Buying and selling prices for risky investments obviously are related to certain equivalents. This problem, however, shows that the prices depend on exactly what is owned in the first place. Suppose that your utility for wealth (A) can be represented by the utility function u(A) = In [(A)] You currently have R1000 in cash. A business deal of interest to you yields a reward of R100 with probability 0,5 and RO with probability 0,5. 2.1 If you own this business deal in addition to the R1000, what is the smallest amount for which you would sell the deal? 2.2 Suppose you do not own the deal. Formulate an appropriate equation and solve with algebra to find the largest amount you would be willing to pay for the deal. 2.3 Explain why the amounts in 2.1 and 2.2 are slightly different.
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- # 4 Consider an individual with a utility function of the form u(w) = √w. The individual has an initial wealth of $4. He has two investments options available to him. He can eitffer keep his wealth in an interest-free account or he can take part in a particularly generous lottery that provides $12 with probability of 1/2 and $0 with probability 1/2. Assume that this person does not have to incur a cost if he decides to take part in the lottery. (a) Will this individual participate in the lottery? (b) Calculate this individual's certainty equivalent associated with the lottery. What is his risk premium?Lukas is a risk-averse farmer. He grows barley on his 1000 acre farm. In a typical year his farm yields 100 bushels of barley per acre. However, in a wet season, the farm only yields 40 bushels per acre. The probability of a typical season is 0.8 and of a wet season is 0.2. Regardless of the productivity of his farm, he expects to earn $3 per bushel (net of all costs of farming). Assume that Lukas has no other income. Write an expression for Lukas's expected utility.Hello can any one help with this Economics question: A contractor spends Dollar 3,000 to prepare for a bid on a construction project which, after deducting manufacturing expenses and the cost of bidding, will yield a profit of dollar 25,000 if the bid is won. If the chance of winning the bid is ten per cent, compute his expected profit and state the likely decision on whether to bid or not to bid?
- Utility Theory You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000. A. Apply Bayes’ decision rule to determine which alternative (take the insurance or not) maximizes yourexpected assets after one year.You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000.Questions 18 through 20 refer to the following information: Shawn's consumption is subject to risk. With probability 0.75 he will enjoy 10000 in consumption, but with probability 0.25 he will have only 3600. His utility function for consumption is given by v(c) = vc. Question 18 What is the expected value of Shawn's consumption? Question 19 What is his expected utility?
- You are considering a $500,000 investment in the fast-food industry and have narrowed your choice to either a McDonald's or a Penn Station East Coast Subs franchise. McDonald's indicates that, based on the location where you are proposing to open a new restaurant, there is a 25 percent probability that aggregate 10-year profits (net of the initial investment) will be $16 million, a 50 percent probability that profits will be $8 million, and a 25 percent probability that profits will be -$1.6 million. The aggregate 10-year profit projections (net of the initial investment) for a Penn Station East Coast Subs franchise is $48 million with a 2.5 percent probability, $8 million with a 95 percent probability, and -$48 million with a 2.5 percent probability. Considering both the risk and expected profitability of these two investment opportunities, which is the better investment? Explain carefully.4) You are a financial professional working in a corporate loan department. A company named Mitch Hedberg Inc. (MH) comes to you for a loan. MH has debt from a previous loan (given by a different firm than yours) of 200. Your company analysts say that MH is likely to earn either 180, 240, or 300 this year - each with a probability of 1/3. MH wants you to lend them 100. MH could use this borrowed 100 to do either project X or project Y. Project X has a guaranteed return of 125 if the 100 is put there. Project Y may return either 0 or 210; each has probability of 1/2 and also costs 100 to do. a) Which project, X or Y, has the larger expected value? b) If you lend MH the 100, what will they do with the money? Why? Show your math. c) Should you lend MH the money or not? Show your math. d) Why did I choose the letters "MH" for this problem? What financial economic concept with initials "MH" is important in this problem?4) Luke is planning an around-the-world trip on which he plans to spend $10,000. The utility from the trip is a function of how much she spends on it (Y ), given by U(Y) = InY a). If there is a 25 percent probability that Luke will lose $1000 of his cash on the trip, what is the trip's expected utility. b). Suppose that Luke can buy insurance to fully against losing the $1,000 with a actuarially fair insurance. What is his expected utility if he purchase this insurance. Will he purchase the insurance? c). Now suppose utility function is U(Y) = Y/1000 What is his expected utility if he purchase the insurance in b). Will he purchase the insurance?
- Johnny is "paid" by his parents $2o if he gets a grade A, $10 if he gets a grade B, whereas he has to pay his parents back $5 if he gets a grade other than A or B. On average 20% of the grades he gets are A, and 30% are grades B. What is the expected value of what he "earns" per grade ? What is the expected value of what he "earns" at school weekly if on average he gets five grades a week ? How long should Jim save until he collects enough money to buy a pair of brand new Hi-Fi headphones that cost $225?A person has wealth of $500,000. In case of a flood her wealth will be reduced to $50,000. The probability of flooding is 1/10. The person can buy flood insurance at a cost of $0.10 for each $1 worth of coverage. Suppose that the satisfaction she derives from c dollars of wealth (or consumption) is given by u(c) = √c. Let CF denote the contingent commodity dollars if there is a flood (horizontal axis) and CNF denote the contingent commodity dollars if there is no flood (vertical axis). (a) Determine the contingent consumption plan if she does not buy insurance. (b) Determine the contingent consumption plan if she buys insurance $K. (c) Use your answer in (b) to eliminate K and construct the budget constraint (BC) that gives the feasible contingent consumption plans for different amounts of insurance K. Determine the slope of budget line (both graphically and by forming the price ratio).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)