Question

(a) Does the diagram exhibit a consumer who is risk averse or risk loving? Explain. (b) E[I] 0.70 denotes the expected value of income when the consumer has a 70% probability of being sick and a 30% chance of being healthy. Suppose Is equals $33,000 and I equals $60,000. Calculate the value of E[I] 0.70 . Show all steps to your work. (c) In words, explain the meaning of full insurance. Also, calculate the insurance payout (q) that would make this consumer fully insured. (d) In words, explain the meaning of actuarially fair insurance. Also, if this consumer were fully insured, calculate the insurance premium (r) that would be actuarially fair. (e) In health insurance markets, most insurance companies do not charge premiums that are actuarially fair. Provide and explain one reason why actuarially unfair premiums are common.

Answer 1

The concept of risk aversion or risk loving depends on additional information, not present here. The expected value of income with given probabilities of sickness and health is $41,100. Full insurance and actuarially fair insurance are defined, with actuarially unfair premiums being common due to high risks and the need for insurance companies to cover costs and generate profits.

Step-by-step explanation:

To determine whether a consumer is risk-averse or risk-loving, we would typically need additional information about their preferences over uncertain outcomes, typically represented by a utility function or graphically shown in a risk profile diagram. However, without such a diagram or additional information, we cannot make this determination.

The calculation of the expected value of income (E[I] 0.70) with a 70% probability of being sick (Is = $33,000) and a 30% chance of being healthy (Ih = $60,000) is performed as follows:
E[I] 0.70 = (0.70 * $33,000) + (0.30 * $60,000) = $23,100 + $18,000 = $41,100.

Full insurance means that the consumer is completely protected against the financial risks associated with the insured event. If the consumer were fully insured for health risks, the insurance payout (q) would equalize their income regardless of whether they are sick or healthy. Assuming insurance covers the income deficit when sick, the payout would be:
q = Ih - Is = $60,000 - $33,000 = $27,000.

Actuarially fair insurance is insurance priced such that the premium paid (r) equals the expected payout. If the consumer is fully insured, the actuarially fair insurance premium would also be $27,000 since this is the amount that would be paid out to them if they were sick.

Actuarially unfair premiums are common in health insurance markets because insurance companies have to cover administrative costs, generate profits, and consider the possibility that high-risk individuals may have higher-than-average claims. High premiums are charged to high-risk individuals to cover the expected higher costs, which may discourage these individuals from buying insurance, leading to a potential lack of protection against risks.