2. The following payoff table provides profits based on various possible decisio

ID: 330533 • Letter: 2

Question

2. The following payoff table provides profits based on various possible decision alternatives and various levels of demand at Robert Klassan's print shop: DEMAND HIGH $30,000 LOW $10,000 Alternative 1 Alternative 2 Alternative 3-$2,000 5,000 $40,000 50,000 The probability of low demand is 0.4, whereas the probability of high demand is 0.6. a) What is the highest possible expected monetary value? b) What is the expected value with perfect information (EVwPID? c) Calculate the expected value of perfect information for this situation?

Explanation / Answer

Robert klassan print shop

Expected monetary value for each decision alternative

=S (payoff for that the alternative in state of nature* probability for the state of nature)

Expected monetary value for decision alternative 1= 10000*0.4+30000*0.6=22000

Expected monetary value for decision alternative 1=5000*0.4+40000*0.6=26000

Expected monetary value for decision alternative 1= (-2000)* 0.4+50000*0.6=29200

Highest possible EMV is for alternative 3 =$ 29200

If we have perfect information about the states of nature:

Based on payoff table if we know for sure that:

The original probabilities for the states of nature are:

The expected payoff under certainty or Expected value with perfect information about the states of nature
= 10000*0.4+50000*0.6= $34000

The largest expected payoff without the perfect information, as calculated in question (a), is

Expected value without perfect information about the states of nature

=max(EMV)

= max( 22000,26000,29200)

= $29200.

Expected value with perfect information about the states of nature =$34000

EVPI( expected value of perfect information)=

Expected value with perfect information about the states of nature - Expected value without perfect information about the states of nature

= 34000-29200

= $4800

pay off for each States of nature

Decision

low

high

EMV of alternative

Alternative 1

10000

30000

22000

Alternative 2

5000

40000

26000

Alternative 3

-2000

50000

29200

Probability

0.4

0.6

Expected value without perfect information = 29200

Expected value with perfect information = 34000

EVPI = 4800