The upper portion, for gains, has the same shape as the usual utility of wealth function, capturing the idea of diminishing sensitivity. But notice that the loss function captures diminishing sensitivity also. The difference between losing $10 and $20 feels much bigger than the difference between losing $1,300 and $1,310. This is different from the standard model, because starting from a given wealth level in figure 1, losses are captured by moving down the utility of wealth line, meaning that each loss gets increasingly painful. (If you care less and less about increases in wealth, then it follows that you care more and more about decreases in wealth.)
The fact that we experience diminishing sensitivity to changes away from the status quo captures another basic human trait—one of the earliest findings in psychology—known as the Weber-Fechner Law. The Weber-Fechner Law holds that the just-noticeable difference in any variable is proportional to the magnitude of that variable. If I gain one ounce, I don’t notice it, but if I am buying fresh herbs, the difference between 2 ounces and 3 ounces is obvious. Psychologists refer to a just noticeable difference as a JND. If you want to impress an academic psychologist, add that term to your cocktail party banter. (“I went for the more expensive sound system in the new car I bought because the increase in price was not a JND.”)
You can test your understanding of the concept behind the Weber-Fechner Law with this example from National Public Radio’s long-running show called Car Talk . The show consisted of brothers Tom and Ray Magliozzi—both MIT graduates—taking calls from people with questions about their cars. Improbably enough, it was hysterically funny, especially to them. They would laugh endlessly at their own jokes. ‡
In one show a caller asked: “Both my headlights went out at the same time. I took the car to the shop but the mechanic said that all I needed was two new bulbs. How can that be right? Isn’t it too big of a coincidence that both bulbs blew out at the same time?”
Tom answered the question in a flash. “Ah, the famous Weber-Fechner Law!” It turns out that Tom also did a PhD in psychology and marketing supervised by Max Bazerman, a leading scholar in judgment and decision-making research. So, what does the caller’s question have to do with the Weber-Fechner Law, and how did this insight help Tom solve the problem?
The answer is that the two bulbs did not in fact burn out at the same time. It is easy to drive around with one bulb burned out and not notice, especially if you live in a well-lit city. Going from two bulbs to one is not always a noticeable difference. But going from one to zero is definitely noticeable. This phenomenon also explains the behavior in one of the examples on the List: being more willing to drive ten minutes to save $10 on a $45 clock radio than on a $495 television set. For the latter purchase, the savings would not be a JND.
The fact that people have diminishing sensitivity to both gains and losses has another implication. People will be risk-averse for gains, but risk-seeking for losses, as illustrated by the experiment reported below which was administered to two different groups of subjects. (Notice that the initial sentence in the two questions differs in a way that makes the two problems identical if subjects are making decisions based on levels of wealth, as was traditionally assumed.) The percentage of subjects choosing each option is shown in brackets.
P ROBLEM 1. Assume yourself richer by $300 than you are today. You are offered a choice between
A. A sure gain of $100, or
[72%]
B. A 50% chance to gain $200 and a 50% chance to lose $0.
[28%]
P ROBLEM 2. Assume yourself richer by $500 than you are today. You are offered a choice between
A. A sure loss of $100, or
[36%]
B. A 50% chance to lose $200 and a 50% chance to lose $0.
[64%]
The reason why people are risk-seeking for losses is the same logic