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 value of a statistical life of a farmer? g

Answer 1

Answer:

The statistical value farmers place on avoiding a tractor accident is $200,000.

The statistical value farmers place on avoiding a tractor fatal accident is $15,000,000.

Step-by-step explanation:

We have two tractors, with different probabilities of non-fatal and fatal accidents, and also different prices.

We will use this price difference to estimate how it is valued a non-fatal and fatal accident.

The difference in prices is:

$\Delta P=125,000-137,000=-12,000$

The expected non-fatal accidents for each tractor is

$FT500\rightarrow 1/10=0.1\\\\FT250 \rightarrow 1/25=0.04$

The difference in expected non-fatal accidents is:

$\Delta NFA = 0.10-0.04=0.06$

For a 6% more chance of having an accident, the farmers discounts 12,000 for the price of the less safe of the tractors.

Then, we can calculate the statistical value farmes place on avoiding a tractor accident as:

$V_{NFA}=\frac{-\Delta P}{\Delta NFA} =\frac{12,000}{0.06} =200,000$

The expected fatal accidents for each tractor is

$FT500\rightarrow 1/1,000=0.0010\\\\FT250 \rightarrow 1/5,000=0.0002$

The difference in expected fatal accidents is:

$\Delta NFA = 0.0010-0.0002=0.0008$

For a 0.08% more chance of having an fatal accident, the farmers discounts 12,000 for the price of the less safe of the tractors.

Then, we can calculate the statistical value farmes place on avoiding a tractor accident as:

$V_{FA}=\frac{-\Delta P}{\Delta FA} =\frac{12,000}{0.0008} =15,000,000$