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*) = -*w ^{2}* + 100

(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*+ 100*w.*

*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.**

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