The following figure shows a utility function for Jasmine. Suppose Jasmine begins with $420 in wealth. Starting from there, would she be willing to accept a coin-flip bet that would result in her winning $120 if the result was "heads" or losing $120 if the result was "tails"? UTILITY CBA
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- 3. Which lottery payout scheme is better? Suppose you win a raffle held at a neighborhood elementary school fundraiser and are given the choice between two different ways to be paid. You can either accept the money in a lump sum immediately or in a series of payments over time. If you choose the lump sum payout, you receive $3,100 today. If you choose to collect payments over time, you receive three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. At an interest rate of 7% per year, the winner would be better off accepting the value. At an interest rate of 9% per year, the winner would be better off accepting since that choice has the greater present O The lump sum is always better. O The payments over time are always better. O It will depend on the interest rate; advise her to get a calculator. O None of these answers is good advice. , since it has the greater present value. A couple years after you win the raffle, you and your friend are back at the…3. Which lottery payout scheme is better? Suppose you win a raffle held at a minor league baseball game and are given the choice between two different ways to be paid. You can either accept the money in a lump sum immediately or in a series of payments over time. If you choose the lump sum payout, you receive $3,000 today. If you choose to collect payments over time, you receive three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. At an interest rate of 6% per year, the winner would be better off accepting the value. , since that choice has the greater present O The lump sum is always better. The payments over time are always better. O It will depend on the interest rate; advise her to get a calculator. O None of these answers is good advice. At an interest rate of 10% per year, the winner would be better off accepting A couple years after you win the raffle, you and your friend are back at the same event. This time, your friend gets lucky and wins the…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.
- 10. Which lottery payout scheme is better? Suppose you win a small lottery and have the choice of two ways to be paid: You can accept the money in a lump sum or in a series of payments over time. If you pick the lump sum payout, you get $3,000 today. If you pick the payments over time payout, you get three payments: $1,000 today, $1,000 one year from today, and $1,000 two years from today. At an interest rate of 6% per year, you would be better off accepting the At an interest rate of 8% per year, you would be better off accepting the It will depend on the interest rate; advise her to get a calculator. lump sum The lump sum payout is always better. The payments over time payout is always better. None of these answers is good advice. payout since it has the greater present value. payments over time Years after you win the lottery, a friend in another country calls to ask your auvice. Dy wild comcidence, she has just won another lottery with the same payout schemes. She must make a quick…3. Consider a home energy storage (battery) system that can store up to 2 units of energy. At every time step, there is a demand for energy in the home which is drawn from 0,1,2 units with equal probability independent of the demands in the previous time steps. At every point in time, you have to satisfy the demand either by discharging the needed energy from the battery or purchasing power from the grid (or a combination of the two). You could also choose to purchase power from the grid to charge your battery. The grid energy price is either H(igh) or L(ow) according to a Markov chain (Price moves from H to L with probability p, and from L to H with probability q). (a) Model the decision making as an infinite horizon MDP where the objective is to minimize the discounted cost of energy purchased over an infinite horizon. (b) Write down a policy a of your choosing. Perform two steps of the operator T, for your policy, followed by one step of T..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.
- Assume that the parcels are essentially identical and that the minimum selling price of each is $575,000. The following table states each person's willingness and ability to purchase a parcel. Willingness and Ability to Purchase Person (Dollars) Andrew 520,000 A-Z Beth 510,000 Lorenzo 750,000 Neha 660,000 Sam 600,000 Teresa 550,000 Which of these people will buy one of the three beachfront parcels? Check all that apply. O Andrew Beth O Lorenzo O Neha O Sam O Teresa Assume that the three beachfront parcels are sold to the people that you indicated in the previous section. Suppose that a few days after the last of those beachfront parcels is sold, another essentially identical beachfront parcel becomes available for sale at a minimum price of $535,000. This fourth will nurchase it from the seller for at least the minimum ncice be sold because parcel MacBook Air F12 O O O4. You have just won a Casino Jackpot prize of $1,000,000 collectable in 10 yearly installments of $100,000 starting today. a) Why is this prize not really $1,000,000? b) What is it really worth today if money can be invested at 10 percent annual interest, compounded monthly?3. Which lottery payout scheme is better? Suppose you win a small lottery and have the choice of two ways to be paid: You can accept the money in a lump sum or in a series of payments over time. If you pick the lump sum, you get $2,800 today. If you pick payments over time, you get three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. A At an interest rate of 6% per year, the winner would be better off accepting the value. At an interest rate of 9% per year, the winner would be better off accepting , since that choice has the greater present The lump sum is always better. O The payments over time are always better. It will depend on the interest rate; advise her to get a calculator. O None of these answers is good advice. since it has the greater present value. Years after you win the lottery, a friend in another country calls to ask your advice. By wild coincidence, she has just won another lottery with the same payout schemes. She must make a quick…
- 43. On June 1, you win $1 million in a lottery and imme- diately acquire numerous "friends," one of whom offers you the deal of a lifetime. In return for the million, she'll pay you a cent today, two cents tomorrow, four cents the next day, eight cents the next, and so on, stopping with the last payment on June 21. (a) Assuming you take this deal, how much money will you receive on June 21? (b) Should you take the deal? Explain. (c) Would you take the deal if payments continued for the entire month of June?6) Leia has $11,000 and she wants to invest in financial market. There are two types of assets. The first one guarantees 0.1 percent return next year. The second one is a risky asset which will yield 0.5 percent return in good times and 0.4 percent of loss in bad times. Suppose the chance of good and bad times is half-half and Leia's utility function is U(Y) = Y 0.5 %3D a). What is the expected utility if she invest in the first asset? b). What is the expected utility if she invest in the second asset? Will Leia chooses the first or the second asset? c). Suppose that Leia can purchase a financial insurance which cost her $100 and cover all her lost when bad times happen. Will she purchase this insurance?2. Ronald has $18,000. But he is forced to bet it on the flip of a fair coin. If he wins he has $36,000. If he loses he has nothing. Ronald's expected utility function is 0.5x0.5 + 0.5y0.5, where x is his wealth if heads comes up and y is his wealth if tails comes up. What safe income would make him exactly as well off as this bet?