What is the value of a worker's life if her compensating differential is $20,000 for a job that has a 2% higher risk of death each year?

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BlackTom AI · Accepted Answer

We’re given a compensating differential of $20,000 for a job that carries a 2% higher risk of death each year. To translate a risk premium into a value of life, we use the relation VSL = compensating differential / change in risk.

Step 1: Identify the two numbers involved. The extra pay is $20,000, and the incremental annual risk is 2%, which is 0.02 in decimal form.

Step 2: Compute the ratio. Divide the monetary compensation by the additional risk: $20,000 ÷ 0.02 = $1,000,000.

Step 3: Interpret the result. The implied value of a statistical life (VSL) from these numbers is $1,000,000. This means society would be willing to pay up to about $1 million to reduce the annual risk of death by 1 unit (i.e., by 100%).

Now consider the other options:
- $19,608: This would correspond to a very small implied risk change, since $19,608 ÷ 0.02 ≈ $980,400, which is not the given $20,000 compensation. It also doesn’t align with a straightforward division of 20,000 by 0.02.
- $20,400: If you divide $20,400 by 0.02, you get $1,020,000, not the stated $20,000 compensation, so it mismatches the given data.
- $1 million: This matches the direct calculation from $20,000 ÷ 0.02, providing a clean and conventional value of a statistical life implied by the problem.
- $20 million: Dividing this by 0.02 would yield $1,000,000,000 (one billion), which is far larger than the given compensating differential and would imply an unrealistically high valuation relative to the data provided.

In summary, the straightforward application of the VSL formula using the provided numbers yields $1,000,000, aligning with the concept of valuing a life at roughly a million dollars in this setup.

AS.440.661.50.SP25 Module 3 Problem Set

What is the value of a worker's life if her compensating differential is $20,000 for a job that has a 2% higher risk of death each year?

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