Question

In: Math

Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in...

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 7 5
Medium complex, d2 14 4
Large complex, d3 20 -8

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 $17 million and as long as the payoff for the weak demand was greater than or equal to -$20 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.

Solutions

Expert Solution

The  probability that demand will be strong (S1) is and a corresponding probability that demand will be weak (S2) is  

a) The payoff for decision d3, to build a large complex is

Let the payoff under strong demand for the medium complex decision be Payoff(S1) and the payoff under weak demand be 4 as before.

The expected payoff for the decision alternative to build medium complex, d2 is

We want this to be less than or equal to the expected payoff for d3, that is we want EV(d2)<=14.4

ans: The payoff for the medium complex under strong demand remains less than or equal to $ 17 million, the large complex remains the best decision.

b) Let the payoff under strong demand for the small complex decision be Payoff(S1) and the payoff under weak demand be 5 as before.

The expected payoff for the decision alternative to build medium complex, d1 is

We want this to be less than or equal to the expected payoff for d3, that is we want EV(d1)<=14.4

ans: The payoff for the small complex under strong demand remains less than or equal to $16.75 million, the large complex remains the best decision


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