An individual makes decisions according to Bayes' decision rule.For her current problem,she has constructed the following payoff table,and she now wishes to maximize the expected payoff.
The value of x currently is 50,but there is an opportunity to increase x by spending some money now.What is the maximum amount that should be spent to increase x to 75?

Question

An individual makes decisions according to Bayes' decision rule.For her current problem,she has constructed the following payoff table,and she now wishes to maximize the expected payoff.  
The value of x currently is 50,but there is an opportunity to increase x by spending some money now.What is the maximum amount that should be spent to increase x to 75?

Quizplus · Accepted Answer

The Answer is For a₁: E[p(a₁,

heta

)] = 0.4(2x)+ 0.2(50)+0.4(10)= 14 + 0.8x For a₂: E[p(a₂,

heta

)] = 0.4(25)+ 0.2(40)+0.4(90)= 54 For a₃: E[p(a₃,

heta

)] = 0.4(35)+ 0.2(3x)+0.4(30)= 26 + 0.6x At x = 50,the optimal decision alternative is a_3,with expected payoff 56.At x = 75,the optimal decision alternative is a_1,with expected payoff 74.The minimum amount that should be spent to increase x to 75 is (74 - 56)= 18.

An Individual Makes Decisions According to Bayes' Decision Rule