You’ve done the math. Accounting for everything from gas to insurance to repair costs, you find that taking Uber and other forms of mass transportation represents significant overall cost savings compared to owning your own car.

Logically, you should sell your car. So why don’t you?

In his 2010 New York Times best-seller Predictably Irrational: The Hidden Forces That Shape Our Decisions, author Dan Ariely contended that most people are far less rational in their decision-making — particularly when it comes to making purchases — than they like to think they are. These “irrationalities” and anomalies in consumer behavior pose a real challenge when a company goes about setting its prices.

From a gym membership to a sandwich at the airport, it turns out the question “What are people willing to pay?” is complex. And the complexity is growing in today’s era of e-commerce, credit cards, autopayments and prepayments, when the moment of purchase is often separated from the moment of consumption. Context and timing, while not quite everything, have a great deal to do with the optimal price.

How’s a company to navigate these subjective factors, and account for them in a methodical way?

A new model developed by Darden Professor Manel Baucells in collaboration with a colleague at HEC Paris, Woonam Hwang, will help companies and managers better account for the most prominent anomalies in consumer behavior. Their model, called the Model of Mental Accounting and Reference Price Adaptation (MARA), represents a second-generation version of an earlier model of mental accounting by Prelec and Loewenstein.[i]

To understand the implications of this model for everyday business practices, a little background and defining of terms are necessary.

How Consumers Think

For years, businesses have been aware of a practice among consumers known as mental accounting, a term first coined by University of Chicago business professor Robert Thaler. To quote Thaler, “Mental accounting is the set of cognitive operations used by individuals and households to organize, evaluate and keep track of financial activities.”[ii]

Mental accounting happens, for instance, when a person considers that she has already spent all of her $100 monthly budget for dining out and decides to bring a bagged lunch from home instead of eating out, even when the diner next-door to her office is advertising a great lunch deal.

A central component of mental accounting is the reference price, which is the price a consumer mentally assigns to a product or service. It’s a moving target and based on multiple factors — for instance, the original price, the price observed at other stores or the price previously paid for the same item. Consumers compare the reference price against (1) the actual price at the time of purchase and (2) the value of the good/service at the time of consumption. These two comparisons lead the consumer to conclude if a purchase is a good deal (transactional utility) and worth the cost (usage utility).

It’s easy to see why a company would want to be able to predict reference prices. Yet, such predictions have typically been quite difficult because they come about through a psychological process.

MARA is novel in that it correctly anticipates consumers’ formulation of reference prices, and predicts if and when loss aversion (the strong desire by consumers to avoid feeling they’re wasting their money) kicks in. The model uses these factors to explain and account for the major anomalies in consumer behavior: sunk-cost effects, payment depreciation, reluctance to trade, flat-rate bias and preference for up-front payment. Previously, no model had accounted for all five of these anomalies at once, and the second and third had gone unexplained. The explanations MARA offers provide immediately applicable insights for businesses and managers.

Implications for Managers

In short, MARA means that determining optimal pricing has just become much less of a guessing game.

The Flat-Rate Bias, Explained

The first anomaly, the flat-rate bias, is observed with any regular/repeated service, such as cellphone or Internet services; gym or museum memberships; and magazine, music or video library subscriptions. For the sake of illustration, let’s consider gym membership.

Gyms have generally enjoyed larger profits by selling semiannual flat-rate memberships, as opposed to monthly or pay-per-use pricing plans (assuming the single fee is sufficiently affordable in the customer’s eyes). The question is, why? MARA tells us that this is because, for five out of six months, the consumer does not make a payment. Over time, the reference price gradually decreases in the customer’s mind. Thus, when comparing the value of the good to the (low) reference price, they feel good about using the gym because the mental cost (i.e., reference price) approaches zero. Logically, if the gym-goer were to pay by visit or by month, the cost may be identical or higher if you do the math, but it would feel more expensive. Indeed, a pay-per-use plan keeps the reference price high in the consumer’s mind, and the gym user feels the full cost every time he or she uses the gym.

Flat rates produce what Baucells and Hwang call “the feeling of free consumption.” According to Baucells, “It’s a win-win situation: The customer feels happier, while the company makes more money.”

Payment Depreciation and the Effects of Dissociating Payment from Consumption

To understand the phenomenon of payment depreciation, let’s say a person buys tickets to an event at the Summer Olympic Games. The day of the event, however, the person wakes up with the flu. Does the person attend anyway or not?

Past research has shown that the person who bought the tickets at full price or bought them more recently will tend to go to the event anyway, whereas the person who got a “bargain” and/or purchased the tickets long ago would be less likely to attend. The aversion to waste or loss can be explained by MARA through reference price adaptation. For the recent and full-price buyers, the reference price is higher; for the bargain-price buyers and people who bought the tickets months in advance, the reference price is lower — and the feeling of waste lower.

“Companies have been aware of these two and the other three prominent anomalies in consumer behavior for a long time, but they didn’t know how to explain them or account for them with a single model,” Baucells says. “Our model fills the gaps of previous models and makes it simpler for companies to predict optimal pricing without trying to guess which model to use.”

Baucells adds: “In developing MARA, we found that reference prices are in much greater flux than we thought. Just how much they’re in flux, and the degree to which consumers differ on how quickly they adapt them in their minds, we are continuing to research. Are some consumers fast adapters and others slow adapters? If so, companies may need to consider marketing to each in different ways.”

Manel Baucells co-authored “A Model of Mental Accounting and Reference Price Adaptation,” forthcoming in Management Science, with Woonam Hwang of HEC Paris.


[i] Prelec & Loewenstein (1998), “The Red and the Black: Mental Accounting of Savings and Debt,” Marketing Science 17(1), 1998. This article introduces the first dynamic model of mental accounting.

[ii] Thaler (1999), “Mental Accounting Matters” (Abstract), Journal of Behavioral Decision Making 12(3): 183.

About the Expert

Manel Baucells

David M. LaCross Associate Professor of Business Administration

Baucells researches the incorporation of psychological realism into consumer behavior models, focusing on factors like anticipation, reference point comparison, mental accounting, psychological distance and satiation. He is an expert in consumer behavior, decision analysis and game theory.

Prior to his time at Darden, Baucells taught at IESE Business School and the University Pompeu Fabra in Barcelona, as well as served as senior economist at the Rand Corporation in California. He is co-author of the book Engineering Happiness, which applies principles of behavioral economics to happiness, and which was honored with the Decision Analysis Society Publication Award in 2014.

M.S., Universitat Politècnica de Catalunya; MBA, IESE Business School; Ph.D., UCLA Anderson School of Management