Abstract: The purpose of this study was to improve the understanding of the economic relationships between landowner and sharecropper in the semi-arid region of Northeastern Brazil. The specific objectives were, for small and sharecropper farms, to determine (a) the risk associated with different enterprise combinations; (b) an efficient set of farm plans for three different farm sizes which minimize income variance for given levels of expected income; (c) the effects of changes in sharecropping conditions, dropping cotton production, changes in cotton prices, and reductions in credit availability on employment, enterprise combinations, output, incomes, and risk. The municípios (counties) of Caicó and Florânia in the State of Rio Grande do Norte were selected as the study area because of their representative characteristics of the semi-arid region. Most of the primary data used were taken from a random sample of farms conducted in 1973/7974 by the SUDENE/World Bank Project. Linear and quadratic programming models were used to estimate minimum risk (income variance) for given levels of income for each farm size and for the sharecropper unit. The programming models accounted for major relationships between sharecroppers and landowners such as production activities on owner-operated and sharecropped parts of the farm, sharecropper's share of production, market margin on sharecroppers'production, sharecropper labor ("sujeição" labor), and sharecropper consumption. A sharecropper sub-model was developed and its optimized results were introduced as activities in the medium and large farm models. The basic assumption underlying the models was that the sharecropper has some decision-making power within the framework of the sharecropper contract. The major result of the study was that opportunities for increasing incomes and reducing risks by reallocating existing resources are very limited. Thus, there is a need for major research efforts to develop new opportunities. Dissertation Discovery Company and University of Florida are dedicated to making scholarly works more discoverable and accessible throughout the world. This dissertation, "Economics of Small and Sharecropper Farms Under Risk in the Sertao of Northeastern Brazil" by Léo da Rocha. Ferreira, was obtained from University of Florida and is being sold with permission from the author. A digital copy of this work may also be found in the university's institutional repository, IR@UF. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation.