4 You have initial wealth of 500 and are offered the followi

4. You have initial wealth of $500 and are offered the following gamble. You flip a coin and if you get heads, you win $1000. If you get tails you lose $500. a. What is the expected value of the gamble? (5 points) b. You have utility in the form of U = M^1/2 with initial wealth of $500. What is the expected utility of the gamble? Should you take the gamble? (10 points) C. Why would a person with risk neutral preferences always take this gamble? (5 points)

Solution

a. Expected value of the gamble = expected return x probability = 1,000 x 0.5 - 500 x 0.5 = $250

b. U = M1/2, M = $500
Expected utility = 500 x 1/2 = $250
Since, utility is not zero we may play the gamble.

c. A Risk neutral person will always play the gamble. A risk neytral person doesn\'t considers the risk while gambling. Such person takes all the decisions only on the basis of return. Since, here there is a return and expected return is not zero or negative, thus, he will play the game.