1. A household derives utility from the number of children n and consumption c according to the utility function U(z, n) = z?n? (?here? + ? = 1) The income of the household is Y and the price of children is pn. With the price of consumption set equal to one the household's budget constraint is a. I = Pnn + PzZ Calculate the utility maximizing demand for children as a function of income and prices. b. How does the demand for children change as I increases in this model? c. How would the demand for children change as preferences for children increase (that is, as gets larger)?