1. A household derives utility from the number of children n and consumption c according to the utility function Ulz,n.: =zan3( wherecr +3: 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 I = pun-+102 z a. 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 [3 gets larger)