Consider the same capacity curve as in problem (6a). Suppose that a family of five members each have this capacity curve. Assume that this family has access to a source of nonlabor income, valued at $400. Assume furthermore that each unit of capacity can fetch an income of 50 cents, and that all income is spent on nutrition. We are going to examine the division of income among the family members.

a) Show that if all nonlabor income is divided equally among the family members, then no one will be able to sustain any work capacity so that labor income will be zero.

Find allocations of the nonlabor income that give rise to positive wage income. Compare and contrast these allocations with equal division allocation, using various criteria (including Pareto-optimality).