1. (i) A utility function has the form U(w) = aw³ +bw2 where a, b E R. Assuming w > 0 and a 0, is U(w) ever suitable for a non-satiated and risk-averse investor? If it is, state the range of values of w this holds for as a function of a and b. You must include your working. (ii) Give an example of a utility function with DARA. Show all your working. (iii) An investor has IRRA. Would this investor prefer a fair gamble or to do nothing? Provide a short explanation of your answer.

1. (i) A utility function has the form U(w) = aw³ +bw2 where a, b E R. Assuming w > 0 and a 0, is U(w) ever suitable for a non-satiated and risk-averse investor? If it is, state the range of values of w this holds for as a function of a and b. You must include your working. (ii) Give an example of a utility function with DARA. Show all your working. (iii) An investor has IRRA. Would this investor prefer a fair gamble or to do nothing? Provide a short explanation of your answer.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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F3
Consider a single consumption good and two states of nature {a, b}. An investor has preferences and a (random) endowment of this commodity as follows: • u (x(a), x(b)) = logx(a) + logx(b), (e(a), e(b)) = (0, 2) In order to hedge against risk this investor can trade two securities with returns (1). denominated in units of the commodity: rị = trading at a price q1 = 3 per unit and r2 = C), trading at a price = 4 per unit. Answer: q2 Find the optimal consumption plan of this investor and answer: If instead of asset markets this investor faced contingent markets, for what (rela- tive) contingent market prices P would this investor choose THE SAME optimal consumption plan? p(b)
Scenario 2 Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function (sqrt c) . Both could experience an adverse event that results in earnings of $0 per year. Tess has a 1% chance of experiencing an adverse event and Lex has a 12% chance of experiencing an adverse event. Tess and Lex are both aware of their risk of an adverse event. Refer to Scenario 2 If an insurance company knows the probability of Tess experiencing an adverse event, what is the actuarially fair premium charged to Tess per $1 of benefit? Round to two decimal places
7.7 A farmer believes there is a 50-50 chance that the next growing season will be abnormally rainy. His expected utility function has the form 1 expected utility =In n YNR +In YR, where YNR and YR represent the farmer's income in the states of “normal rain" and “rainy," respectively. a. Suppose the farmer must choose between two crops that promise the following income prospects: Crop YNR YR Wheat $28,000 $10,000 $15,000 Corn $19,000 Which of the crops will he plant? b. Suppose the farmer can plant half his field with each crop. Would he choose to do so? Explain your result. c. What mix of wheat and corn would provide maximum expected utility to this farmer? d. Would wheat crop insurance-which is available to farmers who grow only wheat and which costs $4,000 and pays off $8,000 in the event of a rainy growing season-cause this farmer to change what he plants?
4) Consider investors with preferences represented by the utility function U = E(r) – Ao². (a) Draw the indifference curve representing a utility level of 10% for an in- vestor with a risk aversion parameter A = 3 in expected return-standard deviation space. (b) In the same graph, draw the indifference curve representing a utility level of 15% for an investor with a risk aversion parameter A = 3. (c) In the same graph, draw the indifference curve representing a utility level of 10% for an investor with a risk aversion parameter A = 5.
not use ai please
View image and calculate for second funciton.
Economics A risk neutral worker has a reservation wage of 500 and a cost of high effort of 187. Depending on the effort put by the worker and some random luck factor, the employer will earn 2500 (if the worker puts high effort and he gets lucky), or 1500 (if the worker puts high effort and he gets unlucky OR if the worker puts low effort and he gets lucky), or 500 (if the worker puts low effort and he gets unlucky). Assume the worker gets lucky with probability 0.4. The employer wants to incentivize the worker to put high effort and decides to pay the worker an incentive contract comprised of a fixed wage of $500 plus a bonus paid only if the profit of 2500 is realized. Calculate the optimal such bonus that the employer should pay, if it wants to incentivize the worker and maximize its profits at the same time. Round your answer to 2 decimals, if needed.
# 4 Consider an individual with a utility function of the form u(w) = √w. The individual has an initial wealth of $4. He has two investments options available to him. He can eitffer keep his wealth in an interest-free account or he can take part in a particularly generous lottery that provides $12 with probability of 1/2 and $0 with probability 1/2. Assume that this person does not have to incur a cost if he decides to take part in the lottery. (a) Will this individual participate in the lottery? (b) Calculate this individual's certainty equivalent associated with the lottery. What is his risk premium?
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5. You are a risk-averse decision maker with a utility function U(1) = VI, where I denotes your income. Your income is $100,000 (thus, I=100). However, there is a 0.2 chance that you will have an accident that results in a loss of $10,000. Now, suppose you have the opportunity to purchase an insurance policy that fully insures you against this loss (i.e., that pays you $10,000 in the event that you incur the loss). What is the highest premium that you would be willing to pay for this insurance policy?
! plz solved all parts