Consider two consumers with Bernoulli utility functions

u1(x)=a1x2+b1x

u2(x)=a2x2+b2x

where ai<0<bi , and x(min)i(bi/2ai) for i=1,2.

(1) Are these consumers risk averse?

(2) Can you state a condition under which consumer 1 is more risk

averse than consumer 2?

(3) Prove that if an individual has a Bernoulli utility function u(x)

with the quadratic form

u(x)=x2+x

then her expected utility from a distribution F is determined

by the mean and the variance of the distribution.