utility functions U(c1, c2) = c1C2, where c1 is consumption this year and c2 is consumption next year. Rats eat 10% of any grain that is stored for a year. How much grain could the villagers consume next year if they consume 1,000 bushels of grain
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- A woman with current wealth X has the opportunity to bet an amount on the occurrence of an event that she knows will occur with probability P. If she wagers W, she will received 2W, if the event occur and if it does not. Assume that the Bernoulli utility function takes the form u(x) = with r > 0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA? Alex plays football for a local club in Kumasi. If he does not suffer any injury by the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coach worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = Assume he could buy insurance at price P that could pay $9,900 in case of injury. What is the highest value of P that makes it worthwhile for Alex to purchase insurance? What is the certainty…Suppose Var(X) = 36, Var(Y) = 42, and X and Y are independent. What is Var(.25X + .75Y)? Suppose Var(X) = 63, Var(Y) = 87, and X and Y are independent. What is Var(.79X + .21Y)? Suppose that Var(X) = 907.96, Var(X) = 10219.44, and Cov(X,Y) = 2694.59. What is Var(.33X + .67Y)?Suppose your utility function for money is a square-root function of its value in US dollars. So, for instance, $400 is worth 20 utils for you, $961 is worth 31 utils for you, and $62.5K is worth 250 utils for you. Now, let’s say your annual salary is $90K, although there is a small risk (p = 0.05) that something catastrophic will happen and reduce your income for the year to $14.4K. An insurance company comes along and offers to insure you against the loss of your salary. The cost of the insurance is $4,736. If you buy the policy and catastrophe strikes, the insurance company will pay out the $75,600 that you would otherwise have lost. From the standpoint of maximizing expected utility, would buying this insurance be a good deal for you? What would be the insurance company’s expected monetary value of selling you the policy?
- Now, imagine that Port Chester decides to crack down on motorists who park illegally by increasing the number of officers issuing parking tickets (thus, raising the probability of a ticket). If the cost of a ticket is $100, and the opportunity cost for the average driver of searching for parking is $12, which of the following probabilities would make the average person stop parking illegally? Assume that people will not park illegally if the expected value of doing so is negative. Check all that apply.Suppose that Var(X) = 661.1, Var(X) = 8021.53, and Cov(X,Y) = 1922.11. What is Var(.64X + .36Y)? Suppose that Var(X) = 869.03, Var(X) = 7850.84, and Cov(X,Y) = 2238.69. What is Var(.67X + .33Y)?An investor with capital x can invest any amount between0 and x; if y is invested then y is eitherwon or lost, with respectiveprobabilities p and 1− p. If p > 1/2, how much should be invested byan investor having a exponential utility function u(x) = 1 − e −bx ,b > 0.
- Suppose Martha earns an of income 400 Birr currently, and her utility function is given by: U(m) = 4m, where m represents income. She has two options: Option 1: to buy a share. If she is successful her income will be 700 Birr and if she is not successful her income will be 100 Birr. Option 2: to do nothing and keep on earning 400 Birr. Assuming that success and failure are equally likely, a) What would be her expected income if she buys the share? b) What would be her expected utility of buying the share? c) Would Martha buy the share? Why? and Is Martha risk averse, risk lover or risk neutral?Suppose Var(X) = 88, Var(Y) = 82, and X and Y are independent. What is Var(.36X + .64Y)? Suppose Var(X) = 26, Var(Y) = 74, and X and Y are independent. What is Var(.36X + .64Y)?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
- If Firm 1 chooses to release the console in October with probability of 0.692 or December with a probability of 0.308, then Firm 2 is indifferent between choosing a release date. If Firm 2 released the console in October with probability of 0.50 or December with a probability of 0.50, then Firm 1 is indifferent between choosing a release date Suppose now that instead of choosing the release date at the same time, the firms choose sequentially (but still in advance). Firm A chooses its release date first, then firm B observes that date and chooses its own date. Thepayoffs are otherwise the same as above. Represent the game tree corresponding to this dynamic game.Y = 1million + 56.43*X + error By how much does the expected value of Y change if X increases by 2 units? (Round your answer to two decimal places: ex: 123.45) Y = 50 + 3X + error By how much does the expected value of Y change if X decreases by 10 units?An amount of money is accumulating; in period t (= 1, 2, . . . , T) its size is $2t. In each period two people simultaneously decide whether to claim the money. If only one person does so, she gets all the money; if both people do so, they split the money equally; and if neither person does so, both people have the opportunity to do so in the next period. If neither person claims the money in period T, each person obtains $T. Each person cares only about the amount of money she obtains. Formulate this situation as an extensive game with perfect information and simultaneous moves, and find its subgame perfect equilibria). (Start by considering the cases T = 1 and T = 2.)