(a) We showed that with a large supply of labor (and with no long-term storage or borrowing effects), the equilibrium piece rate settles at the level where the line describing the piece rate is tangent to the capacity curve. Explain why this is the case.

(b) To help you understand how piece rates work in this market, begin with the situation described in the previous paragraph. Now imagine that all the laborers are given a small amount of nonlabor income. Using a diagram, show that the relationship between wage income and total capacity is affected as a result. Now with the same total amount of labor, try to predict what will happen to the new equilibrium piece rate. Show carefully that it must fall.

(c) Prove that if there is unemployment both before and after the change in nonlabor income, the total income (not just the labor income) of employed labor must fall as well. What gives rise to this paradoxical result?

(d) Compare the result in(c) with the observation (see text) that if there is a mix of some people with nonlabor income and some people without nonlabor income, then the individuals with nonlabor income will always do better than the individuals with no such income.