Hidden information problems in the design of family allowances

We consider a case where some of the parents have higher ability to raise children than others. First-best policy gives both types of parents the same level of utility. If parental actions are not fully observable, however, the policy maker has to take into account the incentive-compatibility constraint that more able parents should not find it profitable to misrepresent their true ability by investing less in their children, and having a lower number of children. The second-best policy induces more able parents to have the first-best number of children, and to invest in each child at the first-best level. Less able parents are induced to have fewer children than in first best, and will underinvest in each child. Whether the government should subsidize more the more able parents, or the less able ones, depends on the properties of the cost function. In second best, however, less able parents will end up with lower utility than more able parents whatever the cost function.