There are two types of farming tractors on the market, the FT250 and the FT500.

Question

There are two types of farming tractors on the market, the FT250 and the FT500. The only difference between the two is that the FT250 is more prone to accidents than the FT500. Over their lifetime, 1 in 10 FT250s is expected to result in an accident, as compared to 1 in 25 FT500s. Further, 1 in 1,000 FT250s is expected to result in a fatal accident, as compared to only 1 in 5,000 FT500s. The FT250 sells for $125,000 while the FT500 sells for $137,000. At these prices, 2,000 of each model are purchased each year. What is the statistical value farmers place on avoiding a tractor accident? What is the statistical value of a life of a farmer?

Explanation / Answer

Extra cost paid for FT500 = $137000 - $125000 = $12000

Farmers are willing to pay $24 million ($12000 * 2000 units) in exchange for 200 - 80 i.e. 120 accidents.
Thus, value placed on each accident = $24 million / 120 accidents = $200,000

Farmers are willing to pay $24 million ($12000 * 2000 units) in exchange for 2 - 0.40 i.e. 1.60 fatal accidents.
Thus, value placed on each life = $24 million / 1.60 fatal accidents = $15 millions

FT250 FT500 Accident Rate 1 in 10
i.e. 10% 1 in 25
i.e. 4% Fatal Accident Rate 1 in 1000
i.e. 0.10% 1 in 5000
i.e. 0.02% Cost $125,000 $137,000 Total units sold           2,000           2,000

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