3. Consider an event which has a probability of occurring to any individual 0.01

Question

3. Consider an event which has a probability of occurring to any individual 0.01 once each year, and never occurs twice in a year.. If this event occurs, it costs the person $100,000. a) Explain why a company could stay in business if it sold insurance which covered their losses if this event occurs to them, but charges them $1200 per year for the insurance. (1 point) b) Explain why people might be willing to buy this insurance.(1 point) Now assume that, there are instead, two types of people in the world. Half the population has a probability of this event occurring 0.0005, the other half have a probability of 0.0195. The cost is the same to each group if the event occurs. c) Explain why, if an "average" person buys the insurance, the insurance company still makes money. (1 point) d) Explain why now, it is less likely people in one of these groups will buy the insurance. Explain why either the insurance will no longer be offered, or how only one of the groups will be willing to buy it? (2 points)

Explanation / Answer

a) The probability of the event occurring to any individual in a year = 0.01; therefore, if the company provides insurance to 100 people, the probability is that 100 × 0.01 =1 person will meet the event. In that case, the company will have to pay the person $100,000. However, the company earns a total of $1200 × 100 =$120,000. So, the profit of the company is $120,000 - $100,000 = $20,000. Therefore, the company earns a profit and can survive easily.

b) People will be willing to buy insurance as they can receive a compensation of $120,000 by paying only $1,200 in a year in case the event takes place.

c) In this case, the probability of an average person meeting the event is = (0.0005 + 0.0195)/2 = 0.0200 = 0.01. Therefore, if the company provides insurance to 100 people, the probability is that the event will occur to 100 × 0.01 = 1 person. Therefore, in case the event occurs, the cost to the company is $100,000; however, the company earns a total of $1200 × 100 =$120,000. So, the profit of the company is $120,000 - $100,000 = $20,000. Therefore, when an average person buys insurance, the insurance company still earns money.

d) The people who face less probability of meeting the event may not like to buy the insurance. This is because the insurance company is charging him/her the same price ($1,200) as the people from high-risk group. Therefore, the insurance company may have to devise differentiated pricing (high premium for high-risk group and low premium for low-risk group). However, in case the differentiated pricing is not offered, the low-risk group will be less willing to avail this insurance and the high-risk group will be more likely to avail this insurance. As a result, the probability of the event for an ‘average’ person will go high and the insurance company might not be willing to offer this insurance.

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