Probability p of winning the indicated amount-probability

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Reference no: EM132463968

Each gamble has 2 outcomes, where you receive a possible gain or a possible loss. Each gamble has a potential loss of $1000 but possible gains increase with each successive gamble (from receiving $1000 to $8000). Since the idea of welfare or "utility" is a relative one and purely subjective. I have specified (numerically, in units known as "utils") your welfare, should you suffer a $1000 loss in a gamble, your utility (welfare) from the loss as -10.

a) 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 of gain") list that 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). There is no upfront cost to you from either choice. For each gamble, list this probability in the corresponding cell.

b) 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. We're 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 you've determined your own value of p for a given gamble, you can solve for your implied U(gain) through:

0 = pU(gain) + (1-p)U(loss)

c) Once you've done this for each of the eights 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 Table 1 and the corresponding graph for U(gain).

Reference no: EM132463968

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