Question

The Environmental Protection Agency (EPA) wants to investigate the value workers place on being able to work in “clean” mines over “dirty” mines.  The EPA conducts a study and finds the average annual wage in clean mines to be $42,250 and the average annual salary in dirty mines to be $47,250.  If the probability of fatal lung disease after 10 years of work in a dirty mine is 3%, and is 1% in the clean mine, what is the statistical value of a life, reflected in the compensating differential?  Note: the wage differential should be calculated over ten years.

Answer 1

This is a very interesting question and is a type of a primary question that you answer when you start understanding the concept of Statistical Value of life.

Solution:

We have been given that there is a wage difference of $5,000 ($47,250 - $42,250) between a dirty mine and a clean mine worker's salary.

Now we will assume here that the difference in wages is due to the difference in the working condition in the two mines and that the higher paying job (in our case a dirty mine worker job) is to compensate for the increased life threat.

We also know exactly the "danger" of working in the dirty mine compared to the danger of working in the clean mine and it is 2% (3%-1%), meaning you are 2 percentage-points more at risk when you work in a dirty mine than when you work in a clean mine.

So, therefore we are being compensated $5,000 more for the 2% extra "danger" than we put in, or in other words we are being given $5,000/2% "extra" compensation for every percetange-point increase in danger. Thus our SVL should come out to be equal to $5,000/2% = $250,000.