Question

1. 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 (yH ) and the subsidy-inclusive income of a low-wage worker (yL ) 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 (yH , yL ) that can occur in this economy.

2. Consider an economy like the one above, except that the wages paid in the high-wage industry fall as the number of workers in that industry rises. In particular, assume that each worker’s wage income is w H = 4 + 3/p where p is again the fraction of workers in that industry. The wage income of lowwage workers continues to be fixed at $4. Find all of the pairs (yH , yL ) that can occur in this economy.

Answer 1