Question 3 [20 marks] Consider two utility functions u(x) and ˜u(x) where x is the amount of money consumed by the agent.
a) Explain formally what it means that an agent with utility function u is more risk averse than an agent with utility function ˜u.
b) Show that an agent with utility function u(x) = log x is more risk averse than an agent with utility function ˜u(x) = √ x.
