Consider a quantity-quality fertility choice model where parents have preferences:

c + _n*ln(n) + _q*ln(s)

over consumption c, number of children n, and their children's education s (i.e., assume q = s). Assume that _n > _q. Further assume only one parent works at wage w. There is a financial cost of education and a time cost of raising children. The parent's budget constraint is:

c + sn = w(1 bn).

• (a)Write down and solve the parents' maximization problem. (Note that this is a maximization
• in two variables!)
• (b)Suppose the preference for children, _n, increases. How does this affect the number of
• children, n, and the education input, s?
• (c)Suppose the wage, w, increases. How does this affect the number of children, n, and the
• education input, s?
• (d)Explain the term "quality-quantity trade-off" (in the context of fertility choice). Is there a
• quality-quantity trade-off at play in this model?