Question

Problem 1B:

You want to invest money in real estate. The following table summarizes the payoffs of the investment in good or bad economic situations.

	States of nature
Actions	Good	Poor
Apartment building	$ 50,000	$ 30,000
Office building	$ 100,000	- $40,000
Warehouse	$ 30,000	$ 10,000

You estimate that the probabilities of having good or bad economic situations are 70% and 30%, respectively.

1. Find the optimal action based on the expected monetary value (EMV) criterion using your prior probability estimates.
2. Find the optimal action based on the expected opportunity loss (EOL) criterion using your prior probability estimates.
3. Determine the expected value of perfect information (EVPI).

You decide to consult a financial advisor about his opinion of "for" or "against" the investment. In the past, the advisor's opinion has been "for" in 85% of the cases where the economic situation was "good", and the opinion has been "against" in 90% of the cases where the economic situation was "poor".

4. Draw the decision tree.

5. Under "for" recommendation, determine the posterior probabilities for "good" and "poor" economic situations, and find the optimal action based on the EMV using the posterior probabilities.

6. Under "against" recommendation, determine the posterior probabilities for "good" and "poor" economic situations, and find the optimal action based on the EMV using the posterior probabilities.

7. Determine the expected value of sampling information (EVSI) and the efficiency of sampling information.

*******************   End of the problem set *********************

Please help show work please

Answer 1

EVM of apartment building = .7*50,000 +.3*30,000= 35000 +9000=44,000

EVM of Office building = .7*100,000 +.3*-40,000= 70000 -12000=58,000  

EVM of Warehouse   = .7*30,000 +.3*10,000= 21000 +3000=24,000  

Office building has the highest EVM and same is 58000.

For EOL we will substract the probability from 1

EOL of apartment building = .3*50,000 +.7*30,000= 15000 +21000=34,000

EOL of Office building = .3*100,000 +.7*-40,000= 30000 -28000=2,000  

EOL of Warehouse   = .3*30,000 +.7*10,000= 9000 +7000=16,000

Apartment building has the highest EOL and same is 34000.

Expected Value of perfect information = .7*100,000+.3*30,000 -$58,000 = 70000+9000-58000 = 79000 - 58000 = 21000