This chapter, "Interaction between Quantity and Quality of Children," by Gary S. Becker and H. Gregg Lewis, explores the relationship between the number of children (quantity) and their perceived quality. The authors argue that the negative correlation between quantity and quality observed in data can be understood without assuming a strong substitution effect in the utility function or household production. Instead, they focus on the shadow prices of children, which are higher for higher-quality children and for more children. This leads to the conclusion that increasing the number of children or their quality can be more expensive, depending on the current level of the other variable. The chapter discusses the implications of these shadow prices for income and price effects. It shows that observed income elasticities of demand for quantity and quality are generally smaller than true elasticities due to the downward bias caused by changes in shadow prices. For example, an increase in income can lead to a decrease in quantity if the shadow price of quantity rises more than the shadow price of quality. Similarly, price effects, such as those from improvements in contraceptive technology or wage rates, can lead to a decrease in quantity and an increase in quality. The authors also derive the observed income and price elasticities for quantity and quality, showing that the observed price elasticity of quantity exceeds that of quality, which is the opposite of what would be expected if quantity and quality were perfectly substitutable. This finding is consistent with empirical observations that improvements in birth control knowledge and wage rates lead to a decrease in the number of children and an increase in their quality.This chapter, "Interaction between Quantity and Quality of Children," by Gary S. Becker and H. Gregg Lewis, explores the relationship between the number of children (quantity) and their perceived quality. The authors argue that the negative correlation between quantity and quality observed in data can be understood without assuming a strong substitution effect in the utility function or household production. Instead, they focus on the shadow prices of children, which are higher for higher-quality children and for more children. This leads to the conclusion that increasing the number of children or their quality can be more expensive, depending on the current level of the other variable. The chapter discusses the implications of these shadow prices for income and price effects. It shows that observed income elasticities of demand for quantity and quality are generally smaller than true elasticities due to the downward bias caused by changes in shadow prices. For example, an increase in income can lead to a decrease in quantity if the shadow price of quantity rises more than the shadow price of quality. Similarly, price effects, such as those from improvements in contraceptive technology or wage rates, can lead to a decrease in quantity and an increase in quality. The authors also derive the observed income and price elasticities for quantity and quality, showing that the observed price elasticity of quantity exceeds that of quality, which is the opposite of what would be expected if quantity and quality were perfectly substitutable. This finding is consistent with empirical observations that improvements in birth control knowledge and wage rates lead to a decrease in the number of children and an increase in their quality.