Question

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?

Short answer

The utility function is shown below:

The utility function will be S-shaped.

Such a utility function describes people’s preferences because an individual's risk preferences change with a change in the stock of resources.

Step-by-step solution

Explanation

Suppose an individual needs an I* to sustain. The diagram below shows that after level I*, the individual will experience diminishing marginal utility. Below the income level I*, the individual will be a risk lover. The return will also be high; thus, the individual may take unfavorable gambles to increase the income. Above the income level I*, the individual will be risk averter as the required level of income to sustain life is covered; thus,the individual will take up insurance to cover the losses.

The utility function is shown below:

The utility function will be S-shaped.