Implication of the concavity of u?

Question

>Suppose that we have the following inequality: >$u( y- d) - u(y-d') \\ge u(y' - d) - u( y' -d')$.>The concavity of $u$ together with $y\\le y'$ then implies that $d \\le d'$.I sometimes come across this problem in economic papers, but I don't understand the logic behind this. Can anyone explain this?

Answer 1

The concavity of the utility function illustrates how the individual views risk. If a utility function is concave, they are said to be risk-adverse. If the utility function is a straight line, then the individual is said to be risk-neutral. If the utility function is convex, then they are said to be risk-loving.

A useful concept that illustrates this is the certainty equivalent and risk premium. In brief, an individual's certainty equivalent is the amount of money you would have to pay to an individual such that they would be indifferent between taking that amount of money, say $X, and taking some gamble.

For those who are risk-adverse, their certainty equivalent will be below the expected return on a gamble, as they prefer to avoid the risk. For those who are risk-loving, their certainty equivalent will be above the expected return on a gamble, as they enjoy the risk and must be compensated in order to give up some of that risk.

I hope that helps!