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Suppose there are 100 workers in the economy in which all workers must choose to work a risky or a safe job
Suppose there are 100 workers in the economy in which all workers must choose to work a risky or a safe job. Worker 1's reservation price for accepting the risky job is $1; Worker 2's reservation price is $2, and so on. Because of technological reasons, there are only 10 risky jobs and the demand for risky jobs is completely inelastic. Suppose the wage paid for the safe job is $8 per worker.
a) How much will the firm have to pay to have 10 workers take the risky jobs? What is compensation wage differential?
b) Suppose now that an advertising campaign, paid for by the employers who offer risky jobs, stresses the excitement associated with the "thrill of injury," and this campaign changes the attitudes of the work force toward being employed in a risky job. Worker 1 now has a reservation price of -$10 (that is, she is willing to pay $10 for the right to work in the risky job); Worker 2's reservation price is -$9, and so on. There are still only 10 risky jobs. What is the new compensating wage differential?
Expert Solution
a. The firm has to pay $10 to have 10 workers, and the compensation differential is $2.
A worker is willing to worker only if the wage is higher than her reservation wage. To induce 10 workers to work, the firm must offer a wage such that the worker 10 is willing to worker (and we know worker 1 - 9 will also be willing to work because they have a lower reservation wage). Since the worker 10 has a reservation of 10, the wage must be at least 10.
The compensation differential = wage for risky job - wage for safe job = 10 - 8 = 2.
b. Given the new reservation wage, the firm can offer $0 wage and 10 workers will be willing to worker, and the 10th worker has a reservation wage that is exactly 0. In this case, the new compensation differential = 0 - 8 = $-8.
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