Question

Consider the market for workers to glue together foam cushions for chairs and couches sold under high-end furniture brands. During this manufacturing process, workers are typically exposed to fumes from the glue. The chemical they handle — known as n-propyl bromide, or nPB causes neurological damage and infertility when inhaled at low levels over long periods of time.
However, firms that have installed expensive air purification systems are able to eliminate fumes from the glue inside the plants. Suppose that 50 of these pillow-manufacturing jobs exist in firms with air purification systems, while the other 150 of these jobs are in firms without air purification systems. Assume that the number of firms without air purification systems is fixed. Thus, the demand for workers in jobs with impure air is perfectly inelastic.
Assume that there are 200 workers who need to find jobs in this market (western foothills of North Carolina). The workers preferences are uniformly distributed between 11 cents and 2 dollars 10 cents such that Worker 1’s reservation wage (?w) for accepting a job with impure air is 11 cents; worker 2’s reservation price is 12 cents; worker 3’s reservation price is 13 cents and so on.   
a.   Draw the supply curve to jobs with impure air labeling as many points as you can.

b.   Draw the demand curve for jobs with impure air labeling as many points as you can.

c.   Find the equilibrium wage differential between jobs with impure and pure air. What is the interpretation of this equilibrium wage differential? Draw this equilibrium labeling as many points as you can.

d.   Which workers will be employed at firms with impure air? What is their average reservation wage for accepting a job with impure air?

e.   Which workers will be employed at firms with pure air? What is their average reservation wage (?w) for accepting a job with impure

f.   Suppose the above New York Times article, which stresses the hazards associated to exposure to this dangerous chemical, changes the attitudes of the work force toward being employed in firms with impure air. Worker 1 now has a reservation price of 41 cents; worker 2’s reservation price is 42 cents; worker 3’s reservation price is 43 cents, and so on. As before, there are 150 jobs in firms without air purification systems, and this number is fixed. Thus, the demand for workers in jobs with impure air is perfectly inelastic. Find the new equilibrium wage differential between safe and risky jobs. Draw this equilibrium labeling as many points as you can.

g.   Suppose now that the Occupational Safety and Health Administration (OSHA) forced additional firms to install air purification systems, bringing the number of jobs in firms without air purification systems down to 90. Find the new equilibrium wage differential between pure and impure air jobs. Draw this equilibrium, labeling as many points as you can.

Answer 1

Because of the type of industry firms face upward sloping supply curve of labore, where firms must pay higher wages in order to attract more workers. And each wage rate paid to hire an additional worker is its reservation wage rate.

1. A firm may be perfectly discriminating, where it would pay differently to differently workers. for eg, in hiring 1st labour the firm will pay 11 cents and for hiring of 2nd labor it would pay 12 cents to the 2nd labour. thus, the marginal cost of hiring is identical to the supply curve of hiring. For such condition, the graph is given below:

Here the supply curve shows that at 11 cent 1st worker is supplied (available to the industry) and at 210 cents that is 2 dollars and 10 cents 200th worker is available to the market.

2. Demand curve is perfectly inelastic as the demand is fixed at 150 labours hence the demand curve would be: