6 (A) Sudesh invests in the business which will give him a return of 64 if it turns out to be successful, and Rs. 36 if it is a failure. The probability of failure is 2/3 and that of success is 1/3. The utility function derived from the wealth from this business is given by u(w) = w². Suppose the insurance company offers to insure Sudesh against low earnings. The price of the insurance is 75 paisa for each rupee of benefit. How much of the insurance will she buy to maximize his utility?

6 (A) Sudesh invests in the business which will give him a return of 64 if it turns out to be successful, and Rs. 36 if it is a failure. The probability of failure is 2/3 and that of success is 1/3. The utility function derived from the wealth from this business is given by u(w) = w². Suppose the insurance company offers to insure Sudesh against low earnings. The price of the insurance is 75 paisa for each rupee of benefit. How much of the insurance will she buy to maximize his utility?

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter18: Auctions

Section: Chapter Questions

Problem 9MC

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Utility Theory You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000. A. Apply Bayes’ decision rule to determine which alternative (take the insurance or not) maximizes yourexpected assets after one year.
Farmer Brown faces a 25% chance of there being a year with prolonged drought, with zero yields and zero profit, and he faces a 75% chance of a normal year, with good yields and $100,000 profit. These probabilities are well-known. Suppose that an insurance company offered a drought insurance policy that pays the farmer $80,000 if a prolonged drought occurs. Assume that the farmer’s utility function is u(c) = ln(c). He has initial wealth of $25,000. a Let Y be the expected amount of money that the insurance company will pay Farmer Brown, in the case that Farmer Brown is insured. Compute Y. b. Let X be the most amount of money X Farmer Brown is willing to pay for the insurance. Set up the equation that defines X. Either carefully explain in words what your equation says or put short captions explaining the different parts of your equation. c Determine X to the nearest dollar. d What is the economic intuition on why X > Y?
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