You have an initial wealth of

$5

. A lottery pays a prize of

$4

with probability 0.25 and nothing with probability 0.75 . It costs

$1

to play this lottery.\ a. Write out the prospect of your net wealth if you play the lottery and the prospect if you don't. Compare the expected value of these two prospects.\ b. Suppose your utility function is

u(x)=\\\\sqrt(x)

. Compute your expected utility if you play the lottery and if you don't. Will you play the lottery?\ c. Suppose your utility function is

u(x)=x

. Redo part (b).\ d. Suppose your utility function is

u(x)=x^(2)

. Redo part (b).\ e. Which of the above utility function corresponds to risk aversion? Which to risk loving? And which to risk neutrality?\ 12

6. You have an initial wealth of $5. A lottery pays a prize of $4 with probability 0.25 and nothing with probability 0.75 . It costs $1 to play this lottery. a. Write out the prospect of your net wealth if you play the lottery and the prospect if you don't. Compare the expected value of these two prospects. b. Suppose your utility function is u(x)=x. Compute your expected utility if you play the lottery and if you don't. Will you play the lottery? c. Suppose your utility function is u(x)=x. Redo part (b). d. Suppose your utility function is u(x)=x2. Redo part (b). e. Which of the above utility function corresponds to risk aversion? Which to risk loving? And which to risk neutrality