Assume you have the following von Neumann-Morgenstern utility function: U(w) = 5000 − (50 − w 1000) 2 where w denotes wealth. Work out the utility maximisation problem and illustrate the answer in a diagram.
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A: Answer in Step 2
Assume you have the following von Neumann-Morgenstern utility function: U(w) = 5000 − (50 − w 1000) 2 where w denotes wealth.
Work out the utility maximisation problem and illustrate the answer in a diagram.
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- Suppose your classmate Cho offers you a wager: She will choose a playing card at random from a deck and pay you $3,000 if it is red, but you have to pay her $3,000 if it is black. Assume your wealth is currently $9,000. The graph shown below plots your utility as a function of wealth. Use the graph to answer the questions that follow. UTILITY (Units of utility) 100 90 80 60 50 40 30 20 10 0 0 3 CX T² B 9 WEALTH (Thousands of dollars) 12 The shape of your utility function implies that you are a the difference in utility between B and A is 15 (2.) ? individual, and, therefore, you the difference between A and C. accept the wager because Which of the following sentences most appropriately describe why the pain of losing $3,000 is greater than the joy of winning $3,000 for individuals who are risk averse? Check all that apply. Risk-averse people overestimate the probability of losing money. The more wealth that risk-averse people have, the less satisfaction they receive from an additional…Suppose your classmate Shen offers you a wager: He will choose a playing card at random from a deck and pay you $1,000 if it is red, but you have to pay him $1,000 if it is black. Assume your wealth is currently $3,000. The graph shown below plots your utility as a function of wealth. Use the graph to answer the questions that follow. UTILITY (Units of utility) 100 90 80 70 60 50 40 30 20 10 0 0 1 B +++ A 2 * 3 WEALTH (Thousands of dollars) The shape of your utility function implies that you are a the difference in utility between C and A is less than 4 5 ? risk-averse individual, and, therefore, you would not the difference between A and B. accept the wager because Which of the following sentences most appropriately describe why the pain of losing $1,000 is greater than the joy of winning $1,000 for individuals who are risk averse? Check all that apply. Risk-averse people are relatively wealthy and simply do not need the additional money. ✔ The utility function of a risk-averse person…Suppose your classmate Edison offers you a wager: He will choose a playing card at random from a deck and pay you $3,000 if it is red, but you have to pay him $3,000 if it is black. Assume your wealth is currently $9,000. The graph shown below plots your utility as a function of wealth. Use the graph to answer the questions that follow. UTILITY (Units of utility) 100 90 80 70 60 50 40 30 20 10 0 0 3 6, 55 A C + 6 B 9 WEALTH (Thousands of dollars) 12 15 ? individual, and, therefore, you would The shape of your utility function implies that you are a risk-averse the difference in utility between B and A is greater than the difference between A and C. Which of the following sentences most appropriately describe why the pain of losing $3,000 is greater than the joy of winning $3,000 for individuals who are risk averse? Check all that apply. Risk-averse people are relatively wealthy and simply do not need the additional money. Risk-averse people overestimate the probability of losing money.…
- Suppose your classmate Andrew offers you a wager: He will choose a playing card at random from a deck and pay you $1,000 if it is red, but you have to pay him $1,000 if it is black. Assume your wealth is currently $3,000. The graph shown below plots your utility as a function of wealth. Use the graph to answer the questions that follow. UTILITY (Units of utility) 100 90 80 70 60 40 30 20 10 0 0 B 3 WEALTH (Thousands of dollars) The shape of your utility function implies that you are a the difference in utility between B and A is ? individual, and, therefore, you the difference between A and C. accept the wager because Which of the following sentences most appropriately describe why the pain of losing $1,000 is greater than the joy of winning $1,000 for individuals who are risk averse? Check all that apply. Risk-averse people are relatively poor and cannot afford to lose any money. The more wealth that risk-averse people have, the more satisfaction they receive from an additional…Suppose your classmate Tim offers you a wager: He will choose a playing card at random from a deck and pay you $3,000 if it is red, but you have to pay him $3,000 if it is black. Assume your wealth is currently $9,000. The graph shown below plots your utility as a function of wealth. Use the graph to answer the questions that follow. UTILITY (Units of utility) 100 90 80 70 60 50 40 30 20 10 0 0 32 + 6 U + 9 B ?***PLEASE NOTE: QUESTION HAS TWO PARTS REQUIRING ANSWER*** Q: Johnny Football has a utility function of the form ? = √?. Johnny 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 any injury ends his football career, he will take a job as a refuse removal facilitator in his hometown that pays $10,000. There is a 10% chance that Johnny will be injured badly enough to end his career. a. What is Johnny’s expected utility? b. How much would Johnny be willing to pay to remove the financial riskhe faces? That is, what $p would he pay for a $1,000,000 insurancepolicy so that he would have $1,000,000-$p even if he had a seriousinjury? Assume he wouldn’t work for $10,000 if he had the insuranceand he was injured. Hint: You should set his utility with certainty(U($1,000,000-$p)) equal to his expected utility with risk (found inpart a) and solve for p.
