make any number of arguments to reconcile these old findings with the two recent successes. Perhaps the American consumers of 1936 were not sensitized and attuned to what just-below prices signify as today’s customers are. Ginzberg doesn’t mention this, but it could be that this mail-order house was already using just-below prices earlier, or its competitors used just-below prices in their catalogs to a significant degree, either of which would have diluted the manipulation’s effect. Or maybe there were some confounds generated from regional disparities or the products assigned to the two conditions. We can only speculate.
The left-digit bias is unreliable.
However, here’s why we should take Ginzberg’s communication seriously. Over the years from 1936 to 2023, there have been numerous published studies, not to mention all the unsuccessful experiments and studies that never got published and were thrown away that have found exactly what Ginzberg found, which is that just-below prices sometimes worked, sometimes didn’t work, and sometimes worked so badly that it would have been better to use round prices. I won’t list all these studies here, but a recent meta-analysis by Troll, Frankenbach, Friese, and Loschelder (2023)5 does so. Their main conclusion also largely echoes Ginzberg:
Our meta-analysis of 362 effect sizes from 69 studies with an overall N = 40,541 found empirical support for the predicted higher demand (purchase decisions: g = 0.13), advantageous price image effect (i.e., price image: g = 0.28), and level effect (i.e., underestimated recall: g = 0.67) of just-below compared with round prices. These effects—particularly for purchase decisions and price image—were rather small according to common conventions (Cohen, 1988) and average effect sizes in marketing research (Eisend, 2015), and showed a very high degree of effect heterogeneity…While prior research has shown rather large just-below-pricing effects on purchase decisions (e.g., Choi et al., 2014), as well as price image and quality image (e.g., Schindler & Kibarian, 2001), the present meta-analysis suggests that these effects are considerably smaller (or even nonexistent).”
Essentially, the left-digit bias is unreliable. I want to mention one final point. Earlier, I mentioned 99 Cents Only Stores, which has built its brand and business around using just-below prices. However, its two major competitors are Dollar General and Dollar Tree. Both retailers are bigger and more profitable than 99 Cents Only Stores, and neither one uses just-below prices.
Instead, as their ads illustrate, each retailer has chosen unique approaches to communicate value through prices to their respective bases of price-sensitive shoppers - an emphasis on the $1.25 price point for Dollar Tree and the consistent use of cleanly presented round prices for Dollar General.
The main takeaway is that a just-below pricing approach may not be as much of a sure-shot as many practitioners seem to think. We have Professor Ginzberg’s work from before the Second World War to thank for this still-valid insight.
Thank you for reading this post. If you liked it, you may also like:
How managers made pricing decisions in 1939.
Holloway, R. (1973). Book review of Odd-Even Retail Price Endings by , Journal of Retailing, 49(1), 77-78.
Strulov-Shlain, A. (2023). More than a penny’s worth: Left-digit bias and firm pricing. Review of Economic Studies, 90(5), 2612-2645.
Ginzberg, E. (1936). Customary prices. The American Economic Review, 26(2), 296.
List, J. A., Muir, I., Pope, D., & Sun, G. (2023). Left-Digit Bias at Lyft. Review of Economic Studies, rdad014.
Troll, E. S., Frankenbach, J., Friese, M., & Loschelder, D. D. (2023). A meta‐analysis on the effects of just‐below versus round prices. Journal of Consumer Psychology, in press.