Consider a married couple with utility function

c + ln(n)

over consumption c and number of children n. Husband and wife each have one unit of time. Raising one child takes fraction b of one parent's time and comes with financial costs given by d. Suppose it is optimal for the husband to specialize in market production and work full time and for the wife split up her time between work and child care. The couple's budget constraint is:

c+dn = (1bn)*w_f +w_m

(a) Solve the couple's maximization problem. Provide the first order condition of the maximization problem and the optimal number of children, n . You do not need to provide the details of how you have arrived at your solution!

• (b)How does fertility depend on the husband's wage, w_m?
• (c)How does fertility depend on the wife's wage, w_f ? Is it unambiguous whether wf increases
• or decreases fertility?
• (d)Explain the intuition for the effects of wife's and husband's wage on fertility in terms of income and substitution effects.