Consider the following payoff table. Based upon these probabilities, a person would select Alternative 3.Suppose there is concern about the accuracy of these probabilities.A few of the analysts feel that the likelihood of State 1 is higher and that the likelihood of State 2 is much lower.If the likelihood of State 2 is reduced at the expense of State 1, how much lower can State 2's likelihood fall before Alternative 3 is no longer optimal?
A)0.05
B)0.06
C)0.07
D)0.08

Question

Consider the following payoff table.  Based upon these probabilities, a person would select Alternative 3.Suppose there is concern about the accuracy of these probabilities.A few of the analysts feel that the likelihood of State 1 is higher and that the likelihood of State 2 is much lower.If the likelihood of State 2 is reduced at the expense of State 1, how much lower can State 2's likelihood fall before Alternative 3 is no longer optimal?
A)0.05 
B)0.06 
C)0.07 
D)0.08

Quizplus · Accepted Answer

To determine this, we need to calculate the expected payoff for Alternative 3 with a lowered probability for State 2. Let's say we reduce the probability of State 2 by x, and increase the probability of State 1 by the same amount. 
Expected payoff for Alternative 3 with reduced State 2 likelihood:
(0.6 + 0.1x)(60) + (0.4 - 0.1x)(-20) = 36 + 4x 
We want to know the value of x that makes this expected payoff equal to or less than the expected payoff for Alternative 2, which is 40. 
(0.6 + 0.1x)(60) + (0.4 - 0.1x)(-20) ≤ 40 
Solving for x, we get x ≤ 0.06. Therefore, we can reduce the likelihood of State 2 by up to 0.06 before Alternative 3 is no longer optimal.

Consider the Following Payoff Table