1. In order to boost funding for the state of Florida or Mississippi, depending

Question

1. In order to boost funding for the state of Florida or Mississippi, depending on where you are, each state has decided to start a daily drawing where people can purchase a ticket for $1 with a 3-digit number from 000-999. If the number on the ticket matches the number drawn, the person wins $500. Suppose a person is risk neutral, i.e., their utility is linear in income. In this case U=Y. Show that a risk neutral person will never purchase a lottery ticket. Why then do so many people purchase these types of lottery games? (Hint: what is the Expected outcome from the gamble?) 2. Your firm has been sued for $3 million by a supplier for breach of contract. Your lawyers believe that there are three possible outcomes if the suit goes to trial. One, which the lawyers term “highly improbably,” is that your supplier will win the lawsuit and be awarded $3 million. Another, which the lawyer term “unlikely,” is that your supplier will win the lawsuit and be awarded $500,000. The third which the lawyers term “likely,” is that your supplier will lose and the lawsuit and be awarded $0. You have to decide whether to try to settle the case. To do so you need to assign probabilities to “highly improbable,” “unlikely” and “likely”. What probabilities correspond to these statements? Going to trial will cost you $100,000 in legal fees. One of your lawyers believes that your supplier will settle for $100,000 (and you will have legal fees of $25,000). Should you settle?

Explanation / Answer

1.

Let Y is income and utility is given to in linear relationship with income, U=Y

and

utility without playing is Y.

The fee for playing the lottery is $1 and winning probability is 1/1000 =0.001 but the returns are 500, which means winning will increase income by 500 and cost $1 (Y-1+500) and loss will reduce income by $1 (Y-1)

Expected utility of ticket

E(U) = (0.999)(Y-1) + (0.001)(Y-1+500)

= Y -1 +.001($500)

= Y - 1 + 0.5

= Y - 0.5.

Which means that the income will reduce by 0.5

U= Y > E(U) = Y – 0.5,

so, this person would not play the lottery.

People play the lottery because there is a utility value from playing the lottery, which is not based in this simple model.

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