Question

Two pioneers of the field of behavioral economics, Daniel Kahneman and Amos Tversky (winners of the Nobel Prize in economics in 2002 , conducted an experiment in which they presented different groups of subjects with one of the following two scenarios: Scenario 1: In addition to \(\$ 1,000\) up front, the subject must choose between two gambles. Gamble \(A\) offers an even chance of winning \(\$ 1,000\) or nothing. Gamble \(B\) provides \(\$ 500\) with certainty. Scenario 2: In addition to \(\$ 2,000\) given up front, the subject must choose between two gambles. Gamble \(C\) offers an even chance of losing \(\$ 1,000\) or nothing. Gamble \(D\) results in the loss of \(\$ 500\) with certainty. a. Suppose Standard Stan makes choices under uncertainty according to expected utility theory. If Stan is risk neutral, what choice would he make in each scenario? b. What choice would Stan make if he is risk averse? c. Kahneman and Tversky found 16 percent of subjects chose \(A\) in the first scenario and 68 percent chose \(C\) in the second scenario. Based on your preceding answers, explain why these findings are hard to reconcile with expected utility theory. d. Kahneman and Tversky proposed an alternative to expected utility theory, called prospect theory, to explain the experimental results. The theory is that people's current income level functions as an "anchor point" for them. They are risk averse over gains beyond this point but sensitive to small losses below this point. This sensitivity to small losses is the opposite of risk aversion: \(A\) risk-averse person suffers disproportionately more from a large than a small loss. (1) Prospect Pete makes choices under uncertainty according to prospect theory. What choices would he make in Kahneman and Tversky's experiment? Explain. (2) Draw a schematic diagram of a utility curve over money for Prospect Pete in the first scenario. Draw a utility curve for him in the second scenario. Can the same curve suffice for both scenarios, or must it shift? How do Pete's utility curves differ from the ones we are used to drawing for people like Standard \(\operatorname{Stan} ?\)

Short answer

What are the choices of Prospect Pete according to prospect theory? Answer: According to expected utility theory, Risk-neutral Stan would choose gamble A in Scenario 1 and gamble C in Scenario 2. Risk-averse Stan would choose gamble B in Scenario 1 and gamble D in Scenario 2. According to prospect theory, Prospect Pete would choose gamble B in Scenario 1 and gamble C in Scenario 2.

Step-by-step solution

Calculate expected value for the gambles in Scenario 1

To find the expected value, we need to find the average of all possible outcomes. For gamble \(A\), we will calculate: \(\frac{\$0+\$1,000}{2} = \$500\). For gamble \(B\), the expected value would be the same because Stan would be certain to win \(\$500\).

Calculate expected value for the gambles in Scenario 2

Similarly, for gamble \(C\), we will calculate: \(\frac{-\$0-\$1,000}{2} = -\$500\). For gamble \(D\), the expected value would be the same because Stan would be certain to lose \(\$500\).

Determine risk-neutral Stan's choices

Since both gamble \(A\) and \(B\) have the same expected value, as well as gamble \(C\) and \(D\), a risk-neutral Stan would be indifferent between the options in both scenarios. However, we can assume that he chooses \(A\) and \(C\), as he's not averse to risk. #b. Risk-averse Stan's Choices#

Determine risk-averse Stan's choices in Scenario 1

A risk-averse person would choose the option with the least risk in each situation. In Scenario 1, Stan would choose gamble \(B\), because it guarantees \(\$500\) instead of a chance to win or lose.

Determine risk-averse Stan's choices in Scenario 2

Similarly, in Scenario 2, Stan would choose gamble \(D\) because it guarantees a loss of \(\$500\) instead of the possibility of losing more. #c. Difficulty in reconciling with expected utility theory#

Discuss the findings of Kahneman and Tversky

The findings show that 16% of subjects chose \(A\) in Scenario 1, while 68% chose \(C\) in Scenario 2. This is difficult to reconcile with expected utility theory, as the theory would indicate that each individual should consistently adhere to risk-averse or risk-neutral behavior. #d. Prospect theory and choices of Prospect Pete#

Determine Prospect Pete's choices

According to prospect theory, people are risk-averse to gains and more sensitive to losses. Thus, Prospect Pete would choose gamble \(B\) in Scenario 1, which guarantees a gain of \(\$500\) and gamble \(C\) in Scenario 2, which gives an even chance of not losing anything.

