In: Statistics and Probability
Problem 13-11 (Algorithmic)
Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars.
State of Nature | ||
Decision Alternative | Strong Demand S1 | Weak Demand S2 |
Small complex, d1 | 9 | 7 |
Medium complex, d2 | 13 | 3 |
Large complex, d3 | 21 | -9 |
Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.8 that demand will be strong (S1) and a corresponding probability of 0.2 that demand will be weak (S2). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $16 million and as long as the payoff for the weak demand was greater than or equal to -$29 million.
ANSWER:
A.
States of Nature | EMV | ||
Decision | S1 | S2 | |
d1 | 9 | 7 | 8.6 |
d2 | 13 | 3 | 11 |
d3 | 21 | -9 | 15 |
Prob | 0.8 | 0.2 |
The superiority of d3 will vanish when EMV of d2 will be equal to 15. Let that happen at payoff under strong demand for d2 be Ds2 so that
Ds2*0.8 + 3*0.2 = 15 or, Ds2 = 14.4/0.8 = 18
So, The payoff for the medium complex under strong demand remains less than or equal to $18 million, the large complex remains the best decision.
B.
Similarly, The superiority of d3 will vanish when EMV of d1 will be equal to 15. Let that happen at payoff under strong demand for d1 be Ds1 so that
Ds1*0.8 + 7*0.2 = 15 or, Ds1 = 13.6/0.8 = 17
So, The payoff for the small complex under strong demand remains less than or equal to $17 million, the large complex remains the best decision.
NOTE:: I HOPE YOUR HAPPY WITH MY ANSWER....***PLEASE SUPPORT ME WITH YOUR RATING...
***PLEASE GIVE ME "LIKE"...ITS VERY IMPORTANT FOR ME NOW....PLEASE SUPPORT ME ....THANK YOU