Question

Lecture Exercise #15 Consider the following payoff matrix: State of Nature Alternative High Demand (Prob. = 0.7) Low Demand (Prob. = 0.3) Build Large Plant $150,000 $70,000 Build Small Plant $110,000 $90,000 Do Nothing 0 0 . Without any additional information, what is the best decision? What is the EMV? If perfect information is available, what is the EVPI? .

Answer 1

a.

EMV for an alternative =

Payoffof StateOf Nature * ProbabilityOfThat State of Nature

EMV for Build large plant = 150,000*0.7+ 70,000*0.3 = 126000

EMV for Build small plant = 110,000*0.7+ 90,000*0.3 = 104000

EMV for doing nothing = 0*0.7+0*0.3 = 0

Best option is Build large Plant is best option as it has highest EMV.

b.

THEORY:

The expected value of perfect information (EVPI) is the maximum price that an individual would be willing to pay to get perfect information (PI).

EVPI = Expected value with perfect information- Expected value without perfect information

The expected value without perfect information is same as Maximum EMV which was determined to be $126,000 for build large plant in part a.

Expected value with perfect information =

Best Payoffof Each StateOf Nature* ProbabilityOfThatStateOf Nature

Expected value with perfect information (EVPI) = 150,000*0.7 + 90,000*0.3 = $ 132,000

EVPI = 132,000 - 126,000 = $ 6,000