1.A household derives utility from the number of children n and consumption c according to the utility function

U (z,n)=z^a n^b (where a+b=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=Pn(n)+Pz(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 gets larger)?

Now replace I 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 day and k*n is the total amount of time that women spend raising their n children.

d.Rearrange terms to get a new price of children, p_n*, which includes both explicit and opportunity costs of children.How does this price vary with the woman's wage?

e.Now find the household's demand for children as a function of this new price, pn*.(Hint: You may substitute p_n* for p_nand 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?Why do we say that the effect of a female wage increase on fertility is ambiguous?