A Bank has foreclosed on a home mortgage and is selling the house at auction. There are two bidders for the house, Zeke and Heidi. The bank does not know the willingness to pay of these three bidders for the house, but on the basis of its previous experience, the bank believes that each of these bidders has a probability of 1/3 of valuing it at $800,000, a probability of 1/3 of valuing at $600,000, and a probability of 1/3 of valuing it at $300,000. The bank believes that these probabilities are independent among buyers. If the bank sells the house by means of a second- bidder, sealed-bid auction, what will be the bank’s expected revenue from the sale? The answer is 455, 556. Please show the steps in details thank you!

Amy likes to go fast in her new Mustang GT. Their utility function over wealth is v(w) where w is wealth. If Amy goes fast she gets an increase in utility equal to F. But when Amy drives fast, she is more likely to crash: when she drives fast the probability of a crash is 10%, but when she obeys the speed limit, the probability of a crash is only 5%. Amy's car is worth $2000 unless she crashes, in which case it is worth $0. If Amy doesn't have insurance, driving fast isn't worth the risk, so she will alway obey the speed limit. If Amy is offered an insurance contract with full insurance for a premium P with the deductible D, which of the inequalites below is her incentive compatibility constraint that makes sure that she will still obey the speed limit even when she is fully insured? 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.05U(0 – P – D + 2000) + 0.95U(2000 – P) 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.1(U(2000 – P – D) + F) + 0.90(U(2000 – P) + F) 0.05U(2000 – P – D) + 0.95U(2000)…

Suppose that you graduate from college next year and you have two career options: 1) You will start a job in an investment bank paying a $100,000 annual salary. 2) You will start a Ph.D. in economics and, as a student, you will receive a $20,000 salary. You are bad with decisions, so you are letting a friend of yours decide for you by flipping a coin. The probabilities of options 1 and 2 are, therefore, each 50%. a) Illustrate, using indifference curves, your preferences regarding consumption choices in the two different states of the world. Assume that you are risk-averse. [Include also the 45 degrees line in your figure] b) Now show how the indifference curves would change if you were substantially more risk averse than before. Explain. c) Now show the indifference curves if you are risk neutral and if you are risk loving. d) Show your expected utility preferences from point a) mathematically.

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 $15,000. With probability p = 0.9 the palace will succeed and Max's wealth will grow from $15,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $10,000, 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 $15,000 with certainty? (Please round your final answer to the whole dollar, if necessary)

Bill owes Bob $36. Just before Bill pays him the money, he gives Bob the opportunity to play a dice game to potentially win more money. The rules of this game are as follows: If Bob rolls doubles (probability 1/6), Bill will Bob double ($72). If he misses doubles on pay the first try, he can try again or settle for half the money ($18). If he makes doubles on the second try Bill will again pay-up double ($72), but if Bob misses doubles on the second try Bill will only pay him one-third ($12). Should Bob decide to play the dice game with Bill, or insist that he pay the $36 now? Use a decision tree to support your answer.

A drug company is considering investing $100 million today to bring a weight loss pill to the market. At the end of one year, the firm will know the payoff; there is a 0.50 probability that the pill will sell at a high price and generate $37 million per year of profit forever and a 0.50 probability that the pill will sell at a low price and generate $1 million per year of profit forever. The interest rate is 10%. Suppose the firm decides to wait one year to determine whether the pill will sell at a high or low price. The firm will not invest if it learns that the pill will sell at a low price. What is the net present value of waiting one year to make the investment? $107.44 million $64.5 million $201.22 million $88 million

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

Max 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 $15,000. With probability p = 0.7 the palace will succeed and Max's wealth will grow from $15,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $10,000, 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 $15,000 with certainty? (Please round your final answer to the whole dollar, if necessary)

A drug company is considering investing $100 million today to bring a weight loss pill to the market. At the end of one year, the firm will know the payoff; there is a 0.50 probability that the pill will sell at a high price and generate $37 million per year of profit forever and a 0.50 probability that the pill will sell at a low price and generate $I million per year of profit forever. The interest rate is 10%. Suppose the firm decides to wait one year to determine whether the pill will sell at a high or low price. The firm will not invest if it learns that the pill will sell at a low price. What is the net present value of waiting one year to make the investment?O $88 millionO$122.72 millionO $201.22 millionO $64.5 million

Thelma is indifferent between $100 and a bet with a 0.6 chance of no return and a 0.4 chance of $200. If U(0) = 20 and U(200) = 220, then U(100) = :