Assume an investor has the utility function W1/ 2 , where W is wealth. The
government issues a lottery ticket that pays the winner NT$300. The lottery ticket costs
NT$1. The chance of winning the lottery is 1/200. The investor has NT$270 in original
wealth. (20%)
(一) What is the expected value of this lottery?
(二) What is the investor’s expected utility if he buys the lottery?
(三) Is the investor a risk-averter, risk-neutral, or risk-lover? Use the lottery case to
show it.
(四) Will the investor buy the lottery ticket if his utility function is W3 ? Use the lottery
case to show it.
A bag contains two coins: One is a normal coin, with heads and tails, while the other is
a coin with heads on both sides. A coin is chosen at random from the bag and tossed 2
times. The results are all heads. What is the probability that the coin tossed is a
two-headed one? (11%)
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