the following lottery scenarios. Which of these is an example of the Allais Paradox, a well-known deviation from expected utility theory? O a. Lottery P offers a 1% chance of winning $10,000 and a 99% chance of winning nothing, while Lottery Q offers a 50% chance of winning $200 and a 50% chance of winning nothing. Even though the expected value of Lottery P is greater, most people choose Lottery Q because they overweight the low probability event in P. O b. Lottery M offers a 90% chance of winning $5,000,000 and a 10% chance of winning nothing, while Lottery N offers a 10% chance of winning $50,000,000 and a 90% chance of winning nothing. Despite Lottery N having a higher expected value, a majority of people choose Lottery M. O c. Lottery X offers a 50% chance of winning $1,000 and a 50% chance of winning nothing, while Lottery Y offers a guaranteed win of $450. Despite the higher expected value of Lottery X ($500 vs $450), a majority of people choose Lottery Y. O d. Lottery G offers a 100% chance of losing $10, while Lottery H offers a 60% chance of losing $20 and a 40% chance of losing nothing. Despite the higher expected loss in Lottery H, people choose it more often because they hope to avoid loss entirely.

Are the following preferences consistent with von Neumann Morgenstern’s axioms to maximize expected utility? Explain. a. You would rather have a sure $200 to a gamble with p=0.7 chance of $200, p=0.1 chance of $50, p=0.2 chance of $300. b. You prefer the gamble of p=2/3 chance of $300 and p=1/3 chance of $50 than a sure $250 win.

Your friend is contemplating buying a local restaurant. He has assessed the lifetime profits, including resale, to be $11 million with 20% chance, $6 million with 60% chance or $3 million with 20% chance. Knowing the most your friend would pay for the restaurant is $6.4 million, what can you infer about the situation? O A. The expected payoff of the restaurant is $6.333 million, the risk-discount being offered by your friend is $77.000 and your friend is risk averse with respect to this purchase. O B. The expected payoff of the restaurant is $6.4 million, the risk-premium being required by your friend $0 and your friend is risk neutral with respect to this purchase. o C. The expected payoff of the restaurant is $6.4 million, the risk-premium being required by your friend $200,000 and your friend is risk seeking with respect to this purchase. O D. The expected payoff of the restaurant is $6.333 million, the risk-premium being required by your friend is $333,000 and your friend is risk…

. Explain the interpretation of a utility function and why such a function should be increasing. is said that the utility function of a decision maker is given by Ua(x) = 2ax – x², r € R for some a > 0.For which lotteries with random outcomes X is the above function a utility function? Explain your answer and give an example of a lottery or specify a distibution of the random variable X for which the function mentioned in relation 2 is not a utility function. 3. Consider a decision maker with initial wealth 0 and this decision maker needs to play a lottery L having a random outcome X bounded above by a > 0. This means P(X 0 be given and L a lotery with random outcome X having cumulative distribution function if r a and assume that the utility function of the decision maker having initial wealth w = 0 is given by the function uq listed in relation 2. Compute the expected utility of this lottery and the certainty equivalence of this lottery.