This study contains several unique features that add to the literature documenting the health benefits of breastfeeding. The underlying theoretical framework for this study is the household economics model of Gary Becker. In particular, health production functions are specified and estimated. Data from the 1989 Brazilian National Health and Nutrition Survey are used to analyze the effects of breastfeeding on child morbidity (the absence of health). Binomial probit equations are estimated in which the dependent variable is whether the child required medical assistance during the previous two weeks for any of eight illness symptoms: fever, sore throat, loss of appetite, stomach ache, vomiting, diarrhea, respiratory problem, or a problem sleeping. The analysis is structured to be consistent with the WHO breastfeeding recommendations. For children 0-23 months, the impact of current breastfeeding on the need for medical care is analyzed and for infants 0-5 months, the effect of exclusive breastfeeding. Although the focus is on the impact of breastfeeding, the analysis is multivariate. Other possible determinants, which if excluded could bias the results, are included as additional explanatory variables. Several of the explanatory variables, including breastfeeding, are appropriately treated as endogenously determined and estimated with instrumental variables. Many studies end with a discussion of the econometric results. In this paper, the results of the probit analysis are used to simulate the possible reduction in the need for medical care if all children in Brazil were breastfed according to the WHO recommendations.