Question

Steve, a private taxi driver, is considering having a car insurance. The probability that Steve causes...

Steve, a private taxi driver, is considering having a car insurance. The probability that Steve causes a car accident is 0.05. With no car accident, Steve would earn $1,000. However, if Steve causes a car accident, he would earn only $500. With all the information given, answer the following questions a ~ d.

a. Calculate the expected income of Steve.

b. Let’s say that a car insurance premium is P and an insurance payment is C. Then, what is the condition for a car “fair” insurance for Steve? (Hint: Express as an equation using P, C, and Steve’ accident probability)

c. Assume that Steve is risk averse, and that the car insurance company would like to offer a fair insurance to him. Then, what would be the amount of the fair car insurance premium for Steve?

d. Assume that Steve became more risk averse after hearing that his friend taxi driver unfortunately got a car accident to death. Let’s say that the extent to which Steve is risk averse is doubled now. Then, with this doubled risk-aversion of Steve, what would be the amount of the fair car insurance premium for Steve?

Homework Answers

Answer #1

a) . The probability that Steve causes a car accident is 0.05. With no car accident, Steve would earn $1,000. However, if Steve causes a car accident, he would earn only $500.

The expected income of Steve= 0.05*500+0.95*1000

25+950

=975

b)An insurance contract is actuarially fair if the premiums paid are equal to the expected value of the compensation received.

P = p ·A

where p is the expected probability of a claim, and C is the amount that the insurance company will pay in the event of an accident

c) A risk averse person will optimally buy full insurance if the insurance is actuarially fair. The insurance mount will cover the full loss.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A is a good driver with a probability of 0.1 of having an accident and B...
A is a good driver with a probability of 0.1 of having an accident and B is less careful and has an accident probability of 0.2. Each has a car initially valued at $10,000, and with a value of zero in the event of an accident. They each have no other wealth. They can each buy fair insurance of any positive amount up to $10,000. If  cb is consumption (in $'s) in the "state" where an accident occurs, and  cg is consumption...
Suppose Alana has personal wealth of $10,000 and there is a probability of 0.2 of losing...
Suppose Alana has personal wealth of $10,000 and there is a probability of 0.2 of losing her car worth $6,400 in an accident.   Her utility (of wealth) function is given by  u(w) =  w0.5, where  w  is wealth.      (a) What is Alana's expected wealth, expected utility, and utility of expected wealth? If she can insure "fully", and if this insurance is fair, how much would it cost her? (b) What is the maximum amount Alana would be prepared to pay for full insurance?...
7: Consider Emily who has a personal wealth of $10,000, and has a probability of 0.2...
7: Consider Emily who has a personal wealth of $10,000, and has a probability of 0.2 of losing her car worth $6,400 in an accident. Her utility (of wealth) function is given by  u(w) =  w0.5, (w = wealth).      (a) What is Emily's expected wealth, expected utility, and utility of expected wealth? How much would it cost her if she can insure "fully", and if this insurance is fair? (b) For full insurance, what is the max amount Emily would pay?...
There are many entrepreneurs in El Alto who are starting their own businesses. However, starting a...
There are many entrepreneurs in El Alto who are starting their own businesses. However, starting a new business is risky, and they are hoping for insurance to smooth their income in the chance that their project does not succeed. To keep things tractable, let’s assume that you are risk-neutral (so all you care about is maximizing profits) and the entrepreneurs have utility ?(?) = ln (?). 1) For this part, assume that an entrepreneur walks into your office with a...
In 2020, Chip, an accomplished professional race car driver, is to receive a signing bonus for...
In 2020, Chip, an accomplished professional race car driver, is to receive a signing bonus for agreeing to drive for Hot-Lap International, a racing team. Hot-Lap agrees to establish a NQDC agreement with Chip to defer the bonus beyond Chip’s peak income producing years. Hot-Lap transfers the bonuses to an escrow agent, subject to the risk of forfeiture to team creditors in bankruptcy, who invests the funds in securities acting as a hedge against inflation. The bonus is deferred until...
What tools could AA leaders have used to increase their awareness of internal and external issues?...
What tools could AA leaders have used to increase their awareness of internal and external issues? ???ALASKA AIRLINES: NAVIGATING CHANGE In the autumn of 2007, Alaska Airlines executives adjourned at the end of a long and stressful day in the midst of a multi-day strategic planning session. Most headed outside to relax, unwind and enjoy a bonfire on the shore of Semiahmoo Spit, outside the meeting venue in Blaine, a seaport town in northwest Washington state. Meanwhile, several members of...