Bob and Carol are risk averse and both are expected utility maximizers. They have the same Bernoulli utility function:
u(w) =(w)^(1/2)
where w is the wealth. Bob’s initial wealth is $10,000 while Carol ‘s initial wealth is $1,000,000.
Suppose neither is facing any risk. An opportunity arises for both to invest in a risky asset with random gross return z: Assume that z follows the uniform distribution on [0; 2.5]. Do both invest in the risky asset?