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March 27, 2005

Get smart for just $9.99



Marketing research has confirmed what many know, that a large number of goods are priced to the end in a 9, for example hamburgers for 99 cents or shoes for 49 dollars, what is referred to as odd-pricing or psychological pricing. With a look at a spreadsheet analysis of both wholesale and retail prices, you will see that wholesale prices (when looking at the last two right digits) are distributed very evenly over the range of 00 to 99, but when you look at retail pricing you see the obvious, that many prices end with 09, 19, ... , 99.

Do consumers do this out of irrationality or only when they expect the time cost of fully calculating the exact price to exceed the expected loss caused by the slightly erroneous but higher price paid by failing to accurately incorporate the rightmost digits? What kind of effect does pricing in the 9’s have on a market where there may be some non-strict equilibrium found where even or non-9 price ending occurs? A recent article out of The Harvard Institute for Economic Research (HIER) investigates what effect this phenomena may have on oligopolistic markets and attempts to build a model of the kinds of markets we may expect to result from pricing in the 9’s.


"The paper fully characterizes the Bertrand equilibria of oligopolistic markets where consumers may ignore the last (i.e. the right-most) digits of prices. Consumers, in this model, do not do this reflexively or out of irrationality, but only when they expect the time cost of acquiring full cognizance of the exact price to exceed the expected loss caused by the slightly erroneous amounts that is likely to be purchased or the slightly higher price that may be paid by virtue of ignoring the information concerning the last digits of prices. It is shown that in this setting there will always exist firms that set prices that end in nine though there may also be some (non-strict) equilibria where a non-nine price ending occurs. It is shown that all firms earn positive profits even in Bertrand equilibria. The model helps us understand in what kinds of markets we are most likely to encounter pricing in the 9's."


"Given the limits of the human brain, it is reasonable to assume human beings will not be fully informed. When a person goes through a supermarket buying goods, is it worthwhile for him to study and take in the price information of each product in full? It is not evident that the answer to this will be yes, contrary to what early textbook models of economics suggested. Indeed it may not be rational to take in so much information.5 If, for instance, he looked only at the dollar part of the prices and took his purchase decisions based on that, he would make a few wrong decisions, true, but the time saved by using this strategy may be well worth that little loss. I shall later model the circumstances where such time-saving is worthwhile."

"The model predicts that prices will generally end in 9s but in some markets there will be two modal price endings, one of which will invariably be 9. It is interesting to note that the asymmetric equilibrium in which the non-9 ending occurs would exist only if the indifference axiom holds. It is arguable that for products where people buy large amounts of some commodity or agree to a per unit price and then buy the commodity or service over a long period of time the indifference axiom is less likely to be satisfied. In such cases a small price difference translates into a large loss or gain for the buyer and hence consumers are more likely to take cognizance of the exact price. Hence for these kinds of goods multiple prices are less likely to occur in the same market."

"There is a large literature in psychology that illustrates how human beings often use simple rules of thumb to make decisions, instead of collecting all relevant information and then making decisions; and how these "fast and frugal" rules may in fact turn out to be reasonable (Gigerenzer and Goldstein, 1996; Gigerenzer and Selten, 2001). If for instance, people were given pairs of cities and asked which of each pair had the higher population and people named the city they were more familiar with*, Goldstein and Gigerenzer (1999) showed that they would be right significantly more often than if they chose the answer at random. Given that the collection of information can be costly in terms of time and money, for certain purposes the use of this heuristic may be the rational course. It is this general idea that I shall now use in the context of consumer decision-making concerning what to buy."

* It would be more correct to say "the city they recognized" - Ed.

"Unlike in the model of monopoly discussed in Basu (1997), we find that firms benefit from this phenomenon of pricing in the nines. This enables (sophisticated) Bertrand oligopolists to sustain a price above the marginal cost (and even above the prices that could prevail in the standard Bertrand oligopoly model with an exogenously fixed smallest unit of change). Also, unlike in a monopoly, some non-9 endings are now possible in equilibrium."

"Another natural way to extend the model is to suppose that, if a person is planning a very large purchase, he takes cognizance of the exact per-unit price of the product since even a tiny difference in per-unit price could make a big difference to his cost. While I have not modeled this formally here, it is reasonable to expect that in such situations the indifference axiom discussed above will be violated and so we will invariably see only one price for each good. If we go a step further and introduce the idea of 'cautious behavior' on the part of consumers, which is defined behavior that takes into account the possibility of 'trembles' in prices whether or not there exists any actual price variability in the market, then it is likely that the dominance of 9 endings will break down. For goods, where the consumer places large orders (that is, several multiples of the unit) on the basis of a per-unit price, there will be a unique price but there will be no special reason for this to have a 9-ending. Hence, for goods like cement, house paint, phone calls and long-term lawn-mowing contracts we will be less likely to see nine price endings. By the same kind of reasoning we would expect to see a wider use of prices ending in 9 in the retail market, where small quantities of goods are purchased, or in the market for perishable goods, as opposed to, for instance, the wholesale market."

"...instead of assuming consumer irrationality and consumer psychological delusion, if we simply recognized that consumers have limited time for decision-making and limited brain capacity and they act rationally subject to these limitations, then we can get results which elude the standard literature on industrial pricing and mimic some of the results which behavioral economics derives only by assuming consumer irrationality. This is not to suggest that consumers are never irrational but simply that we must not be too hasty in jumping to the conclusion of irrationality either."


Kaushik Basu

Haushik Basu.jpg

Kaushik Basu is a Professor of Economics and the Carl Marks Professor of International Studies at The Department of Economics, Cornell University. He received his PhD from The London School of Economics in 1976. His expertise includes Economic development, economic theory, industrial organization and political economy. His research interests include economic development, economic theory, industrial organization, and political economy. He has held visiting positions at CORE (Louvain-la-Neuve, Belgium), the Institute for Advanced Study (Princeton), and the London School of Economics, where he was a Distinguished Visitor in 1993. He also has been a Visiting Professor at Harvard University and Princeton University.

Kaushik Basu Homepage at Cornell University

Posted by DSN at March 27, 2005 09:34 PM