Consider once again the problem described in Worked-Out Problem 21.2 (page 767). Suppose the government taxes wages based on the amount of education a worker has received. For a worker receiving E years of education, the tax is
$5(E - 10) per hour worked
Thus, for a high-ability worker, the utility function becomes
UH(E, W) = W - 5E - 5(E - 10)
For a low-ability worker, the utility function becomes
UL(E, W) = W - 10E - 5(E - 10)
a. Find the most efficient separating equilibrium and compare it to the most efficient separating equilibrium with no tax. Are the high-ability workers better off or worse off? Do they obtain more or less education? What about low-ability workers?
b. Now suppose that high-ability and low-ability workers are equally numerous. The government distributes all revenue back to workers through lump-sum payments (so that no worker thinks her own decisions affect the amount received); every worker receives exactly the same amount. Are high-ability workers better off or worse off? What about low-ability workers? How do your answers change if high-ability workers outnumber low-ability workers? What if low-ability workers outnumber high-ability workers?