Explain why a risk averse individual will purchase full insure if a policy is actuarially fair, but only partially insure or not insure at all, if it is not. Use graphs to support your answer.

Question

What will be an ideal response?

Answer 1

Risk averse individuals avoid risk if possible and thus may purchase insurance to protect themselves against risk. An insurance policy is actuarially fair if it's expected net payoff is zero and purchasing such a policy does not change an individual's expected consumption. Rather it raises it in times of loss and reduces it good times. A risk averse person will purchase full insurance if it is actuarially fair because it permits him to purchase a risky bundle without changing his expected consumption. An insurance policy is less than actuarially fair if the premium exceeds the promised benefit times the probability of loss and individuals' expected consumption falls. A risk averse individual will not fully insure when insurance is actuarially unfair because it reduces his expected consumption and makes him worse off. To be better off, as reflected by being on a higher indifference curve, the individual will partially insure or not insure at all, when insurance in actuarially unfair. The amount of less-than-actuarially-fair insurance bought depends upon the individual's level of risk aversion.