1. [70 MARKS] Consider the following simplified version of the paper “Self-Control at Work”
by Supreet Kaur, Michael Kremer and Sendhil Mullainathan (2015). In period 1 you will
perform a number of data entry task for an employer. The effort cost of completing x
tasks is given by αx2
, where α > 0. In period 2, you will be paid according to how many
task you have done. The (undiscounted) utility for receiving an amount of money y is
equal to y. From the point of view of period 1, the utility from completing x tasks and
getting money y is equal to
−αx2 + βy
where β ∈ [0, 1], while from the point of view of period 0 it is
−αx2 + y.
Assume that you are not resticted to completing whole number of tasks (so you can solve
this problem using derivatives).
(a) [15 MARKS] Assume that you get paid $1 for each task (so if you complete x tasks
you get y = x). In period 1, you are free to choose how much work to do. Calculate
how much you will find optimal to do (as a function of α and β).
(b) [15 MARKS] Derive how much work you would choose to do if you could fix in
period 0 the number of tasks you would do in period 1 (as a function of α). Call this
(α) (the number of task completed under commitment). Assuming β < 1, show whether x ∗ (α) is higher or lower than the effort level you would choose in period 1 for the same α. Interpret your results. (c) [15 MARKS] Assume that α = 1 and β = 1/2 and that you are sophisticated, i.e. you know that the number of tasks you plan at period 0 to do in period 1 is higher than what you will actually choose to do in period 1. Derive how much of your earnings you would be prepared to pay to commit to your preferred effort level in period 0. i.e. calculate the largest amount T that you would be prepared to pay such that you would prefer to fix effort at x ∗ (1) but only receive x ∗ (1) − T in payment, rather than allow your period 1 self to choose effort levels. (d) [20 MARKS] Self-Control problem does not only affect you, but also the employer who you work for and who wants all the tasks to be completed. As a result, both you and the employer have self-interest in the provision of commitment devices. In what follows, we investigate the provision of commitment by the employer, considering a 3 of 10 ECON32152 different wage scheme. In this wage contract you only get paid x if you complete at least as many tasks in period 1 as you would want in period 0, x ≥ x ∗ (1). Your pay, however, will only be λx (with λ < 1) if you complete fewer task in period 1 than what you find optimal in period 0, x < x∗ (1). Show that if λ = 0 (commitment contract) then in period 1 you will choose to produce x ∗ (1) if β ≥ 1 2 , but not otherwise (still assuming α = 1). Show also that this implies that if β = 3 4 , then in period 0 you would prefer the work contract in which λ = 0 to the work contract in which λ = 1 (standard contract). (e) [5 MARKS] Now again assume that β = 3 4 . Using your results above, calculate how much you would choose to work in period 1 if • α = 1 and λ = 0 • α = 1 and λ = 1 • α = 2 and λ = 1 4 of 10 ECON32152 QUESTION 2 2. [30 MARKS] Consider the paper “Myopic Loss Aversion and the Equity Premium Puzzle” by Shlomo Benartzi and Richard H. Thaler (1995). (a) [5 MARKS] Explain shortly what the equity premium puzzle is. (b) [5 MARKS] The authors explain the equity premium puzzle by using two concepts, the concept of loss aversion and mental accounting. Explain what loss aversion is and how it is related to prospect theory. Explain what mental accounting is. (c) [5 MARKS] As in the paper, consider the following simple utility function capturing loss aversion, where x is a change in wealth relative to the status quo. U(x) = ( x if x ≥ 0 2.8x if x < 0 (1) Argue why you would or why you would not accept a bet where you win $100 with 50% probability, while lose $50 with 50%. (d) [5 MARKS] Focusing on mental accounting, now assume that you are offered two of the bet described in Question 2 (c), which are sequentially played out (but you do not watch the bet being played out). Argue why you would or you would not accept the bet now.[Hint: First calculate the distribution of outcomes (outcomes with probabilities) created by the portfolio of two bets and then evaluate the utility function!] (e) [5 MARKS] Explain whether and why your answers to questions (c) and (d) would change if the bet is the same as before, but now your reference point changes to -$50. (f) [5 MARKS] Explain what the examples in Question 2 (c) and 2 (d) imply for the relationship between loss aversion and the frequency of performance evaluation. 5 of 10