Question

Question 1 Consider the following three utility functions defined over quantities of money. These functions are risk-neutral, risk-loving, and risk-averse. Match each utility function to its risk attitude u = x^2 [Choose) [Choose ] risk-averse risk loving risk-neutral u = log(x) [Choose ] u = x + 5

Answer 1

Answer 1

A person is risk lover if a function is convex i.e. d²u/dx² > 0, A person is risk averse if a function is concave i.e. d²u/dx² < 0 and A person is risk neutral if a function is linear i.e. d²u/dx² = 0.

(i) u = x² => du/dx = 2x => i.e. d²u/dx² = 2 > 0 => a function is convex and hence is risk lover.

(ii) u = log(x) => du/dx = 1/x => i.e. d²u/dx² = -1/x² < 0 => a function is concave and hence is risk averse.

(iii) u = x + 5 => du/dx = 1 => i.e. d²u/dx² = 0 > 0 => a function is linear and hence is risk neutral.