Joanne is faced with purchasing tickets in two lotteries. Both lotteries have a high payoff pih...

Joanne is faced with purchasing tickets in two lotteries. Both lotteries have a high payoff pih = 16 dollars or a low payoff pil = 4 dollars. Each outcome happens with equal probability. The outcomes of the two lotteries are perfectly negatively correlated, meaning that when one lottery has a high payoff, the other has a low payoff, and vice versa.

What is the expected payoff of either lottery?

What is the certainty equivalent of either lottery?

If Joanne decides to buy two tickets, one ticket for each lottery, what is the certainty equivalent of the two lotteries combined?

Solutions

Expert Solution

a) Expected payoff of each lottery is

E(A)=E(B)= 16(0.5)+4(0.5) = 10

so expected payoff of either lottery is $10

b) Certainty equival;ent refers to the situation is the lowest amount of money for certain when there is no lottery . it is also known as the selling price.

so the certainty equivalent in each case would be the cash in hand with Joanne . it would be the amount that Joanne is indifferent between buying a ticket or havinh that money as cash

c) Since we are not given the amount that Joanna would invest in buying these ticket, we take it as x . so the selling price or the amount that would be with Joanna in case she doesnt buy the lottery ticket ( becasue she is indifferent ) is x for one ticket which is the certainlty equivalent ie the certain amount Joanna would have in case she doesnt buy tickets

so for two tickets , if we assume that the price is same the certainty equivalent would be 2x

Rahul Sunny answered 1 year ago

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