Figure 28-1 The following figure shows a utility function for Putin. UTILITY CA 600 840 1080 WEALTH (Dollars) Refer to Figure 28-1. Suppose the vertical distance between the points (0, A) and (0, B) is 25. If his wealth increased from $840 to $1,080, then Putin's subjective measure of his well-being would increase by more than 25 units. Putin would change from being a risk-averse person into a person who is not risk averse. Putin would change from being a person who is not risk averse into a risk-averse person. Putin's subiective measure of his well-being would increase by less than 25 units.
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- 4. Show how to construct the reference dependent utility function for two friends Kate and Mary whose gains and losses are listed as follows : Kate's net worth is $ 4.5 million ( decreased from $ 5.5 to $ 4.5 million ) Mary's net worth $ 3.2 million ( increased from $ 3 to $ 3.2 million ) ( First determine the reference point ( use a parameter ) and then derive reference utility function for each ) .Sanjay won a poker game against his friends. Now he has to choose between $600 (the winnings) and the chance to play a new game. In this new game, Sanjay has a 50% chance of winning nothing and a 50% chance of winning $1000. The following graph presents the utility function of Sanjay with respect to money: 1. By how much money would his winnings need to increase or decrease so that Sanjay isindifferent between the $600 and the new game? At a different table, Juan wins $800 in a blackjack game. Similarly, he has to choose between $800 or the chance to win a new game. In this game, Juan has a 45% chance of winning nothing and a 55% chance of winning $1000. The following graph presents the utility function of Juan with respect to money: 2. By how much money would his winnings need to increase or decrease so that Juan is indifferent between the $800 and the new game? Please enter a positive number for an increase or a negative number for a decrease.Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4. a. b. c. d. Graph Jamal’s utility function. Is he risk averse? Explain. (2+2) Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate calculations. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why?
- Antonio has a utility function U = W, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Antonio a choice between (A) $9 million for sure, or (B) a gamble that pays $1 million with probability 0.4 and $16 million with probability 0.6. Use the blue curve (circle points) to graph Antonio's utility function at wealth levels of $0, $1 million, $4 million, $9 million, and $16 million. ? Utility (Thousands) 5.0 4.5 4.0 3.5 3.0 25 2.0 1.5 1.0 0.5 0 + 0 2 4 6 8 10 12 14 Wealth (Millions of dollars) 16 18 True or False: Antonio is risk averse. 20 20 Utility Function Choice True O False offers Antonio a higher expected prize. (Hint: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.) Choice offers Antonio a higher expected utility. Antonio should pick choice,Khalid has a utility function U = W1/2, where W is his wealth in millions of dollarsand U is the utility he obtains from the wealth. In a game show, the host offershim a choice between (A) $4 million for sure, or (B) a gamble that pays $1million with probability 0.6 and $9 million with probability 0.4.i. Graph Khalid’s utility function with the help of above utility function. Ishe risk lover? Explain. ii. Does A or B choice offer Khalid a higher expected prize? Explain yourreasoning with appropriate calculations. iii. Does A or B offer Khalid a higher expected utility? Again, show yourcalculations. iv. Should Jamal pick A or B choice? Why?Jamal has a utility function U= W1/2 where Wis his wealth in millions of 'dollars and Uis the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1million with a probability of 0.6 and $9 million with a probability of 0.4. a. Graph Jamal's utility function. Is he risk-averse? Explain. b. Does A or B offer, Jamal, a higher expected price? Explain your reasoning with appropriate calculations. (Hint: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.) c. Does A or B offer Jamal a higher expected utility? Again, show your calculations. d. Should Jamal pick A or B? Why?
- Alex has a utility function U = W2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Alex a choice between (A) $9 million for sure, or (B) a gamble that pays $1 million with probability 0.4 and $16 million with probability 0.6. Use the blue curve (circle points) to graph Alex's utility function at wealth levels of $0, $1 million, $4 million, $9 million, and $16 million. Utility (Thousands) 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 0 2 4 6 8 10 12 14 Wealth (Millions of dollars) 16 18 20 V Utility Function (?)Jin's Utility Function Wealth Utility (Dollars) 60,000 4,000 61,000 4,110 62,000 4,209 63,000 4,288 Refer to Table 27-1. If Jin's current wealth is $61,000, then O his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Jin is not risk averse. O his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Jin is not risk averse. O his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Jin is risk averse. his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Jin is risk averse.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.
- Adam has just purchased a new car and has to decide whether to buy insurance to cover his new car in the event of a loss. Assume that Adam knows the probability (p) of him having an accident and losing his new car. The car is valued at L and the amount of insurance to purchase for this value is X. Adam’s entire wealth after buying the car is W. Let r be unit price of insurance. Briefly explain the problem of the insurance company and show that for insurance to be actuarially fair, the premium must equal the probability of accident.At a different table, Juan wins $600 in a blackjack game. Similarly, he has to choose between $600 or the chance to play a new game. In this game, Juan has a 60% chance of winning nothing and a 40% of winning $1,000. The following graph presents the utility function of Juan with respect to money: U(w) U(w) U(1,000) U(700) U(600) U(400) 400 600 700 1,000 w 10.2.2 1.0 point possible (graded, results hidden) By how much money would his winnings need to increase or decrease so that Juan is indifferent between the $600 and the new game? (in case of an increase, insert a positive number; in case of a decrease, insert a negative number).T Suppose your classmate Gilberto 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. 100 ips ips 88888 UTILITY (Units of utility) + + 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 individual, and, therefore, you rence between A and B. risk-friendly accept the wager because Which of the following sentences most appropriately des risk-averse pain of losing $1,000 is greater than the joy of winning $1,000 for individuals who are risk averse? Check all that apply. The more wealth that risk-averse people have, the more satisfaction they receive from an additional dollar. The more wealth that risk-averse people have, the less satisfaction they…