For question 2, subparts B&C, how do you find the values for Pi of g and Pi of l?? I know you have to use the probability weighting function, but I'm not able to come up with a value that will give the correct solution when plugged into the rest of the problem. Please help!
ECON 4025: Behavioral Economics: Homework 4 Hard copy due in class on Thursday Apr 11, 2019. 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 his investment. 1. What is the expected value of investing in the project? (0.5) sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Answer: 0.7(1, 200, 000) + 0.3(800, 000) = 1, 080, 000. Give full credit in case a student calculates expected value of Alpha's gain/loss, which equals 0.7(200, 000) 0.3(200, 000) = 80, 000. 2. Suppose Alpha evaluates the project in accordance with prospect theory. Specifically, ( (x r)0.8 if x r v(x) = (r x)0.8 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) Argue (mathematically) that Alpha is loss averse. (0.5) Answer: This follows from the fact that > 1. Gain of $y is worth y 0.8, which is less than not losing $y because the latter is worth y 0.8. (b) What is Alpha's value of investing in the project if = 2? (1) Answer: Alpha's value of investing in the project is g (0.7)(200, 000)0.8 2l (0.3)(200, 000)0.8 = 1859.03. Th (c) Find the value of such that Alpha is indifferent between investing and not investing in the project. (0.5) Answer: Alpha will be indifferent if g (0.7) l (0.3) = 0. Therefore, = 1.66. 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. https://www.coursehero.com/file/47685771/Homework-4-Solutionspdf/ 1 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? (0.5) Answer: Present value equals 36 + 0.8(16) = 48.8. 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) (0.5) Answer: Beta wants to minimize x21 +0.8x22 subject to the constraint that x1 +x2 = sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 10. 3. How many hours does Beta choose to work the task on Monday? (1) Answer: Substitute x2 = 10 x1 in the objective function to get x21 + 0.8(10 x1 )2 . At the point of minimum, the derivative of the objective function must equal zero. That is, 40 2x1 1.6(10 x1 ) = 0 = x1 = . 9 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? (0.5) Answer: Beta now wants to maximize 0.82 (10x1 ) x21 0.8x22 subject to the constraint that x1 + x2 = 10. Substitute x2 = 10 x1 in the objective function to get 0.82 (10x1 ) x21 0.8(10 x1 )2 . At the point of maximum, the derivative of the Th objective function must equal zero. That is, 6.4 2x1 + 1.6(10 x1 ) = 0 = x1 = https://www.coursehero.com/file/47685771/Homework-4-Solutionspdf/ Powered by TCPDF (www.tcpdf.org) 2 56 . 9
