Farming Firms

QSuppose 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 iso profit 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.

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