An individual has a utility function given by (W) - √W, and initial wealth of $100. If he plays a costless lottery in which he can win or lose $10 at the flip of a coin, compute his expected utility. What is the expected gain? Will such a person be categorized as risk neutral?
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- 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?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. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why? I would like help with the unanswered last parts of the questions.2. Consider an individual with a current wealth of $100,000 who faces the prospect of a 25% chance of losing $20,000 through theft of her car during the next year. If the person’s utility function is U(X) = ln(X), where X is wealth: a. calculate expected utility without insurance, b. calculate the actuarially fair premium for full insurance, c. calculate expected utility with full insurance at the actuarially fair premium d. calculate the maximum amount the individual would pay for full insurance.
- 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?What is the difference if any between an individual gambling at a casino and gambling by buying a stock? What is the difference for society? For an individual, gambling at a casino or by buying a stock A. is the same because they have the same expected values. B. is the same insofar that both involve uncertain outcomes C. different because the expected value of gambling in a casino is higher. 2. For society, gambling at a casino or by buying a stock A. is the same because neither redistribute income. B. is different because buying a stock more directly provides capital for companies to make productive investments. C. is the same because both have no effect on the budget deficit.Q. 4 Suppose you, owner and CEO of a corporation, are considering a $25 million project that constructs a building in the downtown area of Toronto. The current market price of the similar building is about $20 million. The future price is uncertain. It may be either $28 million or $22 million in one year from now, depending on the economic situation. The company can borrow at a risk-free rate of 5 percent per year. What is the value of this project? Use a binomial model to value this real option.
- An investor has a power utility function with a coefficient of relative risk aversion of 3. Compare the utility that the investor would receive from a certain income of £2 with that generated by a lottery having equally likely outcomes of £1 and £3. Calculate the certain level of income which, for an investor with preferences as above, would generate identical expected utility to the lottery described. How much of the original certain income of £2 the investor would be willing to pay to avoid the lottery? Detail the calculations and carefully explain your answer.Suppose Investor A has a power utility function with γ = 1, whilst Investor B has a power utility function with γ = 0.5 (i) Which investor is more risk-averse(assuming that w > 0)? (ii) Suppose that Investor B has an initial wealth of 100 and is offered the opportunity to buy Investment X for 100, which offers an equal chance of a payout of 110 or 92. Will she choose to buy Investment X?Jamal has autility function U=W1/2,where W is his wealth in millions of dollars and U is the utitlity he obtains from that wealth.Inthe final stage of a game show,the host offers offers Jamal a choice(A)$4 million dollar for sure,or (B) a gamble that pays $1 million with probability 0.6 and $9million with probability 0.4. a.Graph Jamal's utitility function.Is he risk averse?Explain. b.Does A or B offers Jamal a higher expected price?Explain your reasoning with appropriate calculations. c.Does A or B offer Jamal a higher expected utility? d.Should Jamal pick A or B? Why?
- Suppose you have a house worth $200,000 (wealth). Your utility of wealth is given by U(w) = ln(w). There is a small chance that a fire will damage your house causing a loss of $75,000. You estimate there is a 2% chance of fire. a) What is your expected wealth? b) What is your expected utility from owning the house? c) Suppose you can add a fire detection/prevention system to your house. This would reduce the chance of a bad event to 0 but it would cost you $C to install. What is the most you are willing to pay for the security system? (Here is an identity you will find usefulAngie owns an endive farm that will be worth $90,000 or $0 with equal probability. Her Bernouilli utility function is u(w) =√w, where w is her wealth level (sum of initial wealth and the worth of the endive farm). 1. Suppose her firm is the only asset she has, that is, she has no initial wealth. What is the lowest price P at which she will agree to sell her endive farm before she knows how much it will be worth? 2. Redo part (1) assuming that she has $160,000 in her bank safe. 3. Compare and discuss your results in parts (1) and (2). What relationship can you find between Angie’s initial wealth level (zero versus $160,000) and her risk aversion?Assume that you will earn $90,000 next year. The probability of having an accident in a year is 0.05 and your income will be $22,500 in that case. Your utility function is U(C)= C1/2 where C is consumption. a) What is your expected utility at the end of the year without insurance?b) Calculate an actuarially fair insurance premium for the full insurance. c) What would your expected utility be if you purchase a full insurance with actuarially fair premium? Will you buy this insurance, why or why not?
