The study of parental resource allocation to children with different endowments is based on two seminal models. The first model was proposed Becker and Tomes (1976, 1986), and the second one is an extension of the first model developed by Cunha and Heckman (2007, 2008). In an early paper, Becker and Lewis (1973) assume that each household has a utility function and seeks to maximize it subject to a budget. They defined the household’s utility function as follows: a simple utility functionWhere is the number of children, their quality, and is the rate of consumption of all other commodities. By saying the child quality, authors identified it with the amount and time invested by parents in a child
A simple budget constraint: Where is full income, is the price of and is the price of .