Question

8) Kurt is an expected utility maximizer with a Bernoulli utility u(w) = w1/2 facing the choice between two gambles. Gamble 1 would give him $100 with probability 0.7, $50 with probability 0.1 and $150 otherwise. Gamble 2 would give $200 with probability 0.6, $100 with probability 0.2 and $0 otherwise. Which of the following is true. a. Kurt is indifferent between the two gambles. b. the two gambles yield the same expected wealth. Kurt prefers Gamble 1 over Gamble 2 e é o jo c. more than one of the above are true none of the above

Answer 1

Answer 8

Formula :

Expected wealth is given by:

E(w) = p₁w₁ + p₂w₂ ----------- + p_nw_n

where p_i represents probability of having wealth w_i

Expected utility is given by :

E(U) = p₁u(w₁) + p₂u(w₂)----------- + p_nu(w_n)

where p_i represents probability of having wealth w_i and u(w_i) = utility from wealth w_i

Gamble 1 :

Expected wealth(E(w)) = 0.7*100 + 0.1*50 + 0.2*150 = 105

Expected utility(E(U)) = 0.7*100^1/2 + 0.1*50^1/2 + 0.2*150^1/2 = 10.16

Gamble 2 :

Expected wealth(E(w)) = 0.6*200 + 0.2*100 + 0.2*0 = 140

Expected utility(E(U)) = 0.6*200^0.5 + 0.2*100^0.5 + 0.2*0^0.5 = 10.49

Hence, E(w) is higher for gamble 2. and also, E(U) is higher for gamble 2 and hence he will prefer Gamble 2.

Hence, the correct answer is (e) None of the above