Find all of the pairs that can occur in the economy

Question

Problem

Consider an economy in which there are two industries. The wage income of a worker in one industry is $10, while the wage income of a worker in the other industry is only $4. The government, however, imposes a tax of τ dollars on each high-wage worker and provides a subsidy of σ dollars to each low-wage worker in order to reduce the income differential. The government's tax revenue is equal to the cost of the subsidies

One-quarter of the workers are qualified to work only in the low-wage industry. The remaining workers are able to work in either industry. These workers choose to work in the high-wage industry if the difference between the after-tax income of a high-wage worker (y_H) and the subsidy-inclusive income of a low-wage worker (y_L) is more than $4. If this difference is less than $4, they will choose to work in the low-wage industry. If it is exactly $4, they do not care where they work, and any division of these workers between the two industries is possible.

Find all of the pairs (y_H , y_L ) that can occur in this economy.

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.