Question

Suppose Feng have $50 and you would like to purchase some lottery tickets. Assume that he can win with 40% probability, and if he win, he can earn 100% of his investment (i.e., double the investment). On the other hand, if he lose, he loses 100% of his investment. Further assume that his utility function is given by u(w) = -w² + 100w. Answer each of the following.

(a) Is Feng risk-averse, risk-neutral, or risk-loving? How do you know?
(b) What is the expected value of the lottery if Feng invests all $50?
(c) If Feng want to maximize his expected utility, how much should he invest?

Answer 1

Feng has $50 and would like to spent it on lottery tickets.

There is a 40% probability of him winning.

If he wins he will get 100% of his investment and gets back $100.

But if he loses, he will lose 100% of his investment that is $50.

a. His utility function is u(w) = -w2+ 100w.

On differentiating this we get,

Since the second derivative is negative, we can say that the person is risk averse.

b. Expected value of lottery will be

So,expected value of lottery will be $40.

c. Utility is maximized when the first derivative is equal to zero

So, utility will be maximized when he invests $50 in lottery.