There are 100 workers in the economy and all must choose to work either a risky or safe job. Worker 1's reservation price for accepting the risky job is $1, worker 2's reservation price is $2, and so on. There are only 10 risky jobs available. What is the equilibrium wage differential between safe and risky jobs.
If the wage rate for non-risky is w, the wage rate for risky should be w+10.
To find the equilibrium wage differential between safe and risky jobs, we need to consider the reservation prices of the workers and the number of risky jobs available.
Given that there are 100 workers and 10 risky jobs, it's clear that not all workers who are willing to take a risky job will be able to find one. In this scenario, the equilibrium will be determined by the 10 workers with the lowest reservation prices who are willing to take a risky job.
Let's sort the workers based on their reservation prices:
Worker 1: Reservation price = $1
Worker 2: Reservation price = $2
Worker 3: Reservation price = $3
...
Worker 99: Reservation price = $99
Worker 100: Reservation price = $100
Since there are only 10 risky jobs available, only the first 10 workers (those with the lowest reservation prices) will be able to find and accept a risky job.
To determine the equilibrium wage differential, we need to compare the reservation prices of the 10th risky worker and the 11th risky worker (who is unable to find a risky job):
The 10th risky worker's reservation price = $10
The 11th risky worker's reservation price = $11
The difference between the reservation prices of these two workers represents the equilibrium wage differential between safe and risky jobs. In this case, the equilibrium wage differential is $11 - $10 = $1.
Therefore, the equilibrium wage differential between safe and risky jobs is $1.