Question

In: Statistics and Probability

Problem 13-11 (Algorithmic) Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project....

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.

  1. 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.
  2. 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.

Solutions

Expert Solution

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.

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