Consider the following payoff table and probabilities for the states of nature :
ID: 464578 • Letter: C
Question
Consider the following payoff table and probabilities for the states of nature :Demand Level Alternative. 1. 2. 3. 4 A. $700. $700. $700. $700 B. -$200. $1400. $1400. $1400 C. -$1100. $500. $2100. $2100 D. -$2000. -$400. $1200. $2800 Probability 0.25. 0.35. 0.25. 0.15
A) Choose the best alternative using decision making under risk B) What is the expected value of perfect information?
Consider the following payoff table and probabilities for the states of nature :
Demand Level Alternative. 1. 2. 3. 4 A. $700. $700. $700. $700 B. -$200. $1400. $1400. $1400 C. -$1100. $500. $2100. $2100 D. -$2000. -$400. $1200. $2800 Probability 0.25. 0.35. 0.25. 0.15
A) Choose the best alternative using decision making under risk B) What is the expected value of perfect information?
Demand Level Alternative. 1. 2. 3. 4 A. $700. $700. $700. $700 B. -$200. $1400. $1400. $1400 C. -$1100. $500. $2100. $2100 D. -$2000. -$400. $1200. $2800 Probability 0.25. 0.35. 0.25. 0.15
A) Choose the best alternative using decision making under risk B) What is the expected value of perfect information?
Explanation / Answer
A) For the best alternative using decision making under risk, we multiply the payoffs by their respective probabilities. The calculations are as shown below:
Thus, the best Option is B with a payoff of 1000 (=EVUU)
B) We calculate the Maximum Payoff at each level of demand to obtain the payoff with Perfect Information as shown below:
Thus, EVPP = $1610
Expected Value of Perfect Information = EVPI = EVPP - EVUU = $610
Alternative Demand Level Probability A B C D 1 0.25 $700 ($200) ($1,100) ($2,000) 2 0.35 $700 $1,400 $500 ($400) 3 0.25 $700 $1,400 $2,100 $1,200 4 0.15 $700 $1,400 $2,100 $2,800 Expected Payoff 700 1000 740 80