Question

2. (a) Explain the terms risk averse, risk loving and risk neutral with the aid of diagrams. Jane's utility (U) depends upon her income( Y) according to the following table U(Y) 50 7 100 9.5 150 200一一 14 250 300 350 12 16.5 17 19 She has received a prize with an uncertain value. In particular, with probability 0.25 she wins $300 and with probability 0.75 she wins $100. (b) What is the expected payoff from this prize? What is the expected utility from the prize? Is Jane risk averse, risk neutral or risk loving? Explain. (c) Using the information above, find the certainty equivalent income and the risk premium for this problem.

Answer 1

Risk averse agents who dislike risks that means they are willing to pay risk premium just to avoid variations in payoff promised in lottery The utility function represented by such agents is u^�(middot) > 0 4 u^��(middot) < 0 certainty equivalent far risk averse agents is always less than expected payoff of lottery i.e risk premium > 0 \r\n Risk loving agents are those who accepts risk premium that is they are willing to take the risk certainty equivalent for risk loving agent is always less than expected pay off from lottery i.e Risk premium paid by risk loving agent < 0 u^�(x) > 0: U^��(x) > 0 Risk neutral agents an indifferent betn lottery is certain income \r\n Expected payoff = 025 (300) + 0.75(100) = 75 + 75 = 150 Expected utility = 025 U(300) + 0.75 u(105) = 025(17) + 0.75(9.5) = 4.25 + 7.125 = 11.375 Now certainty Equivalent = U^-1 E(u) = U^-1