Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Student Number: QUIZ 3 Econ 212-Section B Question 1. [10 marks] Consider two lotteries A and B. With A, you win $60 with probability 0.5 and $ 100 with probability 0.5. With lottery B, you win $ 200 with probability 0.4 and $ 0 with probability 0.6. Assume that this lottery costs you nothing and that you have no wealth to start with. a) [4 marks] Compute the expected value and variance of A and B. Which lottery is more risky? Show your work. Answer: EV of B = 0.4*200 = 80 EV of A = (.5)*60 + 0.5*100 = 80 Variance of A = (.5)*(60-80)^2 + 0.5*(100-800)^2 = 200 + 200 = 400 Variance of B = (.6)*(0-80)^2 + 0.4*(200-80)^2 = 9600 Lottery B is more risky. b) [3 marks] If the decision maker’s (your) utility function is U I 100 , what is the expected utility associated with lotteries A and B? Given a choice to pick between the two lotteries, which lottery would you pick and why? Show your work. Answer: The expected utility of A is E (U ) (0.5) * 60 100 0.5 * 100 100 13.396 The expected utility of B is E (U ) (0.6) * 0 100 0.4 * 100 200 12.93 Lottery A has higher expected utility than lottery B, So you would prefer lottery A. 1 c) [3 marks] If the decision maker’s (your) utility function is U I ^2 , what is the expected utility associated with lotteries A and B? Given a choice to pick between the two lotteries, which lottery would you pick and why? Show your work. Answer: Expected Utility of A given above utility function is E (U ) (0.5) * (60) 2 0.5 * (100) 2 6800 Expected Utility of B given above utility function is E (U ) (0.6) * (0) 2 0.4 * ( 200) 2 16000 You would choose lottery B as it gives higher expected utility. Note that the preferences in this part exhibit ‘love for risk’. So you prefer lottery which is risky in terms of returns. 2