Question

2. Consider two lotteries, A and B. With lottery A, there is a 0.90 chance that you receive a payoff of S0 and a 0.10 chance that you receive a payoff of $400. With lottery B, there is a 0.50 chance that you receive a payoff of S30 and a 0.50 chance that you receive a payoff of $50, a) Verify that these two lotteries have the same expected value but that lottery A has a bigger variance than lottery B. b) Suppose that your utility function is U = V1 + 500. Compute the expected utility of cach lottery. Which lottery has the higher expected utility? Why? c) Suppose that your utility function is U = 1 + 500. Compute the expected utility of each have this utility function, are you risk averse, risk neutral, or risk loving? d) Suppose that your utility function is U = (1 + 500). Compute the expected utility of each lottery. If you have this utility function, are you risk averse, risk neutral, or risk loving?

Answer 1

Inswer page-01 the given information. According to expected value a) verifying Expected value = p pay $6.) + (1-P) 2 pay f6 2) ENA 0.910)+0.101400) totuo 40 V = 0.50 (30) +0.50(50) = 15+95 -40 : Therefore both batteries have equal expected value... 1. variance = Gur) - CE E 603) = 0.960194 0.101400) = 16000 €we = 0.50( 30)0.50 (50) = 450 +625 =1075 vasuance of A = 16000 - (40)2 = 14400 vacance of 8. = 1075-(40)2 = -525 Hence lottery A has bigger variance than 8

11.51 +11.72 b) Exported utility [_each tollery page:-02 - Experted utility = port (1-P)4, EUR = 0.9 10+500 + 0.1 1400500 0.94500 + 10.15900 = 20,12+ 3 , .-23.12 Eur 0.5 130+500 +0.5 1507500 = 0.55 530 +0.5.550 = = 23.23 lottery B. has higher expected utility in comparison to A, B offers higher probability of receiving some money in both cases. c) expected whility for each lottery 4= I + 500 EUR = 0.9 10+500) +0.1(400+500) -450 +90. - 540 fue 0,5(30+500) 40,5 (50+500) - 265 +245 * = 540

- If a person's utility of the expected value of page :03. ..a gamble is greater than his expected utility from the gamble itcelf, they are said to be rise-averse and rise - versa for risk loving d) Experted utility for each lottery . 4(I+ 500) EUR = 0.9 10+500)"+ 0.1(400+500) - 225000 + $1000 = 306000 EUR = 0-5 (30+500 140-5(50+500) = 1404507151250 291700 In this case also, you are risk loving .