Problem 13-11 (Algorithmic) Following is the payoff table for the Pittsburgh Dev

Question

Problem 13-11 (Algorithmic)

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 -$25 million.

A. 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.

B. 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.

State of Nature Decision Alternative Strong Demand S1 Weak Demand S2 Small complex, d1 8 6 Medium complex, d2 13 3 Large complex, d3 20 -9

Explanation / Answer

In the question, expected value of d3 with 0.8 probability that demand will be strong (S1) and a corresponding probability of 0.2 that demand will be weak is

EV(d3) = 0.8*20+0.2*(-9) = 14.2 million

Then d3 will remain the optimal solution as long as the expected values for d2 and d1 are less than or equal to $14.2 million. To calculate the maximum payoff under strong demand for d2 that will keep decision alternative d3 the optimal solution is

EV(d2)<=14.2

Let us assume that S is the payoff of decision alternative d2 when demand is strong

0.8S+0.2*3<=14.2

0.8S<=13.6

S<=17

The payoff for the medium complex under strong demand remains less than or equal to 17.

This calculation shows that decision alternative d3 will remain optimal when the payoff for d2 in the event of a strong demand increases to at most $16.5 million.

B. Similarly process is apply.

expected value of d3 with 0.8 probability that demand will be strong (S1) and a corresponding probability of 0.2 that demand will be weak is

EV(d3) = 0.8*20+0.2*(-9) = 14.2 million

Then d3 will remain the optimal solution as long as the expected values for d2 and d1 are less than or equal to $14.2 million. To calculate the maximum payoff under strong demand for d1 that will keep decision alternative d3 the optimal solution

EV(d1)<=14.2

Let us assume that S is the payoff of decision alternative d1 when demand is strong

0.8S+0.2*6<=14.2

0.8S<=13

S<=16.25

The payoff for the medium complex under strong demand remains less than or equal to 17.

This calculation shows that decision alternative d3 will remain optimal when the payoff for d1 in the event of a strong demand increases to at most $16.5 million.

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