Compare Prospect Pete's utility curves in both scenarios

A utility curve for Prospect Pete in the first scenario would show a concave function for over gains, indicating risk aversion. In the second scenario, the utility curve would be convex for losses, showing that Pete is more sensitive to losses and willing to take risks to avoid them. The same curve cannot suffice for both scenarios, as prospect theory offers different predictions depending on whether the situation involves gains or losses. This is different from Standard Stan, whose utility curve would be either a straight line (risk-neutral) or a concave function (risk-averse) in both scenarios.

Key concepts

Behavioral Economics

Behavioral Economics is a fascinating field that blends psychology with traditional economic theory to better understand how humans make decisions. Traditional economics assumes that people always make rational and logical choices. However, this isn't always the case. People often act differently due to biases, emotions, and limited cognitive resources.
Behavioral economics explores these behaviors and aims to create more realistic models of human decision-making. It can explain why people spend impulsively or avoid investments.
By considering the psychological factors that influence decisions, behavioral economics offers deeper insights. It helps fill the gaps where classical theories like expected utility theory fall short.

• Examines how psychological factors influence economic decisions.
• Challenges the assumption of complete human rationality.
• Incorporates aspects like biases and risk perceptions.

Expected Utility Theory

Expected Utility Theory is a cornerstone of traditional economics that people use to make decisions under uncertainty. It assumes that people assess risky options by calculating their expected utility and choose the one with the highest value.
Utility, in this context, is a measure of satisfaction or happiness obtained from a particular outcome. Therefore, expected utility is the sum of the utilities of all possible outcomes, each weighted by its probability.
This theory often assumes people are risk-neutral, which means they would purely consider expected values and ignore the potential variability of outcomes.

• Assumes rational decision-making based on maximizing expected utility.
• Uses probabilities to evaluate different risky options.
• Often doesn't account for behavioral deviations shown in real-life scenarios.

Risk Aversion

Risk Aversion refers to the preference for a sure outcome over a gamble with a potentially higher, but uncertain, payoff. Many people are risk-averse, prioritizing security over larger gains that come with uncertainty.
In the context of Kahneman and Tversky's experiment, a risk-averse individual would prefer Gamble B in Scenario 1 due to its guaranteed gain of $500. Similarly, in Scenario 2, they would stick with Gamble D to avoid the risk of losing an additional amount.
This behavior aligns with expected utility theory by showing how individuals opt for less risk when potential losses are possible, even if the gamble’s expected utility is higher.

• Prefers certain outcomes over risky ones with potentially greater returns.
• Leads to choices that may differ from those predicted by risk-neutrality.
• Can be explained by a concave utility function over money.

Kahneman and Tversky

Daniel Kahneman and Amos Tversky made groundbreaking contributions to the understanding of decision-making through their development of Prospect Theory. Their work revealed that classical economic theories like expected utility theory cannot fully account for how people actually evaluate risk.
They demonstrated through their experiments that people often make inconsistent choices depending on how scenarios are framed. This led to the discovery that framing effects and loss aversion heavily influence decision-making.
Their research showed the real-world inconsistency, where people showed different preferences in equivalent situations, solely based on the context or "frame" of the decision.

• Pioneers of Prospect Theory, offering a new perspective on decision-making.
• Highlighted cognitive biases in economic choices.
• Introduced concepts like loss aversion and anchoring.

Anchoring Effect

The Anchoring Effect is a cognitive bias that influences decision-making. It occurs when people rely too heavily on the first piece of information they receive (the "anchor") when making decisions.
In the experiments by Kahneman and Tversky, individuals' decisions were swayed by the initial amounts stated in the scenarios. The initial $1,000 or $2,000 given in each scenario anchored participants' evaluations of the gambles.
This anchoring skews perceptions and highlights why real-world decision-making deviates from theoretical models. Anchoring is powerful, impacting everything from shopping habits to negotiating prices.

• Influences decisions through initial information presented.
• Demonstrates the non-rational aspects of thinking in economics.
• Can lead to skewed judgments and suboptimal choices.