Question no. 4 a) By using the expected utility concept define risk averse, risk lover and risk neutral and show them into separate graphs. b) What do you mean by risk pooling, adverse selection, and moral hazard.
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- 2. Suppose you asked the following question to Person A and Person B: "How much are you willing to pay to avoid the following fair gamble – win $100 with 50% chance and lose $100 with 50% chance (thus, Variance is equal to 10,000)?" A's answer- $2 B's answer-$10 Assuming that A and B have CARA utility function, a) compute their absolute risk aversion coefficients (approximately) and b) compute their risk premiums for avoiding the following new gamble - win $500 with 50% chance and lose $500 with 50% chance.Question 1 In class we have learned that, given an indirect utility function u(w), there are two relevant measures of risk aversion, namely absolute risk aversion, A(w) = A(w)w. The following questions relate to risk aversion in general, and relationships around these two u" (w) '(w) ' and relative risk aversion, R(w) measures. 1. Utility function u(w) is risk averse if it is concave. Show mathematically that the set of all risk averse functions is a convex set. 2. It is often argued that absolute risk aversion should satisfy DARA (i.e. absolute risk aversion is decreasing in w). Show that, (i) a neccesary but not sufficient condition for DARA is that v(w) = -u'(w) is concave, and (ii) that a necessary and sufficient condition for DARA is that v(w) = -u'(w) is more risk averse than u(w). 3. If u(w) satisfies positive and constant relative risk aversion (CRRA, that is, relative risk aversion is constant in w), show that u(w) also must be DARA. 4. Is the set of all DARA utility functions…The chief executive officer of a publishing company says she is indifferentbetween the certainty of receiving $7,500 and a gamble where there is a 0.5 chance of receiving $5,000 and a 0.5 chance of receiving $10,000. a). Does she seem to be a risk averter, a risk lover, or risk- neutral? Explain. b). What is the coefficient of variation of the risky option (gamble)?
- Utility functions incorporate a decision maker’s attitude towards risk. Let’s assume that the following utilities were assessed for Danica Wary. x u(x) -$2,000 0 -$500 62 $0 75 $400 80 $5,000 100 Would a risk neutral decision maker be willing to take the following deal: 30% chance of winning $5,000, 40% chance of winning $400 and a 30% chance of losing $2,000? Using the utilities given in the table above, determine whether Danica would be willing to take the deal described in part a? Is Danica risk averse or is she a risk taker? What is her risk premium for this deal?Question 3: Jane has utility function over her net income U(Y)=Y2 a. What are Jane's preferences towards risk? Is she risk averse, risk neutral or risk loving? [Briefly explain your answer] b. Jane drives to work every day and she spends a lot of money on parking meters. She is considering of cheating and not paying for the parking. However, she knows that there is a 1/4 probability of being caught on a given day if she cheats, and that the cost of the ticket is $36. Her daily income is $100. What is the maximum amount of she will be willing to pay for one day parking? c. Paul also faces the same dilemma every single day. However, he has a utility function U(Y)-Y. His daily income is also $100. What is Paul's preference towards risk? Is he risk averse, risk neutral or risk loving? d. If the price of one day parking is $9.25, will Paul cheat or pay the parking meter? Will Jane cheat or pay the parking meter?1. Show if the following utility functions represent risk averse, risk neutral or risk loving preferences. u(c) = 10° + 3 u(c) = C2 + 3C i. ii. ii. u(c) = e4C iv. u(c) = 1 – e-C
- a) Explain what is meant by risk aversion, and illustrate with the help of a figure out what we mean by the term "risk premium". Suppose Donald runs hotels and casinos, which makes one very insecure income. With probability 1 the income becomes 100 and with probability 1 the 64th Donald's expected income is thus equal to 82. Further assume that the utility to Donald is a a function of income, and that it is given by U (x) = 2x 12 x is the income level. b) Calculate Donald's expected utility.3. Suppose that Jon Snow's utility function is given by U(I)=501 where I represents annual income in thousands of dollars. a. Is Jon risk loving, risk neutral, or risk averse? Explain b. Suppose that Jon is currently earning an income of $1000 and can earn that income next year with certainty. He is offered a chance to take a new night watch job that offers a 0.25 probability of earning $2000 and a 0.75 probability of earning $500. Should he take the new night watch job?Explain the relationship between U" >0 and risk aversion.
- A risk-averse agent, Andy, has power utility of consumption with riskaversion coefficient γ = 0.5. While standing in line at the conveniencestore, Andy hears that the odds of winning the jackpot in a new statelottery game are 1 in 250. A lottery ticket costs $1. Assume his income isIt = $100. You can assume that there is only one jackpot prize awarded,and there is no chance it will be shared with another player. The lotterywill be drawn shortly after Andy buys the ticket, so you can ignore therole of discounting for time value. For simplicity, assume that ct+1 = 100even if Andy buys the ticket How large would the jackpot have to be in order for Andy to play thelottery? b) What is the fair (expected) value of the lottery with the jackpot youfound in (a)? What is the dollar amount of the risk premium that Andyrequires to play the lottery? Solve for the optimal number of lottery tickets that Andy would buyif the jackpot value were $10,000 (the ticket price, the odds of winning,and Andy’s…What is the mostly commonly used utility functions for the following and why: Risk Aversion Risk Seeking Risk Neutral1. Suppose a company can select among two decisions (d1 and d2) and face three states of nature (s1, s2 and s3) with the following payoff table: Decision s1 s2 s3 d1 d2 150 200 200 50 200 500 The probabilities of s1, s2, and s3 are unknown. Using the optimistic approach, what is the optimal decision and what is the value of the payoff? Place the optimal decision in the first answer box and the maximum payoff used to arrive at this decision in the second. Question 6 options: 2. Suppose a company can select among two decisions (d1 and d2) and face three states of nature (s1, s2 and s3) with the following payoff table: Decision s1 s2 s3 d1 d2 150 200 200 50 200 500 The probabilities of s1, s2, and s3 are unknown. Using the conservative approach, what is the optimal decision and what is the value of the payoff? Place the optimal decision in the first answer box and the maximum payoff used to derive this solution in the second. Question 7 options: 8 3. Suppose a company must consider two…