4. (A) A small building contractor has recently experienced two successive years

Question

4.

(A)

A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm’s capacity. The contractor must now make a decision on capacity for next year. The capacity alternatives are Do Nothing, Expand, and Subcontract. Estimated profits (in thousands) under each of the two possible states of nature (Low Demand, High Demand) are shown in the table below.

Suppose after a certain amount of discussion, the contractor is able to subjectively assess the probability of low demand as 80%, with high demand accounting for the remaining probability.

What is the expected monetary value of the best alternative?

(B)

A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm’s capacity. The contractor must now make a decision on capacity for next year. The capacity alternatives are Do Nothing, Expand, and Subcontract. Estimated profits (in thousands) under each of the two possible states of nature (Low Demand, High Demand) are shown in the table below.

Suppose after a certain amount of discussion, the contractor is able to subjectively assess the probability of low demand as 47%, with high demand accounting for the remaining probability.

What is the expected value with perfect information?

(C)

A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm’s capacity. The contractor must now make a decision on capacity for next year. The capacity alternatives are Do Nothing, Expand, and Subcontract. Estimated profits (in thousands) under each of the two possible states of nature (Low Demand, High Demand) are shown in the table below.

Suppose after a certain amount of discussion, the contractor is able to subjectively assess the probability of low demand as 63%, with high demand accounting for the remaining probability.

What is the expected value OF perfect information?

Alternatives: Low Demand High Demand Do Nothing 47 57 Expand 16 81 Subcontract 38 73

Explanation / Answer

A. Expected monetary value of best alternative is calculated as below:

Probability of low demand = 0.8

Probability of high demand = 0.2

For do nothing, Value = 47*0.8 + 57*0.2 = $49,000.00

For expansion, Value = 16*0.8 + 81*0.2 = $29,000.00

For subcontract, Value = 38*0.8 + 73*0.2 = $45,000.00

So, the contractor should do nothing as the expected monetary value in this case is maximum, i.e. $49,000.00

B. Expected monetary value of best alternative is calculated as below:

Probability of low demand = 0.47

Probability of high demand = 0.53

For do nothing, Value = 47*0.47 + 64*0.53 = $56,010.00

For expansion, Value = 18*0.47 + 77*0.53 = $49,270.00

For subcontract, Value = 37*0.47 + 70*0.53 = $54,490.00

So, the contractor should do nothing as the expected monetary value in this case is maximum, i.e. $56,010.00

C. Expected monetary value of best alternative is calculated as below:

Probability of low demand = 0.63

Probability of high demand = 0.37

For do nothing, Value = 48*0.63 + 62*0.37 = $53,180.00

For expansion, Value = 17*0.63 + 78*0.37 = $39,570.00

For subcontract, Value = 39*0.63 + 73*0.37 = $51,580.00

So, the contractor should do nothing as the expected monetary value in this case is maximum, i.e. $53,180.00

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