You have $10,000 cash in your savings account. A friend tells you about a great "investment" opportunity with one big catch: there is a 50% chance you will either gain $30,000 (i.e. total wealth = $40,000) or a 50% chance you will lose your entire $10,000 investment (i.e. total wealth = $0). Given a personal utility function of U(W) = w(1/3), the gain on the upside is not enough to take the investment. What would your total wealth on the upside have to be greater than to properly incentivize you to take the risk? Multiple Choice 160,000 80,000 120,000 100,000
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- Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person’s utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate δ = 0.05. Hence this person’s goal is to maximize 0ʃ40 e–0.05tu(c(t))dt = 0ʃ40 e–0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = – c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H = e–0.05t(c(t))0.5 + λ(– c(t)) + x(t)(dλ/dt). This person’s wine consumption decreases at a continuous rate of ??? percent per year. The number of bottles being consumed in the 30th year is approximately ???Consider a person with the following utility function over wealth: u(w) = ew, where e is the exponential function (approximately equal to 2.7183) and w = wealth in hundreds of thousands of dollars. Suppose that this person has a 40% chance of wealth of $100,000 and a 60% chance of wealth of $2,000,000 as summarized by P(0.40, $100,000, $2,000,000). a. What is the expected value of wealth? b. Construct a graph of this utility function . c. Is this person risk averse, risk neutral, or a risk seeker? d. What is this person’s certainty equivalent for the prospect?Suppose you have an exponential utility function given by U(x) =1- exp(-x/R) where, for you, R = 1000. Further, suppose you have an investment with a 50/50 chance of returning either 0 or 2000 dollars. Note U(0) = 0 and U(2000) = 0.865, so the utility of the lottery is 0.432. What is the certain equivalent of that investment?
- 2. Alice believes that her car would cost £12500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15. (i) Alice's utility function is given by U(w) = ln(w) for w > 0 and she as £35000 in the bank. Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage (ii) Repeat the calculation in the previous part but now assume Alice has £500000 in the bank.Assume that your utility has a natural log function U(W)=ln(W), which is a concave function. Your car is worth $10,000 and your total wealth is $20,000 including the car. There is a 5% chance that a major accident occurs and you have a total loss of $10,000; a 10% chance that a minor accident occurs and you have a loss of $500; 85% chance you will not have any accident. Given these assumptions, how much are you willing to pay for an insurance that provides full coverage against car accidents? Thank you. Regards, Jim Carroll35. Your current disposable income is $10,000. There is a 10% chance you will get in a serious car accident, incurring damage of $1,900. (There is a 90% chance that nothing will happen.) Your utility function is U = √√T, where I is income. If this policy is priced at $40, what is the change in your expected utility if you purchase the policy rather than no insurance? b) 0.8 c) 0.2 d) 0
- Suppose you have the option of spending $[x] now or saving it until next year. If you save it, the bank will pay you an interest rate of 9.8%. Your utility function is u(w) = w. What does your discount factor & need to be for you to be indifferent between spending the money now and saving it? Round your answer to 3 decimal places (so an answer might be, for example, 0.476).Your Utility function of U = 5, where I is income. You receive an income of 1600 each week from your laundry delivery service in which you face a 50% chance each week of an accident that costs you $700. Calculate your expected income and expected utility.Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)
- AsapBilly John Pigskin of Mule Shoe, Texas, has a von Neumann-Morgenstern utility function of the form u(c) = √c. Billy John also weighs about 300 pounds and can outrun jackrabbits and pizza delivery trucks. Billy John is beginning his senior year of college football. If he is not seriously injured, he will receive a $1,000,000 contract for playing professional football. If an injury ends his football career, he will receive a $10,000 contract as a refuse removal facilitator in his home town. There is a 10% chance that Billy John will be injured badly enough to end his career. If Billy John pays $p for an insurance policy that would give him $1,000,000 if he suffered a career-ending injury while in college, then he would be sure to have an income of $1,000,000 − p no matter what happened to him. Write an equation that can be solved to find the largest price that Billy John would be willing to pay for such an insurance policy. Here is my question: Why is Billy's income 1,000,000 - p even…John and Peter are two representative consumers/investors who maximize the utility of consumption. John's utility of consumption is characterized as ln(x) + 2ln(y) while Peter puts more weight on the current consumption level and has a utility function of 2ln(x) + ln(y). John has a wealth of ($10, $20) thousand, while Peter has a wealth of ($20, $15) thousand now and next year, respectively. (a) What are the optimal consumption plans forJohn and Peter,respectively,if the interest rate is 5% per annum? (b) If John and Peter are the only investors/consumers, what is the equilibrium interest rate? (c) Further to part (b), how much do they borrow or lend to each other?