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ECNM10066

Behavioural Economics

Problem Set 3

February 6, 2024

Topics covered: Generalised prospect theory, intertemporal choice, present bias and sophistication.

To be discussed in Week 5. Deadline to submit your own attempt is Thursday Feb 15th 9am.

Problem 1: expectation-based reference dependence

Consider the “shopping for shoes” example from K¨oszegi and Rabin (2006). Refer to slides 57-67 in Topic 3 and use algebra to:

1. Find pmax – the maximum price at which a loss-averse consumer who expects to buy the shoes prefers to buy the shoes.

2. Find pmin – the maximum price at which a loss-averse consumer who expects to not buy the shoes prefers to buy the shoes.

3. Use diagram to analyse how the number (and type) of Personal Equilibria varies with price.

4. Compare the prices you’ve found in (1-2) to what a rational consumer with the same consumption utility but without gain-loss portion would be willing to pay for the same shoes.

Problem 2: partial-naifs

Consider Example #3 from Topic 3 (pages 33 to 41) where a student chooses when to do a problem set. Suppose now that the student is partially naive – ie β = 1/2, δ = 1, and βˆ = 3/4. That is, the student is present biased but expects her future self to be less present biased. Determine when this student will do the problem set. How would your answer change if βˆ = 0.55? What does it tell you about the behaviour of partially-naive agents?

Problem 3: naifs trump sophisticates

Alice, Bob, and Chloe are students taking this course. They all are (independently) deciding when to go for a movie this term. There are different movies available in the local cinema over the next four weekends (t = 0, 1, 2, 3) and the students like some of them (much more) than others – the utility vector associated with the movies is u = {3, 5, 8, 13}. For simplicity, assume that all three students assign the same utility to each of the movies and each student can (and will go) to exactly one movie. Your task in this problem is to determine which movie will be seen by each of the students. In doing so, you need to make further assumptions:

1. Suppose Alice is an exponential discounter with β = 1 and δ = 1 – ie she has no present bias and does not discount the future at all.

2. Suppose Bob is a fully naif hyperbolic discounter with β = 1/2, δ = 1, and βˆ = 1. That is, Bob is present-biased but thinks his future selves are completely unbiased.

3. Suppose Chloe is a fully rational hyperbolic discounter β = 1/2, δ = 1, and βˆ = 1/2. That is, Chloe is present-biased but is completely aware of her bias.

Looking at your analysis above, can you rank the three students’ choices? What does this problem tell you about the relative superiority of sophisticates over naifs?