Exercise 3: Risky Investment Charlie has von Neumann-Morgenstern utility function u(x) = ln x and has wealth W = 250, 000. She is offered the opportunity to purchase a risky project for price P = 160, 000. With probability p = 1 the project will be a success and return V > 160, 000. With probability 1-p = the project will fail and be worthless (i.e. it returns 0). For simplicity assume there is no interest between the time of the investment and the time of its return, that is r = 0 . How large must V be in order for Charlie to want to purchase the risky project? [Hint: What is Charlie's expected utility is she does not purchase the project? What is Charlie's expected
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- Exercise 3: Risky Investment Charlie has von Neumann-Morgenstern utility function u(x) = In x and has wealth W = 250, 000. She is offered the opportunity to purchase a risky project for price P = 160, 000. 1 the project will be a success and return V > 160, 000. With probability 1-p= 1 With probability p= the project will fail and be worthless (i.e. it returns 0). For simplicity assume there is no interest between the time of the investment and the time of its return, that is r = 0. How large must V be in order for Charlie to want to purchase the risky project? [Hint: What is Charlie's expected utility is she does not purchase the project? What is Charlie's expected utility is she purchases the project?]Adam is considering what skills to study in online school. Her utility function is based on the income she earns, and is defined by U(I) = I0.8. If she learns the skill of SPSS, she will earn $145,000 per year with probability 1. If she learns the skill of Tableau, she will earn $300,000 per year with probability 0.6 (assuming that she gets the certificate) and $30,000 with probability 0.4 (if she learns without earning a certificate and she has to find a waiter job). a. Is she risk averse, risk neutral, or risk loving? Explain.b. Write out the equation for her expected utility for each skill. c.Which skill will she learn? Show your work. d.Suppose someone offers her insurance for the possibility that she does not get a Tableau certificate. This insurance will provide her an amount of income in addition to the waiter job wages that makes her indifferent between learning SPSS and Tableau. What is this amount, and what is the cost of the insurance? (note: many possible answers)Mr Phiri has K10,000 in his account. He is considering investing in a project which has 70 % probability of earning a profit of K10,000 and a 30% probability of incurring a loss of K10,000. His utility at the moment is 20 utiles with the current K10,000. With K20, 000 his utility would be 25 utiles and with K0 his utility would be zero.a) What is the expected profit of the project? b) What is the expected marginal utility of the project? Is Mr Phiri likely to invest in the project? Mr Sinkala also has K10,000 from which he derives 20 utiles. However, Mr Phiri derives 15 utiles from the profit of K10,000.c) What is the expected marginal utility for Mr Sinkala? d) How can you describe Mr Phiri and Mr Sinkala in terms of their attitude towards risk?
- 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?Consider an investment that pays off $700 or $1,600 per $1,000 invested with equal probability. Suppose you have $1,000 but are willing to borrow to increase your expected return. What would happen to the expected value and standard deviation of the investment if you borrowed an additional $1,000 and invested a total of $2,000? What if you borrowed $2,000 to invest a total of $3,000? Instructions: Fill in the table below to answer the questions above. Enter your responses as whole numbers and enter percentage values as percentages not decimals (.e., 20% not 0.20). Enter a negative sign (-) to indicate a negative number if necessary. Invest $1,000 Invest $2,000 Invest $3,000 Expected Value Percent Increase Standard Deviation 1150 S 28 % $ 8 % $ Expected Return N/A Doubled Tripled : #could you answer part b to this question or if you have time part a and part b but part is more important. thank you Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. b) What would be the highest price (premium) that she would be willing to pay for an insurance policy that fully insures her against the flooding damage?
- Exercise 3: Risky Investment Charlie has von Neumann-Morgenstern utility function u(x) = ln x and has wealth W = 250, 000. She is offered the opportunity to purchase a risky project for price P = 160, 000. 1 1 With probability p = 2 the project will be a success and return V > 160, 000. With probability 1 −p = 2 the project will fail and be worthless (i.e. it returns 0). For simplicity assume there is no interest between the time of the investment and the time of its return, that is r = 0 . How large must V be in order for Charlie to want to purchase the risky project? [Hint: What is Charlie’s expected utility is she does not purchase the project? What is Charlie’s expected utility is she purchases the project?]A consumer has the following utility function u(x)= root x where x is the consumer’s total wealth. The consumer's total wealth is the consumer’s cash plus the value of her house. The consumer has $400 in cash (risk free) plus a house. The house is currently worth $756. With probability 70% nothing happens, and the value of the house stays the same. With probability 30%, high winds will cause $580 in damages to the house (in which case, the house value becomes $176). An insurance company offers to fully insure the house at an insurance premium p. What is the maximum insurance premium that the consumer is willing to pay? The consumer is willing to pay at most p=. The fair insurance premium is . In this example, the associated risk premium is .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.
- 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?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.Tasha is planning to invest in a farming project in 2022, but has a reservation given the different forecast (declined (D),the average (A) and takeoff (T)of the economy. She uses the following to guide her decision making. (i) there is 25% chance she will invest if there is a forecast of declined (ii) there is a 75% chance she will invest if there is a forecast of average growth and (iii) there is a 55% chance of investing if there is a forecast that economy will takeoff. Tashanna believes that for 2022 there is a 20% chance of decline and a 40% chance of average growth and a 40% chance the economy will take off. Based on these probabilities what is the chance that Tattiana will invest in the farming project if the stated forecast hold?