Suppose that every driver faces a 3% probability of an automobile accident every year. An accident will, on average, cost each driver $8,000. Suppose there are two types of individuals: those with $40,000.00 in the bank and those with $4,000.00 in the bank. Assume that individuals with $4,000.00 in the bank declare bankruptcy if they get in an accident. In bankruptcy, creditors receive only what individuals have in the bank. Assume that both types of individuals are only slightly risk averse. In this scenario, the actuarially fair price of full insurance, in which all damages are paid by the insurance company, is 5 Assume that the price of insurance is set at the actuarially fair price. At this price, drivers with $4,000.00 in the bank likely buy insurance, and those with $40,000.00 in the bank likely insurance. (Hint: For each type of driver, compare the price of insurance to the expected cost without insurance.) Suppose a state law has been passed forcing all individuals to purchase insurance at the actuarially fair price. True or False: The law will affect the behavior of both types of drivers. buy False True

Suppose that every driver faces a 3% probability of an automobile accident every year. An accident will, on average, cost each driver $8,000. Suppose there are two types of individuals: those with $40,000.00 in the bank and those with $4,000.00 in the bank. Assume that individuals with $4,000.00 in the bank declare bankruptcy if they get in an accident. In bankruptcy, creditors receive only what individuals have in the bank. Assume that both types of individuals are only slightly risk averse. In this scenario, the actuarially fair price of full insurance, in which all damages are paid by the insurance company, is 5 Assume that the price of insurance is set at the actuarially fair price. At this price, drivers with $4,000.00 in the bank likely buy insurance, and those with $40,000.00 in the bank likely insurance. (Hint: For each type of driver, compare the price of insurance to the expected cost without insurance.) Suppose a state law has been passed forcing all individuals to purchase insurance at the actuarially fair price. True or False: The law will affect the behavior of both types of drivers. buy False True

Essentials of Economics (MindTap Course List)

8th Edition

ISBN:9781337091992

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter19: The Basic Tools Of Finance

Section: Chapter Questions

Problem 4CQQ

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4. You own a house worth $700,000 that is located on a river. If the river floodsmoderately, the house will be completely destroyed. Moderate flooding happensabout once every 40 years. If you build a seawall, the river would have to floodheavily to destroy your house, and such heavy flooding happens only about onceevery 150 years.a. What would be the annual premium for a flood insurance policy that offers fullinsurance? Make sure to show your work.b. For a policy that pays only 75% of the home value, what are your expected costswith and without a seawall? Make sure to show your workc. Do the different policies provide an incentive to be safer (i.e., to build theseawall)?
4) You are a financial professional working in a corporate loan department. A company named Mitch Hedberg Inc. (MH) comes to you for a loan. MH has debt from a previous loan (given by a different firm than yours) of 200. Your company analysts say that MH is likely to earn either 180, 240, or 300 this year - each with a probability of 1/3. MH wants you to lend them 100. MH could use this borrowed 100 to do either project X or project Y. Project X has a guaranteed return of 125 if the 100 is put there. Project Y may return either 0 or 210; each has probability of 1/2 and also costs 100 to do. a) Which project, X or Y, has the larger expected value? b) If you lend MH the 100, what will they do with the money? Why? Show your math. c) Should you lend MH the money or not? Show your math. d) Why did I choose the letters "MH" for this problem? What financial economic concept with initials "MH" is important in this problem?
3. The day prior to the release of yearly profits, a stock has price equal to 1. An investor is deciding whether to buy the stock or not. The investor has a wealth equal to 10. Yearly profits can be high with probability 0.4 or low with probability 0.6. If profits are high, the price will double on the following day; if profits are low, the price will halve on the following day. If the investor does not buy the stock, her wealth remains unchanged. If the inverstors buys the stock, she will sell the stock on the following day (regardless of whether the profits are high or low) and she will accrue the relative profit or loss. In other words, she cannot hold the stock for more than one day. The investor does not discount the future and she abides von-Neumann and Morgenstern axioms. Her vNM utility index over money is u (x) = r with 3 E (0,2). • Write down the two possible gambles faced by the investor. • Does the investor buy the stock or not? Explain. • Compute the Arrow-Pratt measure of…
1. Pankti is risk averse. Without insurance, she receives income of $40,000 with a prob- ability of 02 and income of $60,000 with a probability of .98. She is offered fair insurance against income loss. How much insurance does Pankti purchase? What is her consumption in each state? (Note: Pankti forgoes the premnium regardless of which state she ends up in.)
2. Bob's wealth is $2500. However, he faces a 50% chance of suffering a S900 loss. He is an expected utility maximizer and his utility function is U(w) = vw , Where w is his wealth. (a) What is Bob's cost of risk? (b) If Bob can buy insurance against his loss for a price of $500, will he buy it? (c) What is the maximum amount Bob would be willing to pay for insurance?
6- Suppose Firm B is selling 1 -year insurance contracts for houses. Suppose Firm B's customers are divided into three categories with different probabilities of needing a payment. First category will ask for a payment of 500000 with probability 0.10, the second category will ask for a payment of 250000 with probability 0.15 and the third category will ask for a payment of 100000 with probability 0.2 a. Calculate Firm B's expected payment for the year. Suppose Firm B has 120 customers in the first category, 230 in the second category and 405 in the third category. b. Calculate individual premium if Firm B charges the same amount to all its customers. 1 c. Calculate individual premium if Firm B utilizes the risk groups and charges the same amount of premium within groups d. Which group/groups are more likely to buy the insurance with group pricing compared to the case with uniform pricing?
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.
A6. Which of the following provisions can an insured use lo pul a policy in force that has lapsed as a resull of nonpayment of premium? A.Reinstatement B.Regal Actions C.Grace Period D.Time Limil on Certain Defenses
470 8 The slope of the utility curves for a strongly risk averse investor, relative to the slope the utility curves for a less risk averse investor will a. be steeper b. be flatter c be vertical d. be horizontal e. be none of above
In an insurance system, would you expect each person to receive in benefits pretty much what they pay in premiums or is it just that the average benefits paid will equal the average premiums paid?
How can moral hazard lead to more costly insurance premiums than one was expected?