**Decision Making in Farming Under Uncertainty**John is a farmer with $225 of wealth. He can either plant corn or beans. If he plants corn, John earns an income of $675 if the weather is GOOD and $0 if the weather is BAD. If he plants beans, John earns an income of $451 under both GOOD and BAD weather. The probability of GOOD weather is 0.7. The probability of BAD weather is 0.3.John’s utility function is $ u(C) = 5\sqrt{C} $, where $ C $ is the value of consumption. Use this information to fill out the table below. (Don’t forget to include the value of wealth when you compute consumption!). The PDF will round all typed numbers to two decimals; however, you should use all decimals when computing your answers.### Table to Fill Out| | Plant Corn | Plant Beans ||------------------|------------|-------------|| Expected value of consumption | | || Expected value of utility | | || Certainty Equivalent | | || Risk Premium | | |9. **What type of risk preferences does John have?***To be determined based on the filled-out table.*---Mae owns an insurance company in a nearby town and has decided to offer conventional crop insurance to corn farmers in the area. Assume that Mae has perfect information and can write and enforce an insurance contract that requires the farmer to plant corn. Here’s how the insurance contract works. At the beginning of the year, the corn farmer pays an insurance premium of $202.5. If the weather is GOOD, Mae makes no payment to the farmer. If the weather is BAD, Mae makes an indemnity payment of $675 to the farmer.10. **If a farmer buys this insurance contract, what is Mae’s expected profit?***To be calculated based on the probability of weather conditions and the farmer's insurance premium.*---### Diagram Explanations:There are no graphs or diagrams included in the provided text.

Given value of wealth = 225 Utility function = 5 √C Income from planting corn:- 675 with p=0.7…

9. What type of risk preferences does John have? Mae owns an insurance company in a nearby town and has decided to offer conventional crop insurance to corn farmers in the area. Assume that Mae has perfect information and can write and enforce an insurance contract that

9. What type of risk preferences does John have? Mae owns an insurance company in a nearby town and has decided to offer conventional crop insurance to corn farmers in the area. Assume that Mae has perfect information and can write and enforce an insurance contract that

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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5. Larry, who has wealth (w) of 100, faces a 25% probability that a catastrophe will eliminate all of his wealth. Larry's utility function is u(w) = In (w + 1). We will cover insurance on 12/2 in case you want to hold off on parts (b) and (d) until then. Characterize Larry's preference over risk. Is he risk-averse, risk-loving, or risk-neutral? а. Explain. b. What is the highest premium that Larry would accept for full insurance? C. Alternatively, suppose that Larry's utility is u (w) = e". Characterize his preference for risk and explain your answer. d. Under this alternative utility function, what is the highest premium that Larry would accept for full insurance? Explain.
3. The risk free rate is 3%. The optimal risky portfolio has an expected return of 9% and standard deviation of 20%. Answer the following questions. (a) Assume the utility function of an investor is U = E(r) − 0.5Aσ2. What is condition of A to make the investors prefer the optimal risky portfolio than the risk free asset? (b) Assume the utility function of an investor is U = E(r) − 2.5σ2. What is the expected return and standard deviation of the investor’s optimal complete portfolio?
A risk-averse consumer with $100,000 in wealth faces 0.1 probability of losing half of his wealth within the next year. a. What is the consumer's expected wealth one year from now? b. An insurance company offers our consumer full insurance against the possible loss. What premium must the consumer be charged for the insurance company to expect to break even? c. Suppose our risk-averse consumer is indifferent between getting $85,000 wealth with certainty and facing the above described uncertain situation. What is the maximum premium that the insurance company will be able to charge this consumer for its full insurance policy?
2. Consider an individual with a current wealth of $100,000 who faces the prospect of a 25% chance of losing $20,000 through theft of her car during the next year. If the person’s utility function is U(X) = ln(X), where X is wealth: a. calculate expected utility without insurance, b. calculate the actuarially fair premium for full insurance, c. calculate expected utility with full insurance at the actuarially fair premium d. calculate the maximum amount the individual would pay for full insurance.
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4. A taproom owner is trying to determine how to structure his manager's compensation. One option he considers is a flat salary of $70,000 per year. The second option is a base salary of $30,000 plus 15% of the taproom's profit. If the manager puts a lot of effort into her job, the taproom's annual profit will be $500,000 with 75% probability and $100,000 with 25% probability. If the manager exerts only modest effort, the taproom's profit will be $500,000 with 25% probability and $100,000 with 75% probability. The manager's opportunity cost of putting a lot of effort into her job is $50,000, while her opportunity cost of exerting only modest effort is $25,000. a. Draw the game tree for the interaction between the taproom owner and the manager. Assume that the taproom owner moves first. b. What is the equilibrium outcome for this game? What kind of contract should the taproom owner offer? What level of effort will the manager choose? Explain.
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(1) How would a private insurance carrier respond to a client that always took extreme risks and frequently submitted large claims?
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Lucy, the manager of the medical test firm Dubrow Labs, worries about the firm being sued for botched results from blood tests. If it isn't sued, the firm expects to earn profit of $120, but if it is successfully sued, its profit will be only $20. Lucy believes that the probability of a successful suit is 20%. If fair insurance is available and Lucy is risk averse, how much insurance will she buy? Lucy will buy insurance that costs her $ when not successfully sued. (Enter your response as a whole number.)