Question

Jack does not have specific preferences about a lottery with a 50-50 chance the payouts are 0,100. Jack is also assured a payout of 30 dollars. Jack gets a second proposition with also a 50-50 chance payouts are 0,20. He is also assured a payout of 5 despite the outcome. Jack gets a third lottery offer with a 50-50 chance with a payout of (40, 100) and is assured 50 dollars regardless of the outcome. There is also another 50-50 lottery with payout of 10, 100. Jack has no preferences between the lottery and assured payout of x. Assuming Jack is risk averse, what is the maximum x?

Answer 1

First - Payout are 0 , 100 with probability of 50-50

Expected payoff - .50*0 + 100*.50 = $50

Assured payout - $30

Total - 50+ 30 = $80

Second - Payout are 0 ,20 with probability 50-50

Expected payoff - 0*.50 +20*.50 = 10

Assured - $5

Total payout- $15

Third - Payout are 40,100 with 50-50 chances

EXPECTED PAYOFF - 40*.50+100*.50 = $70

Assured - $50

Total - $120

Fourth - payout are 10,100 with 50-50 chances

Expected payoff - 10*.5+100*.5=$55

Total = $55

Jack gets maximum of $120 when he chooses proposition second