Walter is trying to decide what to do. Walter’s annual Dog Show has been schedul
ID: 363111 • Letter: W
Question
Walter is trying to decide what to do. Walter’s annual Dog Show has been scheduled for Cedar Rapids on July 10. The profits obtained in putting on a Dog Show are heavily dependent on the weather. In particular, if the weather is rainy, the Show loses $15,000; if sunny, the Show makes a profit of $10,000. (NOTE: We assume all days are either rainy or sunny.) Walter has already put a $1,000 deposit down on the site, to reserve it – and this deposit (which is a separate matter from the previously mentioned possible loss or profit) will not get this deposit back whether the Dog Show is held or cancelled. Historical records show that rain has occurred on 25% of all July 10th dates over the last 100 years. To help in his decision making, Walter could get a custom forecast of the Cedar Rapids weather from Vick’s Weather Scope, a pay-by-the-forecast business. Vick’s forecasting accuracy is as follows: on days where it does rain, Vick has correctly forecast this weather 90% of the time; but on days where it’s sunny, Vick has correctly forecast this weather only 80% of the time. Part A (10%) – Ignoring entirely the possibility of buying a weather forecast from Vick’s Weather Scope, what is the expected value of perfect information (EVPI) in the decision scenario? (You must provide a properly drawn and analyzed – that is, “folded back” – decision tree – either done by hand or using the TreePlan software – as part of your answer.) Part B (10%) – What is the maximum amount Walter should be willing to pay Vick’s Weather Scope for a forecast – that is, the EVSI?
Explanation / Answer
Solution:
weather is rainy, the Show loses= $15,000
Sunny Weather Show makes a profit = $10,000
Esunny= (Probability of sunny * Profit)
= 0.75 * 10000 = $ 7500
Erain= (Probability of rain * losses)
=0.25 * (-15000) = $ -3750
Not knowing which direction the situation will go (only knowing the probability of the directions), we expect to make the most money with this.
Thus
EMV = $ 7500
Expectation for maximizing profit given the state of the market:
EV/PI= 0.75 * 10000 + 0.25 * 15000 = 7500 + 3750 =$ 11250
Hence
EVPI = 11250 -7500= $3750
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