Insurance Pricing Strategies: Analyzing Decisions and Data

QUESTION

Decision 1 Data: In this decision you did not know if you were healthy or sick. Of the seventy students who participated, 97.1% chose to buy insurance in Decision #1. Thirty six of the students were sick and of those 36, twenty one of them became ill. All of the ill participants were insured except one.

Decision 2 Data: In this decision every person was assigned a type of either healthy or sick. 33 of the 70 students were healthy and the other 37 were sick. 50 people buy insurance. 19 people become Ill. All 19 people who become Ill have purchased insurance.

Discussion question 1: If you purchased insurance in decision 1, what would be the maximum number of points you would have paid to purchase insurance? Explain how you arrive at this number. If you did not purchase insurance, at what price would you be willing to purchase insurance? Explain how you arrive at this number.

Discussion question 2: For this question I want you to think of yourself as the insurance company which is selling insurance. If you knew the data from decision 1, what would be the minimum price you would sell insurance at? Explain how you arrive at this number.

Discussion question 3: Again, for this question I want you to think of yourself as the insurance company which is selling insurance. Given the information from decision 2 and assuming that people know if they are sick or healthy, what would be the minimum price you would sell insurance at in this market? Explain how you arrive at this number.

ANSWER

 Insurance Pricing Strategies: Analyzing Decisions and Data

Introduction

In this essay, we will analyze three decision scenarios involving insurance purchases and illness outcomes. These scenarios involve students facing different degrees of uncertainty regarding their health status and the effectiveness of insurance. By examining the data from Decision 1 and Decision 2, we will discuss the pricing strategies for insurance companies and the considerations individuals should make when purchasing insurance.

Discussion Question 1: Maximum Points Paid for Insurance in Decision 1

In Decision 1, 97.1% of the participants chose to buy insurance, indicating a high preference for coverage. Out of 70 students, 36 were sick, and 21 of them became ill despite being insured. Given that only one ill participant was not insured, it can be assumed that insurance effectively covered healthcare costs for the majority of sick students.

If you purchased insurance in Decision 1, the maximum number of points you would have paid would be equal to the cost of insurance multiplied by the probability of getting sick and not being covered. Since only one sick student was not insured, the probability of becoming ill and not being covered is approximately 1/36 or 2.78%. Thus, the maximum points paid for insurance would be justified if it were significantly lower than the expected healthcare costs for being sick (21/36 or 58.33%).

However, if you did not purchase insurance in Decision 1, the price you would be willing to pay depends on your individual risk tolerance. If you are risk-averse and want to avoid potential financial burdens in case of illness, you might be willing to pay an insurance premium that is slightly higher than the expected healthcare costs for being sick (58.33%). On the other hand, if you are risk-tolerant and confident in your health, you might be willing to pay a lower premium, closer to the probability of getting sick (2.78%).

Discussion Question 2: Minimum Price to Sell Insurance in Decision 1

As the insurance company, determining the minimum price to sell insurance in Decision 1 requires balancing the potential costs of covering illnesses with maximizing profits. To do this, the insurance company must consider the probability of insuring a sick student and the expected healthcare costs for an ill participant.

Since 97.1% of students chose to buy insurance in Decision 1, the insurance company can assume that the majority of students are willing to pay for coverage. To set a competitive premium, the company can use the expected healthcare costs for being sick (58.33%) and the probability of insuring a sick student (35/36 or 97.22%).

Using these values, the minimum price to sell insurance in Decision 1 would be calculated as follows:

Minimum Price = Expected Healthcare Costs for Being Sick * Probability of Insuring a Sick Student
Minimum Price = 58.33% * 97.22%
Minimum Price ≈ 56.70%

Discussion Question 3: Minimum Price to Sell Insurance in Decision 2

In Decision 2, participants are aware of their health status (healthy or sick) before purchasing insurance. This information allows the insurance company to offer personalized premiums based on each student’s individual risk.

To set the minimum price in this scenario, the insurance company needs to consider the probability of insuring a sick student and the expected healthcare costs for an ill participant. Out of 70 students, 37 were sick, and all 19 who became ill had purchased insurance. Thus, the probability of insuring a sick student is 19/37 or 51.35%, and the expected healthcare costs for being sick are 100% since all ill students had insurance coverage.

Minimum Price = Expected Healthcare Costs for Being Sick * Probability of Insuring a Sick Student
Minimum Price = 100% * 51.35%
Minimum Price ≈ 51.35%

Conclusion

In summary, insurance pricing strategies should consider the probability of insuring sick individuals and the expected healthcare costs for ill participants. In Decision 1, individuals willing to pay insurance premiums should evaluate the cost-effectiveness based on their perceived risk and financial security. For the insurance company, setting the minimum price would require considering the percentage of sick students willing to buy insurance and the expected healthcare costs.

In Decision 2, insurance companies can offer personalized premiums based on the known health status of participants. The minimum price should reflect the expected healthcare costs for sick students who choose to purchase insurance. Understanding the data and making informed decisions are crucial for both individuals and insurance companies to achieve a balance between risk coverage and financial sustainability.