1. Consider a household utility U(XP , XC) = X^0.5 P X^0.5 C, where XP is parent's home production and XC is children's home production. Assume the wife spends hw hours at work, and the husband spends hh hours working with hourly wage ww, and wh. And the child does not work. (i.e. Time spends on home production for wife and husband are denoted by tw, and th). Assume that XP is produced directly by YP, where YP is the parent's consumption of goods. And XC is produced by YCt^0.5 h*t^0.5 w, where YC is the goods used in a child's home production.

(a) Please write down the household's budget constraint.

(b) Please write down the time constraints this household is facing (Assume wife and husband both have total time =1 for each of them.)