Following is the payoff table for the Pittsburgh Development Corporation (PDC) C
ID: 3012533 • Letter: F
Question
Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars.
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.
Consider the medium complex decision. How much could the payoff under strong demand increase and still keep decision alternative d3the optimal solution? If required, round your answer to two decimal places.
The payoff for the medium complex under strong demand remains less than or equal to $??? million, the large complex remains the best decision.
Consider the small complex decision. How much could the payoff under strong demand increase and still keep decision alternative d3 the optimal solution? If required, round your answer to two decimal places.
The payoff for the small complex under strong demand remains less than or equal to $??? million, the large complex remains the best decision.
Explanation / Answer
Therefore best choice is to build Large complex because it has maximum Expected Monetary value, EMV = 15.
Sensitivity Analysis:
For Medium Complex Decision
d3 decision alternative will be remained as optimal decision altenative until
EV(d2) <= $15 M
Let S = the payoff of d2 when demand is strong
W = the payoff of d2 when demand is weak
then EV(d2) = 0.8 x S + 0.2 x W
Let W = $4 M
EV(d2) = 0.8 x S + 0.2 x 4 <= 15
S <= 17.75
Therefore payoff for the medium complex under strong demand, that is S <= $17.75.
=> Large complex still remains best decision
For Small Complex Decision
d3 decision alternative will be remained as optimal decision altenative until
EV(d1) <= $15 M
Let S = the payoff of d1 when demand is strong
W = the payoff of d1 when demand is weak
then EV(d1) = 0.8 x S + 0.2 x W
Let W = $6 M
EV(d1) = 0.8 x S + 0.2 x 6 <= 15
S <= 17.25
Therefore payoff for the small complex under strong demand, that is S <= $17.25.
=> Large complex still remains best decision
State of Nature Decision Alternative Strong Demand S1 Weak Demand S2 EMV Small Complex d1 9 7 8.6 Medium Complex d2 13 3 11 Large Complex d3 21 -9 15 Probability 0.8 0.2