- Elizabeth Swann and her husband consume wine (W) and books (B). Elizabeth's utility function is UE(W, B) = W. Her husband's utility function is UH(W, B) = W. Elizabeth's endowment is 16 bottles of wine and 5 books and her husband's endowment is 19 bottles of wine and 14 books. In the Edgeworth box, Elizabeth's consumption is measured from the lower left corner, and her husband's from the upper right corner of the box; the wine is on the horizontal axis and books are on the vertical axis. Therefore, in an Edgeworth box for Elizabeth and her husband, any allocation is Pareto Optimal. True or False? Please submit 1 if True and O if False.Nicolaus I Bernoulli offers his friend Pierre Rémond de Montmort a game where they need to repeatedly toss a fair ducat until they get a head for the first time. The game stops then, and they count the number n of coin tosses it took to get the desired outcome, and Montmort gets 2^n ducats. Assume that Montmort's utility function is u(w)=w^0.14. How much should Montmort pay to play this game?Suppose the Super Bowl is this week, and Raphael is in need of a television to watch the big game. As a college student, Raphael knows that he can either buy his flat-screen television at the local electronics store, or he can shop online for a better deal but have to wait four days for the television to arrive. The following problem uses the economic concept of rate of time preference to help determine which decision is better for Raphael. Throughout the question, assume that Raphael pays for the good the day he buys it, so his wealth is affected in the initial time period no matter where he buys the good. Also, assume the shipping cost and cost to travel to the store are incorporated into their respective given prices. Finally, assume the goods are identical, and there's no cost to gaining information about prices-in other words, he knows the best price online and in the store without having to search. Suppose Raphael receives a utility of 35.11 utils once he actually receives his…
- Suppose your friend Yvette offers you the following bet: She will flip a coin and pay you $3,000 if it lands heads up and collect $3,000 from you if it lands tails up. Currently, your level of wealth is $9,000. The graph shows your utility function from wealth. Use the graph to answer the following questions. UTILITY (Units of utility) 100 90 80 70 60 50 40 30 20 + 10 0 O 0 3 ** 6 с B 9 WEALTH (Thousands of dollars) 12 The shape of your utility function implies that you are a because the difference in utility between A and C is 15 ? individual, and, therefore, you the difference between C and accept the wager Which of the following best explain why the pain of losing $3,000 exceeds the pleasure of winning $3,000 for risk-averse people? Check all that apply. Risk-averse people overestimate the probability of losing money. Risk-averse people are relatively poor and cannot afford to lose any money. The more wealth that risk-averse people have, the less satisfaction they receive from an…Emelia inherits a collection of 100 Michael Jackson’s CDs (good XA) and 50 Madonna’s CDs (good XB). Her utility function is U(XA, XB) = XA^2 XB^2 Initially, the price of Jackson’s CDs PA= £5 and the price of Madonna’s CDs is PB= £10. Following the success of the “This is it”, the price of Michael Jackson’s CDs increases to P'A = £10 while the price of Madonna’s CDs remains unchanged. Show on your diagram how is Emelia's budget constraint affected by the price change? Create a clear and well explained (including all available information) diagram to illustrate her original and new (after the price change) optimal consumption bundles, the substitution effect of the price change, the ordinary income effect of the price change and the endowment income effect of the price change. the diagram should show the original budget constraint, the original and new optimal consumption bundles, the substitution effect, the ordinary income effect, and the endowment income effect. The movement from…Suppose that David and his friend Wilson derive utility from consuming two types of snacks: onion rings (9₁) and chips (9₂). The utility function for each individual is U (9₁, 92) = 9192. Their indifference curves for these two goods are assumed to have the usual (convex) shape. Suppose David has an initial endowment of 35 onion rings and 10 chips, and Wilson's initial endowment consists of 5 onion rings and 20 chips. (1) Draw an Edgeworth box and show the initial allocation of goods, to be labelled e. Indicate the initial quantities of each person's goods on the four axes.