Following is the payoff table for the Pittsburgh Development Corporation (PDC) C
ID: 2738342 • 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 0.81 that demand will be strong (S_1) and a corresponding probability of 0.19 that demand will be weak (S_2). 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 $18.05 million and as long as the payoff for the weak demand was greater than or equal to -$13.05 million. Consider the medium 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 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
step-1: Introduction:
a.Currently, the large complex decision is optimal with EV(d3) = 0.81(19) + 0.19(-9) = 13.68.
In order for d3 to remain optimal, the expected value of d2 must be less than or equal to 13.68.
Lets= payoff under strong demand
EV(d2) = 0.81(s) + 0.19(4) 13.68
0.81s+ 0.76 13.68
0.81s 12.92
Therefore, s 15.95
Thus, if the payoff for the medium complex under strong demand remains less than or equal to $15.95 million, the large complex remains the best decision.
b.A similar analysis is applicable for d1
EV(d1) = 0.81(s) + 0.19(6) 13.68
0.81s+ 1.14 13.68
0.81s 12.54
Therefore, s 15.48
If the payoff for the small complex under strong demand remains less than or equal to $15.48 million, the large complex remains the best decision
State of nature Expected value= sum of Probility * demand Decision Alternative Strong demand S1 (probability = 0.81) Weak demand (probability = 0.19) calculation Expected value small, d1 7 6 7*0.81 + 6*0.19 6.81 medium, d2 15 4 15*0.81 + 4*0.19 15.91 Large, d3 19 -9 19*0.81 + (-9*0.19) 13.68