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.

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

Data from problem (6a)

Discuss the capacity curve and explain why the curve has an initial segment in which work capacity exhibits increasing returns with respect to nutritional input. In Chapter 13, we will discuss the implications of this in more detail, but the following exercise will provide you with some advance intuition. Suppose that you need 8,000 units of work (in capacity units) to be performed, and you can hire all the laborers that you want. Assume that all income earned by the laborers is paid to them by you, and that all income is spent on nutrition. The capacity curve for each laborer is described as follows: for all payments up to $100, capacity is zero and then begins to rise by 2 units for every additional dollar paid. This happens until an income of $500 is paid out. Thereafter, an additional dollar paid out increase's capacity by only 1.1 units, until total income paid is $1,000. At this point additional payments have no effect on work capacity.

(a) Assume that you would like to get your work done at minimum cost. Describe how many laborers you would hire to get your work done and how much you would pay each of them.