Question

This question considers aspects of calculating the value of a statistical life.

1. Suppose there are two jobs in the economy: farmer and coal miner. Farming firms (which are all identical) can produce a safer work environment more cheaply than coal mining firms (which are all identical). Show how the isoprofit curves of these two firm types compare (in a graph with risk of death (d) on the X-axis and wages (w) on the Y-axis).

2. Suppose initially that all workers in the economy have the same preferences (i.e. they have the same indifference curves). In equilibrium, farmers get paid $50,000 a year and have a probability of death of 1 in 10,000. Coal miners get paid $52,000 and have a probability of death of 1 in 5,000. Show this equilibrium on a graph (hint: since all workers have the same preferences, what must be true in order for some workers to choose to be farmers but others choose to be coal miners?).

3. In this economy, how much are individuals willing to pay to lower their probability of death on the job by 1 in 10,000? What is the value of a statistical life (VSL)?

4. Now imagine that instead of all workers having the same preferences, there are 2 types of workers: those who hate risk a lot (type A) and those who don’t mind risk as much (type B). On a new graph, show how the indifference curves compare for the two types of individuals.

5. With the 2 types of workers, suppose the equilibrium is still at the same wages (w) and risk of death (d) for farmers and coal miners as in Part #2. Show the equilibrium on a graph. Which type of firm employs type A workers? Which type employs type B workers? How do you know? 1

6. Given the different preferences of type A and type B workers, how does the VSL of those who become farmers compare to what you found in Part #3 (i.e. is it bigger or smaller)? How does the VSL of those who become coal miners compare to what you found in Part #3? Briefly explain.

Answer 1

Answer 1:

Answer 2:

Answer 3: Let's say the society has 100,000 tax payers and each tax payer is ready to pay $200 annually as tax to make it less risky for the workers in the working environment.

$200 x 100,000 = $20,000,000 which can be used to minimize the risk of death of 1 in 10000 workers

Hence the VSL can be approximated to $20 m.

Answer 4:

Answer 5:

Justification : The Farming firm employs the Type A workers mainly since the risk of death is less as compared to the type B workers who are employed by Coal mining Firms. The Type B workers tend to mind the risk less than type A(who hate risk a lot).

The above graph explains how the type A and type B workers compare with their wages and risks of Death.

Answer 6: What we derived in part # 3 was considering the fact that the need to lower the probability of death was 1 in 10,000 , here if we examine the risk of death of farmers which is again the same 1 in 10000, the value of statistical life of a farmer would be the same as derived in part 3. However, the VSL of a coal miner will be more than that of a farmer since the VSL depends on the wages also to an extent and is also derived based on the the risk of injury or death which is higher (2 times) the death risk of a farmer. So the VSL will be more in case of a coal miner.