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Thought Questions

 

89

 

 

 

 

 

 

 

 

 

 

 

 

 

Biographical Note

© Barbara Tversky

Amos N. Tversky (19371996)

B.A., Hebrew University, 1961; Ph.D. University of Michigan, 1965; held faculty positions at the Hebrew University and Stanford University

Trained as a cognitive psychologist, Amos Tversky pioneered the examination of systematic bias in reasoning. His works include studies of how people misjudge the probabilities of random outcomes, the valuation of gains versus losses, the impacts of framing on decision making, and dealing with

ambiguous choices. Much of his best work was conducted in collaboration with Daniel Kahneman, who, after Tverskys death, won the Nobel Prize for economics primarily for their joint work. Tverkys work developed the notions of decision heuristics as an alternative to the rational choice model, with the implication that people may be making mistakes in judgment owing to their inability to carry out the necessary calculations. The biases were not limited to uneducated people but could be found even in articles in peer-reviewed physics journals. He helped to found the Stanford Center for Conict Resolution and Negotiation, an interdisciplinary research center. In the course of his career he was honored with a MacArthur Fellowship, was elected to the American Academy of Arts and Sciences and the National Academy of Science, and was awarded numerous honorary doctorates. In addition to his academic contributions, Tversky was a war hero in Israel, serving in three wars. At one point, he saved the life of a fellow soldier who had fallen on an explosive about to detonate, throwing him to safety while risking his own life and sustaining some injuries in the blast. Tversky died from cancer at the age of 59.

T H O U G H T Q U E S T I O N S

1.Default options have proved to be effective in guiding public behavior, possibly by helping to shape individual preferences where none existed. Suppose, in an attempt to increase calcium intake by children, a school decided to include a small carton of plain skim milk with each school lunch purchased. The children are very familiar with milk and have well-formed preferences. Alternatively, children could request milk with higher fat content, chocolate milk, or no milk, if they desired, at no extra cost. How might this default function differently from the default examples given in this chapter?

2.It is generally found that those who are willing to change jobs earn greater amounts of money. Essentially, these people apply for alternative jobs on a regular basis and change jobs when they receive better offers than their current employment. However, a relatively small percentage of employed workers ever seek other jobs unless they are informed they might lose their job. Using the terminology and models of behavioral economics, explain why such a small percentage of employees would actively look for alternative jobs when they are secure in their employment. Additionally, consider employees who are informed

 

 

 

 

 

90

 

STATUS QUO BIAS AND DEFAULT OPTIONS

that they might lose their job shortly. Considering that the potential job loss is not based on performance but is based rather on the structural conditions of the rm, they might expect to earn more upon nding a new job. What does the endowment effect have to say regarding how the employee values the outcome of the job hunt before and after nding their new job?

3.A novelty store is worried that customers may be unfamiliar with the items they sell and thus reluctant to purchase. The owner is considering either using instore demonstrations of the objects they are selling or providing some sort of money-back guarantee. Use diagrams representing the value function of the consumer to describe the tradeoffs in prot for each option. What impact should each policy have on the pricing of the items in the store?

4.Consider again the problem of determining the maximum amount one is willing to pay to obtain a good versus the amount willing to accept to part with a good.

R E F E R E N C E S

Ariely, D., G. Loewenstein, and D. Prelec. “‘Coherent Arbitrariness: Stable Demand Curves without Stable Preferences.” Quarterly Journal of Economics 118(2003): 73105.

Chen, K., V. Lakshminarayanan, and L. Santos. The Evolution of Our Preferences: Evidence from Capuchin Monkey Trading Behavior.Cowles Foundation Discussion Behavior No. 1524, Yale University, 2006.

Johnson, E.J., and D. Goldstein. Do Defaults Save Lives?” Science

302(2003): 13381339.

Johnson, E.J., J. Hershey, J. Meszaros, and H. Kunreuther. Framing, Probability Distortions, and Insurance Decisions.” Journal of Risk and Uncertainty 7(1993): 3551.

Kahneman, D., J.L. Knetsch, and R.H. Thaler. Experimental Tests of the Endowment Effect and the Coase Theorem.” Journal of Political Economy 98(1990): 13251348.

Kahneman, D., J.L. Knetsch, and R.H. Thaler. The Endowment Effect, Loss Aversion, and Status Quo Bias.” Journal of Economic Perspectives 5(1991): 193206.

