Alice prefers having more money to less. She is an expected utility maximiser with a wealth of W = 800.She faces a lottery where she will be left with- of her wealth with probability p• 4 times her wealth with probability p4where 0>p>. She will keep her initial wealth with remaining probability 1 – 2p.Consider a Marschak triangle with the probability of the "worst" event on the horizontal axis and the probability of the"best" event on the vertical axis.Alice is risk-averse if the slope of her indifference curves is greater than(fill in the blank)

Alice prefers having more money to less. She is an expected utility maximiser with a wealth of W = 800. She faces a lottery where she will be left with - of her wealth with probability p • 4 times her wealth with probability p where 0>p>. She will keep her initial wealth with remaining probability 1 – 2р. Consider a Marschak triangle with the probability of the "worst" event on the horizontal axis and the probability of the "best" event on the vertical axis. Alice is risk-averse if the slope of her indifference curves is greater than (fill in the blank)

Alice prefers having more money to less. She is an expected utility maximiser with a wealth of W = 800. She faces a lottery where she will be left with - of her wealth with probability p • 4 times her wealth with probability p where 0>p>. She will keep her initial wealth with remaining probability 1 – 2р. Consider a Marschak triangle with the probability of the "worst" event on the horizontal axis and the probability of the "best" event on the vertical axis. Alice is risk-averse if the slope of her indifference curves is greater than (fill in the blank)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.7P

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A salesperson is trying to sell cars. The number of cars that she will sell depends on her effort "e" and her luck. Given her effort e, with probability 4e she is able to sell four cars, and with probability (1 - 4e) she is able to sell only one car. Her personal cost of effort is 100e². The dealership pays her a bonus b for each car sold. The salesperson is risk-neutral, and wants to maximize her expected utility, which is her expected income minus her effort cost. a) Given the bonus b, the salesperson's best response function is b) Suppose the dealership pays b = 2. Then the expected number of cars sold will be E(Q)=
The investor is considering how to optimally invest 1000 euros in stocks and bonds. Let's assume that the optimal decision is made based on expected utility. Suppose the investor has a utility function u(x)=ln(1+x), where x is their wealth. Let y be the proportion invested in stocks and 1−y be the proportion invested in bonds. By investing in stocks, the investor earns 1% with a probability of 39.5% and 4% with a probability of 60.5%. By investing in bonds, the investor earns a certain 2.8%. What proportion of the investment will the investor allocate to stocks and what proportion to bonds?
Arielle is a risk-averse traveler who is planning a trip to Canada. She is planning on carrying $400 in her backpack. Walking the streets of Canada, however, can be dangerous and there is some chance that she will have her backpack stolen. If she is only carrying cash and her backpack is stolen, she will have no money ($0). The probability that her backpack is stolen is 1/5. Finally assume that her preferences over money can be represented by the utility function U(x)=(x)^0.5 Suppose that she has the option to buy traveler’s checks. If her backpack is stolen and she is carrying traveler’s checks then she can have those checks replaced at no cost. National Express charges a fee of $p per $1 traveler’s check. In other words, the price of a $1 traveler’s check is $(1+p). If the purchase of traveler’s checks is a fair bet, then we know that the purchase of traveler checks will not change her expected income. Show that if the purchase is a fair bet, then the price (1+p) = $1.25.
# 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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17. A salesperson at Joe's Exotic Pets is trying to sell iguanas. The number of iguanas that she sells depends on her effort "e" as well as her luck. Given her effort e, she will sell four iguanas with probability 4e, and only one iguana with probability (1-4e). Her personal cost of effort is 200e. The pet shop pays her a bonus b for each iguana sold. The salesperson is risk-neutral, and wants to maximize her expected utility, which is expected income minus her effort cost. If the pet shop pays b-5, how many iguanas do they expect to sell? a. 1 b. 2.5 c. 2.8 d. 3.55 e. 4 om v sec w you page back
Your utility function is U = w, where W is your wealth. Your current wealth is $800. There is a 25% chance that you will suffer a loss of $600. You are: O Risk Averse O Risk seeking O Risk neutral O Risk encumbered
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A person has wealth of $500,000. In case of a flood her wealth will be reduced to $50,000. The probability of flooding is 1/10. The person can buy flood insurance at a cost of $0.10 for each $1 worth of coverage. Suppose that the satisfaction she derives from c dollars of wealth (or consumption) is given by u(c) = √c. Let C denote the contingent commodity dollars if there is a flood (horizontal axis) and CNF denote the contingent commodity dollars if there is no flood (vertical axis). 1 Determine the contingent consumption plan if she does not buy insurance. 2 Assume that the person has von Neumann-Morgenstern utility function on the contingent consumption plans. Write down the expected utility U(CF, CNF) and derive the MRS. 3 Solve for optimal (CF, CNF). To this end, first use the tangency condition (TC) to find the relation between the two contingent commodities (CF, CNF). Next, use (BC) to solve for their values. What is the optimal amount of insurance K the person will buy? (Note:…