10. Discosering Your Own Risk Preferences: Although our discussion of financial risk and risk aversion may have seemed abstract, this question involves discovering your own expected utility function and your general attitude toward risk, precisely as in Lecture Two. Table 1 below displays eight hypothetical gambles with which you are presented. Each gamble has two outcomes, where you receive a possible gain or a possible loss. Each gamble has a potential loss of $1, 000.00 but possible gains increase with each successive gamble (from receiving $1, 000.00 to receiving $8, 000.00.) Since the idea of welfare or utility is a relative one and purely subjective, I have specified (numerically, in units known as str/s ) your welfare, should you suffer a $1, 000.00 loss in a gamble, your utility (welfare) from the loss as 10. Your mission, should you choose to accept it (and please do, there is no right or wrong answer, but the results can be enlightening to you), is to do the following for each of the eight gambles:

• each gamble (one gamble per row of the table) presents you with a probability p of winning the indicated amount and probability (1 p) of losing the corresponding amount (specified respectively in the first two columns). In the fourth column ( probability oJ porn) list that Think about what probability or likelihood of winning would leave you indifferent between taking that specific gamble in real life or just walking away from it, in which case you both win and lose nothing ($0.00). There is no upfront cost to you from either choice. For each gamble, list this probability in the corresponding cell.
• Now, for each gamble, use the probability you listed to determine the corresponding level of welfare or utility you get from winning the corresponding prize money. Were assuming that walking away from a gamble, which both gives you and costs you no money, your level of utility or welfare is itself zero: U(0) 0). So once youve determined your own value of p for a given gamble, you can solve for your implied U(gain) through:

0 pU(gQ3Tt) -I- (1 p)U(loss)

• Once youve done this for each of the eight gambles, graph your values for U(gain) (with dollars on the horizontal axis and U(gain) on the vertical axis.) Is your graph concave everywhere? Convex everywhere? Concave for some level of prize money and convex for others?
• Your answer to this question should consist of your completed version of Table 1 and the corre- sponding graph for U(gain).

EXAMPLE OF WHAT TABLE SHOULD LOOK LIKE. PLEASE FILL IN TABLE

Possible Loss	Possible Gain	"Utility" of Loss	Probability of Gain	"Utility" of Gain
-$1,000.00	$1,000.00	-10.00	0.60	6.67
-$1,000.00	$2,000.00	-10.00	0.55	8.18
-$1,000.00	$3,000.00	-10.00	0.45	12.22
-$1,000.00	$4,000.00	-10.00	0.40	15.00
-$1,000.00	$5,000.00	-10.00	0.37	17.03
-$1,000.00	$6,000.00	-10.00	0.35	18.57
-$1,000.00	$7,000.00	-10.00	0.34	19.41
-$1,000.00	$8,000.00	-10.00	0.33	20.30