3. (40 marks) Jane owns a house worth $100,000. Assume that her wealth consists entirely of the house. In any given year, there is a 2% percent chance that the house will burn down. If it does, its scrap value will be $30,000. Jane's utility function is U(w) = 2/w. a. Draw Jane's utility function (plotting utility against wealth). b. Show whether Jane is risk averse. c. If the insurance premium is 2.5 cents per dollar insured, how much insurance will Jane buy? d. Heidi, Jane's sister, owns a house with the same value ($100, 000) and with the same chance (2%) of burning down. The scrap value of the burned house is also $30,000. Find the expected utility foe Jane if the two sisters share the losses equally. Assume the accidents of fire for the two houses are independent.

3. (40 marks) Jane owns a house worth $100,000. Assume that her wealth consists entirely of the house. In any given year, there is a 2% percent chance that the house will burn down. If it does, its scrap value will be $30,000. Jane's utility function is U(w) = 2/w. a. Draw Jane's utility function (plotting utility against wealth). b. Show whether Jane is risk averse. c. If the insurance premium is 2.5 cents per dollar insured, how much insurance will Jane buy? d. Heidi, Jane's sister, owns a house with the same value ($100, 000) and with the same chance (2%) of burning down. The scrap value of the burned house is also $30,000. Find the expected utility foe Jane if the two sisters share the losses equally. Assume the accidents of fire for the two houses are independent.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

6.
1. Rosie has just written a book. Assume that her preferences are consistent with expected utility theory. There is 30% chance that her book will be a best-seller and make $500,000 in profit (after the costs of production) and a 70% chance it will just break even (i.e. no profit after the costs of production). Her current income is $150,000 (which she will receive regardless of what happens with her book) and her utility function is u (I) = ln (I) (a) Is Rosie risk-averse, risk-neutral, or risk-loving? How do you know? (b) Assume that Rosie will receive all of the profits (if any) from her book. Draw a diagram illustrating (i) Rosie's total income if her book just breaks even, (ii) her total income if her book is a best-seller, (iii) her expected income, (iv) her expected utility, (v) her certainty equivalent, and (vi) her risk premium. (c) Compute the numerical values associated with each of the six amounts you found in (b). (d) Acme Publishing Company has offered Rosie $100,000 for…
2. Alice believes that her car would cost £12500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15. (i) Alice's utility function is given by U(w) = ln(w) for w > 0 and she as £35000 in the bank. Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage (ii) Repeat the calculation in the previous part but now assume Alice has £500000 in the bank.
6. Expected Utility. Consider a Princeton student who feels that a "normal" year on campus is like gaining $A, compared to taking the year off, which gives utility u(wof). But she fears Princeton will renege on its promise of a normal year, and move everything online; she feels that this is like losing $L (compared to a normal on-campus year). If she expects this to happen with probability p, (a) Write out the expected utility from enrolling. (b) Write out the expected utility from taking the year off. (c) Show: if the student chooses to take the year off, and is risk-loving, it must be that L> A/p.
2a see picture to solve
Only typed answer
26) can i please get help ?
3. Consider a parent who is altruistic towards her child, but also cares about her own consumption. The parent's utility over her own consumption and that of her child is up = log(co) +a log(ci) where c is the child's consumption, and a > 0 is the degree of parental altruism. Suppose that the parent can invest in the child's human capital by spending money (e) on her education; education generates human capital h /() and human capital is paid at rate w. The parent has a total income of (a) Write down an expression for the child's future consumption in terms of the parent's choice of e. (b) Now write down the Lagrangian for the parent's decision problem.
3. Which lottery payout scheme is better? Suppose you win a raffle held at a neighborhood elementary school fundraiser and are given the choice between two different ways to be paid. You can either accept the money in a lump sum immediately or in a series of payments over time. If you choose the lump sum payout, you receive $3,000 today. If you choose to collect payments over time, you receive three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today At an interest rate of 6% per year, the winner would be better off accepting the value. since that choice has the greater present At an interest rate of 10% per year, the winner would be better off accepting A couple years after you win the raffle, you and your friend are back at the same event. This time, your friend gets lucky and wins the contest, and you both realize the payout schemes are the same as they were back when you won. They now face the decision between collecting their prize as a lump sum or as a…
3. Which lottery payout scheme is better? Suppose you win a raffle held at a minor league baseball game and are given the choice between two different ways to be paid. You can either accept the money in a lump sum immediately or in a series of payments over time. If you choose the lump sum payout, you receive $3,000 today. If you choose to collect payments over time, you receive three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. At an interest rate of 6% per year, the winner would be better off accepting the value. , since that choice has the greater present O The lump sum is always better. The payments over time are always better. O It will depend on the interest rate; advise her to get a calculator. O None of these answers is good advice. At an interest rate of 10% per year, the winner would be better off accepting A couple years after you win the raffle, you and your friend are back at the same event. This time, your friend gets lucky and wins the…
Clare is contemplating her possible consumption patter for this year and next. She know that she will have income of $50,000 this year and $55,000 next yea. Her plan is to consume $40,000 this year (t=0). She is also going to invest 30,000. This investment has a positive NPV of $450. She decides to take the investment; in addition, the return on the investment is 9.62%. What consumption she can expect at t=1? (show a detailed procedure)
5) Philippina's utility of wealth function is VW. She has stocks, bonds and cash worth $360,000 and a house worth $280,000. There is a 1% chance of her house being completely destroyed by fire. Unfortunately, if she has insurance, she is less responsible and so the risk of her house being burned down rises to 2%. a. What is the most Philippina is willing to pay for insurance?