Consider Terry, who behaves according to the model presented in equations 4.4 and 4.7. Let the utility function be given by ux1, x2= x.15 + x.25, wealth is given by w = 100, and p2 = 1, so that x*2 = 100. Derive the maximum willingness to pay and the minimum willingness to accept for 100 units of good 1. Which measure of value is larger? How do you answers change if instead we considered only 1 unit of good 1? Under which scenario are the measures of value more

nearly the same? Why? How do these answers change if ux1, x2= x.15x.25?

5.Now suppose Terry displays constant additive loss aversion, with vrx1, x2= Rx1+ Rx2, with

R xi

=

xi − ri

if

xi ≥ ri

2 xi − ri

if

xi < ri.

 

 

Complete the same exercise as in question 4. How do these answers differ from those in question 4? Why?

Knetsch, J.L., and J.A. Sinden. Willingness to Pay and Compensation Demanded: Experimental Evidence of an Unexpected Disparity in Measures of Value.” Quarterly Journal of Economics 99 (1984): 507521.

List, J.A. Neoclassical Theory versus Prospect Theory: Evidence from the Marketplace.” Econometrica 72(2004): 615625.

Samuelson, W., and R. Zeckhauser. Status Quo Bias and Decision Making.” Journal of Risk and Uncertainty 1(1988): 759.

Thaler, R. Toward a Positive Theory of Consumer Choice.

Journal of Economic Behavior and Organization 1(1980): 3960.

Tversky, A., and D. Kahneman. Loss Aversion in Riskless Choice: A Reference Dependent Model.” Quarterly Journal of Economics

106(1991): 10391061.

 

 

 

 

References

 

91

 

Advanced Concept

The Shape of Indifference Curves with Constant Loss Aversion

To derive the shape of the indifference curve under constant loss aversion, we must nd all points that satisfy

vr x = U R1 x1 , R2 x2 = k,

4 A

where k is an arbitrary constant and where we now limit ourselves to the two-good case. So long as we do not evaluate at a reference point, the function in equation (4. A) is differentiable, and thus we can totally differentiate (4.A) to nd

R1 UR1x1, R2x2 x1 R1x1dx1

4B

+ R2 UR1x1, R2x2x2 R2x2dx2 = 0,

or

 

 

dx2

 

 

 

 

U R1 x1 , R2 x2

 

 

 

R1 x1

 

 

 

 

= −

R1

x1

.

4 C

 

 

 

 

 

 

 

 

 

 

 

 

 

dx1

 

 

U R1 x1

, R2 x2

 

 

 

 

R2 x2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

R2

 

 

 

 

x2

 

By differentiating (4.1), we obtain

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ri xi

=

 

 

ui xi

xi

if

 

xi > ri

4 D

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

xi < ri.

 

 

 

 

 

xi

 

λi

ui xi xi

if

 

 

 

 

 

 

 

 

Thus, we can rewrite (4.C) as

 

 

 

 

 

 

 

 

 

 

 

 

dx2

 

 

 

 

 

U R1 x1

, R2 x2

 

 

 

u1 x1

 

 

= −

 

 

R1

 

 

x1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

z,

4 E

dx1

 

 

 

 

 

 

, R2 x2

 

 

 

 

 

 

 

 

 

 

U R1 x1

 

 

 

u2 x2

 

 

 

 

 

R2

 

 

x2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

where

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

if

x1 > r1, x2 > r2

 

 

 

 

 

 

z =

λ1 λ2

if

x1 < r1, x2 < r2

4 F

 

 

 

 

 

 

 

 

 

λ1

if

x1 < r1, x2 > r2

 

 

 

 

 

 

 

 

 

1 λ2

if

x1 > r1, x2 < r2.

 

When crossing the reference point along any dimension, the derivative changes discontinuously according to z. In the northern half of Figure 4.2, as the

 

 

 

 

 

92

 

STATUS QUO BIAS AND DEFAULT OPTIONS

indifference curve crosses r1, the slope of the indifference curve is λ1 times steeper to the left of the reference line than on the right. In the southern hemisphere, the slope of the indifference curve is also λ1 times steeper to the left of the reference line than to the right. Similarly, as one moves from the northern half of the gure to the southern half, the slope of the indifference curve is divided by a factor of λ2, leading to a shallower slope.

In the special case of constant additive risk aversion, (4.E) can be rewritten simply as

dx

2

 

 

u1

x1

 

= −

x1

 

 

 

z,

4 G

dx1

 

 

 

 

u2

x2

 

 

x2

 

 

 

 

 

 

 

which appears much like the standard indifference curve multiplied by the loss aversion factor, z.

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