Draw a utility function over income u( I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. Can you explain why such a utility function might reasonably describe a person’s preferences?

Suppose there is an individual who needs a certain level of income, I°, in order to stay alive.  An increase in income above that level of income I° will have a diminishing marginal utility.  Below I°, the individual will be a risk lover and will take unfair gambles and risks in an effort to make large gains in income. Above I°, the individual will purchase insurance against losses.

(a) when insurance is obtained through a reciprocal insurer, the insureds are sharing the risk of loss with other subscribers of that reciprocal.

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