Question

2. Assume you are faced with the following decision alternatives and two states of nature. The profit payoff table is shown below States of Nature Prob (S D1 D2 D3 S1 0.60 100 50 40 S2 0.40 20 50 80 Decision Alternatives a) Do you think undertaking a market research study, with a cost of 25, would be justified in this case? b) What should the probabilities of states 1 and 2 be that options D1 and D3 will have the same expected profit? c) What should the probabilities of states 1 and 2 be that only the option D1 is the optimal strategy? d) What should the probabilities of states 1 and 2 be that only the option D3 is the optimal strategy? e) What should the probabilities of states 1 and 2 be that EMVPl is equal to 30?

Answer 1

A)

Expected Monetary Value for D1 = 100*0.6 + 20*0.4 = 68

Expected Monetary Value for D2 = 50*0.6 + 50*0.4 = 50

Expected Monetary Value for D3 = 40*0.6 + 80*0.4 = 56

As the Expected Monetary Value for D1 is the highest of all the three decisions, so it is the optimal decision.

As the Expected Monetary Value for D1 is more than 25, so a market research study can be undertaken.

B)

As per the given condition,

100*S1 + 20*S2 = 40*S1 + 80*S2

Or,

60S1 = 60S2

Or, S1 = S2

And,

S1 + S2 = 1

So, if the probabilities are equal then the EMV of D1 and D3 will be equal.

Here S1 = S2 = 0.5 (by solving the given equations)

C)

As per the given probabilities, D1 is already the only available optimal strategy.

Condition... S1 > S2 and S1 + S2 = 1 in order to get D1 as the optimal strategy.

D)

As per the given condition,

40*S1 + 80*S2 > 100*S1 + 20*S2

Or,

60S2 > 60S1

Or, S1 < S2

Let us take S1 as 0.4 and S2 as 0.6,

Then,

Expected Monetary Value for D1 = 100*0.4 + 20*0.6 = 52

Expected Monetary Value for D3 = 40*0.4 + 80*0.6 = 64, so in this case EMV of D3 is highest...

So S1 < S2 in order to get D3 as the optimal strategy...

Condition... S1 < S2 and S1 + S2 = 1 in order to get D3 as the optimal strategy.

E)

As per the given condition,

100*S1 + 80S2 = 30

Or,

10S1 + 8S2 = 3

and S1 + S2 = 1

By solving these equations, the probabilities can be determined.

End of the Solution....