This chapter by Gary S. Becker and H. Gregg Lewis discusses the interaction between the quantity and quality of children in the context of family economics. They argue that the relationship between the number of children and their quality is not merely a negative correlation but is influenced by the shadow prices of children with respect to their number and quality. The shadow price of children with respect to their number increases as their quality increases, and the shadow price with respect to quality increases as the number of children increases. This suggests that higher quality children are more expensive to produce when there are more children, and higher quantity children are more expensive when they are of higher quality.
The authors analyze the economic implications of this interaction, focusing on income and price effects. They show that observed income elasticities for quantity and quality may differ from true elasticities due to the way income is measured and the substitution effects between different commodities. They also demonstrate that price effects can lead to different outcomes, with quantity elasticities often being more significant than quality elasticities in price changes.
The analysis is based on a utility function that incorporates the number of children, their quality, and the consumption of other goods. The authors use a budget constraint to derive the first-order conditions for maximizing utility, showing how changes in income and prices affect the demand for children and their quality. They also discuss the implications of these findings for understanding fertility data and the broader interaction between quantity and quality in various goods and services. The chapter concludes that the relationship between quantity and quality is not special but is a result of the way shadow prices and substitution effects operate in household production.This chapter by Gary S. Becker and H. Gregg Lewis discusses the interaction between the quantity and quality of children in the context of family economics. They argue that the relationship between the number of children and their quality is not merely a negative correlation but is influenced by the shadow prices of children with respect to their number and quality. The shadow price of children with respect to their number increases as their quality increases, and the shadow price with respect to quality increases as the number of children increases. This suggests that higher quality children are more expensive to produce when there are more children, and higher quantity children are more expensive when they are of higher quality.
The authors analyze the economic implications of this interaction, focusing on income and price effects. They show that observed income elasticities for quantity and quality may differ from true elasticities due to the way income is measured and the substitution effects between different commodities. They also demonstrate that price effects can lead to different outcomes, with quantity elasticities often being more significant than quality elasticities in price changes.
The analysis is based on a utility function that incorporates the number of children, their quality, and the consumption of other goods. The authors use a budget constraint to derive the first-order conditions for maximizing utility, showing how changes in income and prices affect the demand for children and their quality. They also discuss the implications of these findings for understanding fertility data and the broader interaction between quantity and quality in various goods and services. The chapter concludes that the relationship between quantity and quality is not special but is a result of the way shadow prices and substitution effects operate in household production.