Investor A is an expected utility maximizer with Bernoulli utility function U x( ) = y / x .

Currently, Investor A is contemplating two investment opportunities, both with uncertain outcomes. Investment 1 is a coin toss: the payoff can be eitherY₁ or Y₂ dollars, each with probability 1/2. Investment 2 is a roll of a fair six-sided die, and the payoff is Y₃ dollars times the number that lands face up (1; 2; 3; 4; 5 or 6). Assume for simplicity that initial wealth is zero.

A) Which investment will Investor A choose using the following values for Y, Y₁, Y₂ andY₃,

Y=−1,Y₁ = $20,Y₂ = $50,Y₃ = $10?

B) Investor A 's friend Investor B is also contemplating the following two investment opportunities. Investment 1 is a coin toss: the payoff can be either $20 or $50, each with a probability 1/2. Investment 2 is a roll of a fair six-sided die, and the payoff is $10 times the number that lands face-up (1; 2; 3; 4; 5 or 6).

Assume for simplicity that initial wealth is zero. Like Investor A, Investor B is a risk-averse expected utility maximizer. Without knowing Investor B's precise utility function, is it possible to tell which investment Investor B will choose?