Respuesta :
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:
[tex]\Delta P=125,000-137,000=-12,000[/tex]
The expected non-fatal accidents for each tractor is
[tex]FT500\rightarrow 1/10=0.1\\\\FT250 \rightarrow 1/25=0.04[/tex]
The difference in expected non-fatal accidents is:
[tex]\Delta NFA = 0.10-0.04=0.06[/tex]
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:
[tex]V_{NFA}=\frac{-\Delta P}{\Delta NFA} =\frac{12,000}{0.06} =200,000[/tex]
The expected fatal accidents for each tractor is
[tex]FT500\rightarrow 1/1,000=0.0010\\\\FT250 \rightarrow 1/5,000=0.0002[/tex]
The difference in expected fatal accidents is:
[tex]\Delta NFA = 0.0010-0.0002=0.0008[/tex]
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:
[tex]V_{FA}=\frac{-\Delta P}{\Delta FA} =\frac{12,000}{0.0008} =15,000,000[/tex]
