1. Construct the decision tree for William Jaeger.
2. What should he do?
Jaeger should choose to harvest later and wait for the storm.
If the storm does come but destroys the grapes, he can decide whether to bottle wine or not to protect winery’s reputation. In either way, he will gain higher revenues from harvesting later than harvesting immediately: EV of “Do not harvest & Bottling”: $39240
EV of “Do not harvest & Not bottling”: $39240-$12000*0.6*0.5=$35640 EV of “Harvest”: $34200
If the winery’s reputation is of great importance for long term profitability, he should choose to sell the wine in bulk, or sell the grapes directly to avoid impairing reputation.
Besides, Riesling wines contribute only about 1,000 cases of wine, and the whole winery produced about 25,000 cases of wine bottled each year. Since the Riesling takes only about 4% of winery’s total production and the decision analysis only affects a small proportion of winery revenues, an expected value approach is used (not expected utility approach).
However, if Jaeger is extremely risk average or the winery could not afford any risks at that time, he could choose to harvest immediately to reduce uncertainty.
3. Incorporate the option that Jaeger can obtain perfect weather information on the path of the storm into your decision tree. Note that the type of storm remains uncertain.
4. What should he do now? And at most how much he is willing to pay for this piece of information? With perfect information of whether storm strikes or not, Jaeger should still choose to harvest later and wait for the storm. EV of “Harvest” stream: $34200
EV of “Do not harvest” stream: $39240 (no matter Jaeger decides to bottle not-up-to-standard wine or not) When Jaeger decides to “bottling” not up-to-standard wine, EV of “Information” stream: $39240
When Jaeger decides to “not bottling” not-up-to-standard wine, EV of “Information” stream: $34200*0.5+$37200*0.5=$35700 (“Information, Storm strike, Do not harvest & Not bottling”: this option will not be chosen as its EV is $34080, smaller than EV of “Information, Storm strike & Harvest” $34200) As the option “harvest later and wait for the storm” will bring the highest revenues no matter Jaeger decides to bottle not-up-to-standard wine or not to protect reputation, he should stick to the strategy of harvesting later.
Even if the perfect information is free-of-charge, and he decides to bottle not-up-to-standard wine to get more monetary returns, the expected value is the same as “do not harvest and do not gain perfect information”. If he chooses to get perfect information, and decides to not bottle not-up-to-standard wine, the expected value will be lower. Because the perfect information cannot affect his choice from an ex ante position, it is worthless and he is willing to pay for zero. In this case, the information cannot predict the storm type, so the perfect information is worthless for Jaeger. If the perfect information can predict the storm type, it is valuable and Jaeger will be willing to pay.