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.
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- 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.
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- Jacob is considering buying hurricane insurance. Currently, without insurance, he has a wealth of $80,000. A hurricane ripping through his home will reduce his wealth by $60,000. The chance of this happening is 1%. An insurance company will offer to compensate Jacob for 80% of the damage that any tornado imposes, provided he pays a premium. Jacob’s utility function for wealth is given by U(w) = In (w). (A) What is the maximum amount Jacob is willing to pay for this insurance? Show work and explain.Draw a utility function over income u( I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. Can you explain why such a utility function might reasonably describe a person’s preferences?. 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.
- Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary’s boat wins, Donna would give him $31. If Gary’s boat does not win, Gary would give her $31. Gary’s utility function is p1x^21+p2x^22, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and x2 are his wealth if events 1 and 2 occur respectively. Gary’s total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). Taking the bet would reduce his expected utility. Taking the bet would leave his expected utility unchanged. Taking the bet would increase his expected utility. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. The information given in the problem is self-contradictory.Consider a risk averse individual who has utility function u(a) which is increasing with u(0) = 0. There are two risky assets: A,B. For A, every dollar invested gives return $0 with probability 1/3 and $3 with probability 2/3. For B, every dollar invested gives return is $0 with probability 1/4 and $3 with probability 3/4. The individual has $120 to invest. Consider two investment choices: (1) invest entire $120 in A and (2) invest $60 in A, $60 in B. (a) Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 1. (b)Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 2 when return from A is bad. (c) Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 2 when return from A is good. (d) Drawing diagram of the utility function and showing your work, determine the…Max Pentridge is thinking of starting a pinball palace near a large Melbourne university. His utility is given by u(W) = 1 - (5,000/W), where W is his wealth. Max's total wealth is $10,000. With probability p = 0.9 the palace will succeed and Max's wealth will grow from $10,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $5,000, so that his wealth will be just $5,000. What is the smallest value of x that would be sufficient to make Max want to invest in the pinball palace rather than have a wealth of $10,000 with certainty? ____ (Please round your final answer to the whole dollar, if necessary)
- In the field of financial management, it has been observed that there is a trade-off between the rate of return that one earns on investments and the amount of risk that one must bear to earn that return. a) Draw a set of indifference curves between risk and return for a person that is risk-averse (a person that does not like risk).Suppose a new and terrifying disease called bhtitis has been created in a mad scientist’s laboratory. In a recently-released study, medical researchers determined that the average Pcorian adult has a 0.1% chance of catching bhtitis in the coming year. Suppose all Pcorians have the following utility function: U = √I where I = $100 if the Pcorian is well and I = $0 if the Pcorian catches bhtitis. (a) A young woman hears a brief news item about the research study on the radio, and learns she has a 0.1% chance of catching bhtitis this year. What is her expected utility without insurance? (b) The young woman is offered an insurance contract that has a premium of $1 but pays out $100 if the woman comes down with bhtitis this year. Will she take the contract, according to expected utility theory?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.
- Consider the St. Petersburg Paradox problem first discussed by Daniel Bernoulli in 1738. The game consists of tossing a coin. The player gets a payoff of 2^n where n is the number of times the coin is tossed to get the first head. So, if the sequence of tosses yields TTTH, you get a payoff of 2^4 this payoff occurs with probability (1/2^4). Compute the expected value of playing this game. Next, assume that utility U is a function of wealth X given by U = X.5 and that X = $1,000,000. In this part of the question, assume that the game ends if the first head has not occurred after 40 tosses of the coin. In that case, the payoff is 240 and the game is over. What is the expected payout of this game? Finally, what is the most you would pay to play the game if you require that your expected utility after playing the game must be equal to your utility before playing the game? Use the Goal Seek function (found in Data, What-If Analysis) in Excel.Elena applies for private insurance and resents the number of questions asked on the application. She states that since the primary contribution of insurance companies is to pool the risk of many individuals, they should care less about the characteristics of any one applicant and more about increasing the number of the patients that they insure. Furthermore, she states, when she had insurance through her employer, she hardly had to answer any questions. Use economic reasoning to explain to Elena the insurance company's behavior. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) = square root x. 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?