Investor A is an expected utility maximizer with Bernoulli utility function U x ( ) = y
Question:
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?
Expert Answer:
