Question

In a country, health insurance is provided by one non-profit making health insurance

company. The insurance company charges the same premium to all and pays out full costs
(i.e. the policyholder pays share of the medical costs). Half of the population is healthy and
the other half is unhealthy. If an insured healthy person becomes ill, the full cost to their
health insurance company is €1000. If an insured unhealthy person gets sick, the full cost is
€10000 (as they will need more medical care). Suppose that in any year, the chances of
any individual getting sick is 40% (regardless of how healthy they are generally). People
know whether they are healthy but the insurance company does not

Answer 1

The cost to the health insurance company in a fictional scenario with a non-profit health insurance company charging the same premium to all and paying out full costs can be calculated based on the percentage of healthy and unhealthy individuals and the chances of an individual getting sick.

The subject of this question is Health and the grade level is High School.

The question is about a fictional scenario in a country where a non-profit health insurance company charges the same premium to everyone and pays out full costs.

The question asks about the costs to the insurance company based on the health of the population and the chances of an individual getting sick.

To calculate the costs to the insurance company, we need to consider the percentage of healthy and unhealthy individuals in the population, as well as the chances of an individual getting sick. Let's break it down step by step:

1. Half of the population is healthy and the other half is unhealthy, so we can assume there are 50% healthy and 50% unhealthy individuals.
2. The chances of any individual getting sick are 40%, regardless of their health status. This means that 40% of the healthy individuals and 40% of the unhealthy individuals will get sick.
3. If an insured healthy person becomes ill, the full cost to the insurance company is €1000. Likewise, if an insured unhealthy person gets sick, the full cost is €10000.
4. Based on the percentages from step 1 and step 2, we can calculate the costs to the insurance company: (0.5 x 0.4 x €1000) + (0.5 x 0.4 x €10000) = €2200

Therefore, the insurance company will have a total cost of €2200 for providing health insurance in this scenario.