Question

1. The highest value for the equally likely criterions is ________; this occurs with alternative ______. (1.5 pts)

                                States of Nature                                                                                                                                                 

Alternatives Option 1	S1 $10,000	S2 $30,000
Option 2	$5,000	$45,000
Option 3	$-4,000	$60,000

                               

	States of Nature
Alternatives	S1	S2
p	0.6	0.4
Option 1	200	300
Option 2	50	350

2. What is the EMV for Option 1 in the following decision table?

3. What is the EMV for Option 2 in the following decision table?

4. What is the expected value under certainty in the following decision table? (EVwPI)

5. What is the expected value of perfect information? (EVPI)

Answer 1

1. The highest value for the equally likely criterions is calculated as under:

Option 3 = (-4000x0.50) + (60000x0.50)

= $28000

This occurs with alternative 'Option 3'.

2. EMV for Option 1 = (10000x0.60) + (30000x0.40)

= $18000

3. EMV for Option 2 = (5000x0.60) + (45000x0.40)

= $21000

4. Expected Value under certainty for Option 1 is $10000

Expected Value under certainty for Option 2 is $60000

5. EVPI = EPC – max(EMV)

The best payoff under each state of nature is $10000 and $60000

The probabilities of these states are 0.6 and 0.4

EPC = (10000x0.6) + (60000x0.4) = $30000

Largest expected payoff without perfect information is:

max(EMV) = $10000

EVPI = EPC – max(EMV)

= 30000 - 10000

= $20000