Consider the following FIRE INSURANCE PROBLEM where fire destroys a $100 000 house. FIRE + NO FIRE + PROBABILITY 0.05 0.95€ OUTCOME 0P 100 000 INSURANCE PAYOUT 100 000 0P a) What are the expected payoffs (E(x)) if the agent does not purchase insurance? b) Assume utility is (*)=√(x/1000). What is the expected payoff and utility of having no insurance? c) What is the maximum this person be willing to pay for full coverage insurance that pays $100 000 in case of fire? → d) Now suppose utility is U(*) = (x/1000)². What is the maximum the homeowner will pay for full coverage insurance now?

Utility Theory You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000. A. Apply Bayes’ decision rule to determine which alternative (take the insurance or not) maximizes yourexpected assets after one year.

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1. A dealer decides to sell a rare book by means of an English auction with a reservation price of 54. There are two bidders. The dealer believes that there are only three possible values, 90, 54, and 45, that each bidder’s willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other’s valuation. Assuming that the two bidders bid rationally and do not collude, the dealer’s expected revenue is approximately ______. 2. A seller knows that there are two bidders for the object he is selling. He believes that with probability 1/2, one has a buyer value of 5 and the other has a buyer value of 10 and with probability 1/2, one has a buyer value of 8 and the other has a buyer value of 15. He knows that bidders will want to buy the object so long as they can get it for their buyer value or less. He sells it in an English auction with a reserve price which he must…

Question 1: Using Figure 11.1, illustrate the probability that someone will obtain insurance for treatment for: (a) a hangnail; (b) a broken arm; (c) a bad hair day; (d) viral meningitis

Could you solve last 3 questions  Thank you

2 (a) 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" 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 2¹; this payoff occurs with probability. Compute the expected value of playing this game. (b) Assume that utility U is a function of wealth X given by U = X5 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? (c) 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.