1. A household derives utility from the number of children n and consumption c according to the utility ftmction Mam) = sang (where I: + 3'3 = 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=pnn+pzz Calculate the utility maximizing demand for children as a function of income and prices. 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 f!- gets larger)? Fr!\" Now replace 1 with Y+L*w, where Y is male income, L*w is female wage income, and L=T- k*n. T is the total number of hours in the clay and kfn is the total amount of time that women spend raising their 11 children. d. Rearrange terms to get a new price of children, p..*, which includes both explicit and opporhmity costs of children. How does this price vary with the woman's wage?I e. Now nd the household's demand for children as a flmction of this new price, pn". (Hint: You may substitute p,,* for p11 and Y+Tw for I if you don't want to explicitly re- solve the problem.) How does the demand for children vary with w now? 1Why do we sayr that the effect of a female wage increase on fertility is ambiguous