Question

Consider a person who is offered a choice between two lotteries:

LA: Win $520,000 with a p = 61%, $0 otherwise

LB: Win $500,000 with a p = 63%, $0 otherwise

Out of these two, the decision maker selects lottery A. The decision maker is also given the choice between the following two lotteries:

LC: Win $520,000 with a p = 98%, $0 otherwise

LD: Win $500,000 with a p = 100%, $0 otherwise

If the decision maker behaves according to expected utility, which option do they pick out of the second pair, given that they picked A out of the first? Why is this certain?

Answer 1

Consider the given problem here there are two lotteries “A” and “B”. Now, the expected value of “A” is given by, => $520,000*0.61 + $0 = $317,200. Similarly, the expected value of “B” is given by, => $500,000*0.63 + $0 = $315,000. So, here the expected value of “A” is more compare to “B”, => according to the expected utility theory the individual will choose “A” over “B”.

Now, if there are two lotteries “C” and “D”. SO, the expected value of “C” is “$520,000*0.98 + $0 = $509,600. Now, the same for “D” is that “$500,000*1 + $0 = $500,000 < $509,000. So, according to the expected utility theory the individual will choose “C” over “D”.

Now, the result is certain because the expected value of lottery C is more than lottery D.