Final answer:
Fred would buy 10 health services at a price of $20. An actuarially fair price of health insurance for Fred requires additional information on expected service use or costs when ill. The concept parallels setting fair premiums in life insurance which vary based on an individual's risk factors.
Step-by-step explanation:
Fred's Demand for Health Services and Insurance Pricing
For the student's question regarding how many health services Fred buys at a price of $20, we use his demand curve q = 50 – 2p. Substituting p with 20 gives us q = 50 - 2(20) = 10. So, Fred would buy 10 health services at that price point.
For the actuarially fair price of health insurance with a zero coinsurance rate, you would need to know the expected value of Fred's usage of healthcare services. Since Fred’s probability of illness is 0.25, and assuming that the full cost of his health services without insurance is covered when ill, we can multiply the probability of illness by the cost of his demand for services when ill (p x q) to find this actuarially fair price. However, with the provided information, we cannot directly compute this price; we would need to know Fred's expected service use when ill or the total cost associated with it.
To understand the concept further, let's consider the provided reference example. With life insurance, the actuarially fair premium costs are calculated by considering the risk of death and the monetary benefit upon the event. If companies sell policies separately based on risk factors (like family history of cancer), they calculate a different premium for each group to match their specific risk. If they cannot differentiate, they would average the risk across the entire group, potentially leading to adverse selection, where higher-risk individuals are more likely to buy the insurance, knowing they have a higher chance of needing it.