Let us consider again the sure lottery \(a_{1}\), which guarantees a payoff with probability one, and lottery \(a_{2}\), obtained by the mean-preserving spread  , featuring equally likely outcomes and . Concavity implies risk aversion, since

Since the inequality is not strict, we should say that lottery \(a_{1}\) is at least as preferred as \(a_{2}\), and the decision maker could be indifferent between the two.

As a numerical illustration, let us consider the logarithmic utility

Figure 7.1 illustrates the role of concavity in describing risk aversion.

Data From Figure 7.1