Exercise 12.9 Demand for Children. Consider the utility maximization problem of a parent who lives for two periods and must make a fertility decision. The parent '5 utility function is given by: 11 (Chi-1+1) z 109 (at) + 5106(Ct+1) - where c; and ct.\" denote the parent '3 consumption in each period of life. Suppose that the parent is endowed with to; units of the production good in period t. He can use his production to consume in period t or to miss children. Let n denote the number of children in the family and let y; denote the subsistence consumption of each child in period t. In old age -period 2 of the parent 's life the parent receives an endowment equal to tag\