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- Question 3 Consider a medieval Italian merchant who is a risk averse expected utility maximiser. Their wealth will be equal to y if their ship returns safely from Asia loaded with the finest silk. If the ship sinks, their income will be y − L. The chance of a safe return is 50%. (i) Draw and carefully label the merchant’s endowment point, their expected income, and their cer- tainty equivalent income in a 2-dimensional state-contingent consumption space. (ii) Use the diagram to illustrate and explain how the merchant would benefit from buying insurance in a competitive insurance market. At which point a risk-neutral insurance firm would maximise their profits by offering the merchant full insurance?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?Consider a medieval Italian merchant who is a risk averse expected utility maximiser. Their wealth will beequal to y if their ship returns safely from Asia loaded with the finest silk. If the ship sinks, their incomewill be y − L. The chance of a safe return is 50%.(i) Draw and carefully label the merchant’s endowment point, their expected income, and their certainty equivalent income in a 2-dimensional state-contingent consumption space. Use the diagram to illustrate and explain how the merchant would benefit from buying insurancein a competitive insurance market. At which point a risk-neutral insurance firm would maximisetheir profits by offering the merchant full insurance?
- Prospect Y = ($6, 0.25 ; $15, 0.75) If Will's utility of wealth function is given by u(x)=x0.25, what is the value of CE(Y) for Will? (In other words, what is Will's certainty equivalent for prospect Y?) (The certainty equivalent represents the maximum amount a person would be willing to pay to acquire a risky prospect, and equivalently, the lowest price for which they would be willing to sell a risky prospect if they already owned it) (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)Consider a random-relocation economy where each young person receives 10 units of the consumption good. There are 100 young people born each period. The total stock of money is constant and equal to $500. The consumption good can be transformed, one to one, into capital, which will give a return of x > 1 next period. Suppose a personís preferences are such that they want to consume 1/2 of their endowment when young 2 of ECON20532 and 1/2 when old. They all dislike risk. We also assume that the probability that a person is relocated is 10% (known to everybody) and the gross return on capital is 1.1. A person is notifed whether she needs to relocate or not at the end of period 1. A person who relocates can take with her money, but not capital. Individual agents cannot invest directly in capital, but there exists a (perfectly competitive) banking sector that accepts deposits from all young people. (a) What is the state contingent rate of return o§ered by banks on deposits? (b) Write…Considerations to follow in determining what the moral thing to do might be are: You must determine what alternative actions are available.You must estimate the direct and indirect costs and benefitsthe action would produce for all involved in the foreseeable future.You must choose the alternative that produces the greatest sum total of utility.All the aboveA & C
- Let W0 represents an individual’s current wealth and U(W) is this individual’s von Neumann-Morgenstern utility index (or utility function) that reflects how s/he feels about various levels of wealth. Assume this individual marginal utility of wealth decreases a wealth increases. Which of the following statements is true? a. This individual will prefer to keep his or her current wealth rather than taking a fair gamble. b. For this individual, a 50-50 chance of winning or losing c dollars yields less expected utility than does refusing the bet. c. This individual is said to be risk averse. d. All of the above.Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)Enumerate THREE reasons as to why expected utility of wealth mignt be equally good or even a better measure than expected wealth in evaluating investment opportunities.(maximum of tiwo sentences per reason)
- 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…Consider a person with the following utility function over wealth: u(w) = ew, where e is the exponential function (approximately equal to 2.7183) and w = wealth in hundreds of thousands of dollars. Suppose that this person has a 40% chance of wealth of $100,000 and a 60% chance of wealth of $2,000,000 as summarized by P(0.40, $100,000, $2,000,000). a. What is the expected value of wealth? b. Construct a graph of this utility function . c. Is this person risk averse, risk neutral, or a risk seeker? d. What is this person’s certainty equivalent for the prospect?Q. 5. For auto makers, an important decision is to determine what features a new car model should be provided based on cost-benefit analysis. In what ways can economists help auto manu- facturers estimate the marginal rate of substitution between features such as vehicle interior size and acceleration? (a) Examining production cost data (b) Conducting consumer surveys about willingness to pay for auto features (c) Solving the standard consumer model (d) Statistically analyzing historical data on purchases of different types of autos (e) B and D only Q. 10. When firms determine whether to invest in research and development (R&D), they need to consider many factors. Which of the following is NOT one of the important factors that should be considered? (a) The market size of the product today. (b) The market potential for the product in the next few years. (c) The R&D investment of the competitors on similar products. (d) Potential new products that may be substitutes of the…