A farmer may choose to plant one of the following crops. The profit of the crops

Question

A farmer may choose to plant one of the following crops. The profit of the crops depends on the amount of rainfall according to the following:

Rainfall

Crop A

Crop B

Normal

8,968

3,245

Light

2,341

6,176

The only two rainfall outcomes are Normal and Light. The farmer estimates the chance of Normal rainfall is 0.73. Calculate the maximum price the farmer is willing to pay today for a perfectly accurate forecast (i.e the farmer experiences normal rainfall every time the forecast predicts normal rainfall)? Round you answer to one decimal place.

Rainfall

Crop A

Crop B

Normal

8,968

3,245

Light

2,341

6,176

Explanation / Answer

As the forecast for rainfall is normal, the total profit of Crop A and Crop B is

=8968+3245

=$12,213

So with the accuracy of 0.73, the maximum farmer is willing to pay is 0.73*12213 = $8915.49

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