Consider an individual who has the following value function: v(x) = x^1/2 for gains and v(x) = −2(|x|)^1/2 for losses. This individual is facing a lottery which consist of winning Rs. 25000 with a 25 % chance, Rs. 15000 with a 25 % chance, and losing Rs. 5000 with a 50 % chance. Suppose the probability weight function is p^2. What will be the expected utility of this lottery? What will be the value of this lottery as per the RDU approach? What will be the certainty equivalent of this lottery as per the expected theory approach? What will be the certainty equivalent of this lottery as per the RDU approach?

Consider an individual who has the following value function: v ( x )=√(x /2) for gains and v ( x )=-2 √|x| for losses. This individual is facing a lottery which consist of winning Rs. 1600 with a 25% chance, Rs. 400 with a 25% chance, and winning nothing with a 50% chance. The individual counts all outcomes as losses; that is, he takes as his reference point the best possible outcome under consideration. Suppose the weight function is p^2. What will be the expected value/utility of this lottery as per the prospect theory approach? What will be the expected value/utility of this lottery as per the RDU approach? What will be the certainty equivalent of this lottery as per the prospect theory approach?

Consider the following lottery (3600, 0.35; 2700, 0.35; 200, 0.30). Take the reference point to be 1100. Let the value function be v(w) = w^0.50 for the domain of gain and v(w) = −1.5(−w)^0.50 for the domain of loss. Let the weight function be w(p) = p^2. Derive the certainty equivalent of this lottery as per the prospect theory approach? Is this individual risk averse as per the prospect theory approach? this individual risk averse as per the prospect theory approach?

50% chanceLoss of 25 $50% chanceWin of X $ X should be at least          $ to make the lottery acceptable.

Consider two lotteries L1 = {200, 0.20; 400, 0.50; 500, 0.30} L2 = {500, 0.10; 300, 0.70; 100, 0.20} (a) Check for first-order stochastic dominance between these lotteries. (b) Consider an expected utility maximiser with the utility function u(x) = ln x. Which lottery is going to be preferred? What is the risk premium (RP) of the lottery L1? (c) Consider a decision maker who follows the modified expected utility approach (MEU). Assume the utility function to be u(x) = ln x and the probability weight function to be w(p) = p^0.50/{p^0.50 + (1 − p)^0.50}^2 Which lottery is going to be preferred? (d) Consider a decision maker who follows the rank dependent utility approach (RDU). Assume the utility function to be u(x) = ln x and the probability weight function to be w(p) = p^0.50/{p^0.50 + (1 − p)^0.50}^2 Which lottery is going to be preferred? note - calculate all the answers till their final values, don't leave any calculations incomplete and answer in detail

Consider an expected utility maximiser with utility function u(w) = w^a, a > 0. Verify whether this individual always rejects the lottery {(w + 110), 0.5; (w −100), 0.5} for all wealth level. note - answer this question completely in detail, do not leave any calculations incomplete