Reference no: EM132971295

Winnie owns a small pond for lobster farming. She has about 3,000 lobsters soon to be ready for the market. However, Winnie has to make a decision: should she harvest the lobster immediately, or leave them in the pond despite the approaching storm? A storm just before the harvest is usually destructive, often ruining the yield. A light, warm rain, however, will sometimes cause a conducive environment for boost the quality of lobsters.

• From the weather report, Winnie concluded that there was a fifty-fifty chance that the rainstorm will hit her pond. She also thought that there was a 40% chance that, if the storm did strike, it would lead to a warm rain. If the rain turned out to be cold, the cold rain water will reduce the quality of lobsters. Such lobsters could be packaged under Winnie's brand and would sell wholesale for only $8.56 per lobster, about $2.84 less than Winnie could obtain by harvesting the lobsters immediately and eliminating the risks. Winnie always had the option of selling the lobsters to canned meat manufacturers, or selling the lobsters as private label products. These options would bring only half as much revenue (i.e., $4.28/lobster), but would at least avoid damaging the
• Winnie's reputation, which would be risked by distributing an inferior product to the market.
• If Winnie decided not to harvest the lobsters immediately in the anticipation of the storm, and the storm did not strike, Winnie would probably leave the lobsters to mature more fully. With luck, the yield of lobsters can grow by about 20%, resulting in lobsters selling for around $14/lobster. Even with less favorable weather, the yield would probably grow by about 5%, resulting in lobsters selling for around $12/lobster. Winnie thought these possibilities were equally likely. Moreover, while waiting for lobsters to mature more fully, the level of microorganism in the pond must be monitored. When it exceeds certain threshold, the lobsters must be harvested immediately. If this happened, the lobsters would be priced at only $10/lobster. Winnie felt that this event had only about 0.2 probability.
• The wholesale price for a warm-rain lobster would be about $32/lobster. Unfortunately, the same process that resulted in a higher-quality lobster also cause 30% reduction in the survival rate of lobsters. The higher price was therefore partly offset by a reduction quantity.

Problem 1: Perform a one-way sensitivity analysis by varying the probability that a warm rain develops given that the storm hits Winnie's pond.

Problem 2: What is the most that Winnie should be willing to pay to know in advance whether the storm will come to her lobster pond?

Problem 3: Suppose that Winnie has a cousin who lives wherever this storm is coming from. This cousin could easily tell whether the storm is warm or cold. However, the cousin would not be able to tell whether the storm would actually hit Winnie's lobster pond. What is the most Winnie would be prepared to pay for this information?