Jenny has a quadratic utility function of the form U(w) w-10 w. She has been offered...

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Jenny has a quadratic utility function of the form U(w) w-10 w². She has been offered a job with Company X, in which her salary would depend upon the success or otherwise of the company. If it is successful, which will be the case with probability %, then her salary will be $40,000, whereas if it is unsuccessful she will receive $30,000. (0) (ii) (iii) (iv) (i) (ii) Assuming that Jenny has no other wealth, state the salary range over which U(w) is an appropriate representation of her individual preferences. (iii) (iv) Calculate the expected salary and the expected utility offered by the job. Suppose she was also to be offered a fixed salary by Company Z. Determine the minimum level of fixed salary that she would accept to work for Company Z in preference to Company X. Suppose that Lance and Allan each have a log utility function and an initial wealth of 100 and 200 respectively. Both are offered a gamble such that they will receive a sum equal to 30% of their wealth should they win, whereas they will lose 10% of their wealth should they lose. The probability of winning is %. State whether or not the gamble is fair. Calculate Lance's certainty equivalent for the gamble alone and comment briefly on your answer. Suppose that the owners of Company X are both risk-neutral and very keen that Jenny should join them and not Company Z. Determine whether the firm should agree to pa her a fixed wage, and, if so, how much. Comment briefly on your answer. Repeat part (ii) in respect of Allan and compare your answer with that in part (ii). Confirm that your comments in part (iii) apply irrespective of the individual's wealth. Jayne's utility function can be described as U(w)=√w. She faces a potential loss of £100,000 in the event that her should house burn down, which has a probability of 0.01. (0) Calculate the maximum premium that Jayne would be prepared to pay to insure herself against the total loss of her house if her initial level of wealth was £140,000 and comment on your results. Suppose that UN Life plc has an initial wealth of £100 million and a utility function of the form U(w)=w. Jenny has a quadratic utility function of the form U(w) w-10 w². She has been offered a job with Company X, in which her salary would depend upon the success or otherwise of the company. If it is successful, which will be the case with probability %, then her salary will be $40,000, whereas if it is unsuccessful she will receive $30,000. (0) (ii) (iii) (iv) (i) (ii) Assuming that Jenny has no other wealth, state the salary range over which U(w) is an appropriate representation of her individual preferences. (iii) (iv) Calculate the expected salary and the expected utility offered by the job. Suppose she was also to be offered a fixed salary by Company Z. Determine the minimum level of fixed salary that she would accept to work for Company Z in preference to Company X. Suppose that Lance and Allan each have a log utility function and an initial wealth of 100 and 200 respectively. Both are offered a gamble such that they will receive a sum equal to 30% of their wealth should they win, whereas they will lose 10% of their wealth should they lose. The probability of winning is %. State whether or not the gamble is fair. Calculate Lance's certainty equivalent for the gamble alone and comment briefly on your answer. Suppose that the owners of Company X are both risk-neutral and very keen that Jenny should join them and not Company Z. Determine whether the firm should agree to pa her a fixed wage, and, if so, how much. Comment briefly on your answer. Repeat part (ii) in respect of Allan and compare your answer with that in part (ii). Confirm that your comments in part (iii) apply irrespective of the individual's wealth. Jayne's utility function can be described as U(w)=√w. She faces a potential loss of £100,000 in the event that her should house burn down, which has a probability of 0.01. (0) Calculate the maximum premium that Jayne would be prepared to pay to insure herself against the total loss of her house if her initial level of wealth was £140,000 and comment on your results. Suppose that UN Life plc has an initial wealth of £100 million and a utility function of the form U(w)=w.

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Jennys Utility and Job Offers i Salary Range for Uw A quadratic utility function like Uw w 10w2 is appropriate when the marginal utility of income is positive but diminishing This function reaches a m... View the full answer