3) Farmer Jones must determine whether to plant corn or wheat. If he plants corn

Question

3) Farmer Jones must determine whether to plant corn or wheat. If he plants corn and the weather is warm, he earns $8,000; if he plants corn and the weather is cold, he earns $5,000. If he plants wheat and the weather is warm, he earns $7,000; if he plants wheat and the weather is cold, he earns $6,500. In the past, 40% of all years have been cold and 60% have been warm. Before planting, Jones can pay $600 for an expert weather forecast. If the year is actually cold, there is a 90% chance that the forecaster will predict a cold year. If the year is actually warm, there is an 80% chance that the forecaster will predict a warm year. How can Jones maximize his expected profits? Also find EVSI and EVPI.

Explanation / Answer

Prob 0.6 0.4 Warm Cold EV Corn 8000 5000 6800 Wheat 7000 6500 6800 EVwoPI Best decision Correct info Before planting 8000 6500 7400 EVwPI For EVSI For Warm Accuracy 0.8 Prob 1 NPC Net Prob correct 0.8 0.2 P 0.6 BD Best decision 8000 5000 Evi (NPC*BD) 6400 1000 P*Sum(Evi) 4440 B For Cold Accuracy 0.9 Prob 1 NPC Net Prob correct 0.1 0.9 P 0.4 BD Best decision 7000 6500 Evi (NPC*BD) 700 5850 P*Sum(Evi) 2620 A EVwSI A+B 7060 EVwOSI 6800 EVSI=EVwSI-EVwoSI 260 So not advisable to pay 600 for service EVPI= EVwPI- EVwoPI 600

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