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Last class we talked about the problems with Expected Utility Theory. In this assignment you will use data from the survey to highlight these problems and derive some of the main features of a new theory – Prospect Theory – that we will discuss in detail next week.
Data from the survey are in the following spreadsheet …
This comprises data from 232 people who have taken the decision making survey since 2015. Each column corresponds to a different question and each row corresponds to a different person. All questions involve a choice between a certain option (100% probability of obtaining the outcome) and an uncertain, risky option.
When someone chose the risky option for a particular question, this is represented as a “1” in the data. When someone chose the safe option, this is represented as a “0” in the data.
Q1. The data in Column B corresponds to this question:
By taking the average of the numbers in Column B, what fraction of people chose the risky option in this question? (2 points)
What does this result mean – specifically are people risk averse or risk seeking for this question? (1 point)
What does your result tell you about the shape of the utility curve for gains? Sketch the utility curve as a function of gain. For this sketch, gain should be on the x axis (starting from gain = $0 to gain = $100) and utility should be on the y-axis. (2 points)
Q2 The data in Column C correspond to this question:
By taking the average of the numbers in Column C, what fraction of people chose the risky option in this question? (2 points)
What does this result mean – specifically are people risk averse or risk seeking for this question? (1 point)
What does your result tell you about the shape of the utility curve for losses? Sketch the shape of the utility curve for losses. Gain should be on the x-axis of this plot starting from –$100 and going to $0 (note that negative gains are losses!). Utility should again be on the y-axis. (2 points)
Can you put the two curves together to get the full utility curve for gains and losses? To get the answer correct, you’ll need to consider the response to the third question, in Column D:
What fraction of people choose the risky option in this question?
For the above question, we can write down expressions for the utility of Options A and B as:
\[EU(A) = U(0) = 0\]
\[EU(B) = 0.5 × U(100) + 0.5 × U(-100)\]
What does your answer to a) tell you about the relative sizes of \(U(100)\) and \(U(-100)\)?