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U(W) in an appropriate utility function, where W is the level of wealth. Which of the following is TRUE for a risk-loving investor?
Select one:
A. U[E(W)] < E[U(W)]
B. U[E(W)] > E[U(W)]
C. U[E(W)] = E[U(W)] = 0
D. U[E(W)] = E[U(W)]
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- Need the right answer among choices and also an explanation of the answer.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?7. A risk-neutral principal hires an agent to work on a project at wage to. The agent's utility function is U(w,e₁)=√w-g(₁) where g(e) is the disutility associated with the effort level e, exerted on the project. The agent can choose one of two possible effort levels, ej or ez, with associated disutility levels g(e) = 4, and g(₂) 2.5. If the agent chooses effort level e, the project yields 100 with probability 1/2, and 0 with probability 1/2. If he chooses e2, the project yields 100 with probability 1/4 and 0 with probability 3/4. The reservation utility of the agent is 0. (a) If effort is observable, which effort level should the principal implement? Derive the best wage contract that implements this effort. Does this involve sharing risk with the agent? Explain your answer. (b) If effort is not observable, which effort level should the principal imple- ment? What is the best wage contract that implements this effort? (c) Suppose an insurance company observes the wage contract offered…
- Suppose your wealth is 8 and you are considering a bet of a 50% chance of winning $4 and a 50% chance of losing $4. What is your risk premium given you have In utility ? Draw a diagram and label the relevant values.Suppose Lesley is deciding on career paths. She could choose career A, which earns $50,000 per year and has a 10% chance of layoff each year, or career B, which earns 80,000 per year and has a 30% chance of layoff each year. When laid off, she earns 0. Suppose her utility over annual earnings is equal to U(E) = VE (a) What would be her preferred job if she had to choose one or the other? If she could allocate her time to both jobs (e.g., could spend 90% of time in job A and 10% in job B) what would be her ideal allocation of time between jobs?Suppose that the world is populated entirely with rational but amoral individuals that only get utility from wealth. An individual's utility function is U(W) = ln(W + 1) where W is the wealth of the individual. Some individuals start with 0 initial wealth while other individuals start with a wealth of W > 0. Everyone can decide whether or not to steal x units of wealth. The individual know their wealth when they take the decision to steal or not. Stealing has two consequences: first the individual gains x$ of wealth up to 2$ of wealth. Second, with probability p= 0.6 the individual gets caught and has to pay back 2x$, that is twice the amount stolen. The penalty is capped by the individual's wealth: the individual can never get less than 0$ of wealth in that world. a) How much should the individual steal if they have an initial wealth of w >> 0? b) How much should the individual steal if they started with no initial wealth? c) Now suppose that there is no limit to the amount that can…
- Oliver takes $2500 with him to a camp and there is 50% chance he will lose $900 on his way. Suppose Oliver can buy an insurance policy that will totally cover his loss, what maximal amount will he be willing to pay for such insurance? Oliver’s utility function is given by the function U(E) = E0.5 where E is the amount that he spends on the camp without any saving. a. $325 b. $475 c. $650 d. $535Expected utility in portfolio theoryGive typing answer with explanation and conclusion
- Suppose your preferences can characterized by the simple utility function U = √C, where C is consumption. You enjoy rock climbing, where you have a 10% chance of get- ting injured and losing $50,000. Your income (and therefore consumption) in the uninjured state is $90,000. What is the most you are willing to pay for an insurance policy? What is the fee for a fair insurance?Assume, in producing one unit of a good X, an agent can exert either the good effort (G) or the bad effort (L), which cause production defects with probability 0.25 or 0.75 respectively. His utility function in effort e and wage w is U(w, e) = 100 (10/w) c(e) where c(G) = 2 for the good effort and c(L) = () for the bad effort. Production defects are contractible and so can be included in the agent's contract, but effort is not contractible. Good X sells for $20 if there are no defects and $0 otherwise. The principal is risk-neutral and likes profit. Assume the agent has a reservation utility/outside option of U=0. If effort is not contractible then:: Select one: O a. There is insufficient information to know the principal's choice of contract because we do not know the agent's level of absolute risk aversion. O b. the principal will be indifferent between writing a contract to achieve the good effort level and writing a contract to achieve the bad effort level O c. the principal will…An individual is off ered a choice of either $50 or a lottery which may result in $0 or $100, each with equal probability 1/2. If the individual has a utility function u(w) = w, which one would they choose? If the individual has a utility function u(w) =sqr(w)?
