Under expected utility theory, which of the following implies risk aversion? A) $E u(x)E(x)$ C) $u^{\prime \prime}(x)0$ D) The utility function is convex.

Question

Under expected utility theory, which of the following implies risk aversion?
A) $E u(x)<u(E(x))$.
B) $x_{c e}>E(x)$
C) $u^{\prime \prime}(x)>0$
D) The utility function is convex.

Quizplus · Accepted Answer

Risk aversion is indicated by a concave utility function, which means that the second derivative of the utility function with respect to wealth is negative ($u''(x) < 0$). This leads to the condition $E[u(x)] < u(E[x])$, where the expected utility of a gamble is less than the utility of the expected value of the gamble, reflecting a preference for certainty over risk.

Under Expected Utility Theory, Which of the Following Implies Risk Eu(x)<u(E(x))E u(x)<u(E(x))Eu(x)<u(E(x))

Under Expected Utility Theory, Which of the Following Implies Risk $E u(x)<u(E(x))$