For question 2, subparts B&C, how do you find the values for Pi g and Pi l ??
ECON 4025: Behavioral Economics: Homework 4 Soft copy to be uploaded on Canvas by 11:59 pm on Tuesday Apr 14, 2020. Problem A: Alpha is deciding whether to invest $1 million in a project. There is a 70% chance that the project will be successful, yielding a return of 20% on investment. However, there is a 30% chance that the project will fail, in which case Alpha will only recover 80% of her investment. 1. Let x be the amount of money received by Alpha at the end of the project. What is the expected value of x? (2) 2. Suppose Alpha evaluates the project in accordance with prospect theory. Specifically, ( (x r)0.8 if x r v(x) = 0.8 (r x) if r > x, where > 1, r = $1 million is the reference point, and x is the amount of money received by Alpha at the end of the project. The corresponding probability weighting functions are such that = = 0.6. (a) Show that Alpha is loss averse. (3) (b) What is Alpha's value of investing in the project if = 2? (3) (c) Find the value of such that Alpha is indifferent between investing and not investing in the project. (3) (d) Suppose that instead of the project, Alpha can invest her $1 million in a mutual fund. The mutual fund gives a return of 20% with probability 25%. It gives a return of 10% with probability 50%. Finally, there is a 25% chance that the mutual fund will fall in value and Alpha will lose 80% of her investment. What is Alpha's value of investing in the mutual fund if = 2? (4) Problem B: Beta's boss assigns him a task on Monday which must be completed before Wednesday. The task takes a total of 10 hours. If Beta works on the task for xt hours on day t, then he suffers a disutility of x2t on day t. Throughout the problem t {1, 2, 3}, where 1 stands for Monday, 2 for Tuesday, and 3 for Wednesday. Beta's time preferences are given by exponential discounting with the discount factor of = 0.8 per day. 1. What is the present value (as measured on Monday) of Beta's disutility if he works for 6 hours on Monday and 4 hours on Tuesday? (2.5) 1 2. Beta's problem is to complete the task before Wednesday in such a way to minimize the present value of his distuility (as measured on Monday). Write down the mathematical version of Beta's problem (that is, minimize some function subject to some constraint) (3) 3. How many hours does Beta choose to work on the task on Monday? (3) 4. Now suppose that the boss wants to assign a new task to Beta on Tuesday and would therefore like Beta to have more time on Tuesday. She incentivizes Beta by offering him a reward of r3 = 10x1 on Wednesday if Beta works on Monday for x1 hours on the first task. How many hours does Beta choose to work on Monday? (4) 2
