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In these three essays collectively entitled "Essays on Externalities and Agriculture in the United States and Brazil", I discuss three topics. In the first essay, I review the economic literature on diversification in farming systems and comment on the economic incentives and disincentives for diversification in 21st century agriculture. In the second essay, I focus on deforestation in Brazil, which is an externality associated with the expansion of agricultural production at forest frontiers. Using a natural experiment (changes in international Foot-and-Mouth Disease certification), I identify the portion of annual deforestation that can be attributed to changes in disease status, and suggest that the mechanism for new deforestation may be due to increased prices when beef is considered to be safe for export. In my third essay, I discuss the production economics behind the use of sub-therapeutic antibiotics in U.S. pork and poultry production, and comment in detail on the potential for heterogeneity in the returns to antibiotic use (and costs of regulation). A more detailed summary of each essay follows.Chapter 1: Economic Factors Affecting Diversified Farming SystemsIn response to a shift toward specialization and mechanization during the 20th century, there has been momentum on the part of a vocal contingent of consumers, producers, researchers, and policy makers who call for a transition toward a new model of agriculture. This model employs fewer synthetic inputs, incorporates practices which enhance biodiversity and environmental services at local, regional, and global scales, and takes into account the social implications of production practices, market dynamics, and product mixes. Within this vision, diversified farming systems (DFS) have emerged as a model that incorporates functional biodiversity at multiple temporal and spatial scales to maintain ecosystem services critical to agricultural production. This essay's aim is to provide an economists' perspective on the factors which make diversified farming systems (DFS) economically attractive, or not-so-attractive, to farmers, and to discuss the potential for and roadblocks to widespread adoption. The essay focuses on how a range of existing and emerging factors drive profitability and adoption of DFS, and suggests that, in order for DFS to thrive, a number of structural changes are needed. These include: 1) public and private investment in the development of low-cost, practical technologies that reduce the costs of production in DFS, 2) support for and coordination of evolving markets for ecosystem services and products from DFS and 3) the elimination of subsidies and crop insurance programs that perpetuate the unsustainable production of staple crops. This work suggests that subsidies and funding be directed, instead, toward points 1) and 2), as well as toward incentives for consumption of nutritious food. Chapter 2: Foot-and-Mouth Disease and Deforestation in the Brazilian AmazonDeforestation in the Brazilian Amazon released approximately 5.7 billion tons of CO2 to the atmosphere between 2000 and 2010, and 50-80% of this deforestation was for pasture. Most assume that increasing demand for cattle products produced in Brazil caused this deforestation, but the empirical work to-date on cattle documents only correlations between cattle herd size, pasture expansion, cattle prices, and deforestation. This essay uses panel data on deforestation and Foot-and-Mouth Disease (FMD) status--an exogenous demand shifter--to estimate whether changes in FMD status caused new deforestation in municipalities in the Brazilian Amazon and cerrado biomes during the 2000-2010 period. Becoming certified as FMD-free caused annual deforestation to be 42% to 85% higher than deforestation rates in infected municipalities, on average, during the 2000-2010 period. Chapter 3: Potential for heterogeneity in the returns to sub-therapeutic antibiotics in U.S. pork and poultry operationsEach year, more than 50,000 people in the U.S. die from hospital-acquired bacterial infections, millions experience episodes of foodborne illness, and reported cases of "superbugs" such as Methicillin-resistant Staphylococcus aureus (MRSA) and vancomycin-resistant enterococci (VRE) are on the rise. For those who acquire a resistant infection in their food, in their community, or in a hospital, resistance is associated with a longer duration of treatment, the use of more potent antibiotics, and longer hospital stays. This, in turn, means increased health care costs and costs to society due to antibiotic-resistant infections. Antibiotic resistance is contributing to the scope and severity of this health care crisis, and at least some of the responsibility for antibiotic resistance sits on the shoulders of industrial livestock production. In livestock operations, low or sub-therapeutic doses of antibiotics (STAs) are used to promote growth, in addition to their use to prevent and control disease. Today, more antibiotics are used in livestock production and the production of milk and eggs than in humans. While the use of sub-therapeutic doses of antibiotics is regulated less stringently in the United States than in the European Union, there is movement toward and potential for such regulation. Beginning in the 1970s, economic researchers began to study the potential impacts of bans on the use of sub-therapeutic antibiotics on the pork, poultry, and beef sectors and on U.S. consumers, but there has been little study of how heterogeneity impacts antibiotic use, and in turn, how it impacts returns to using antibiotics in U.S. livestock operations. I concentrate on U.S. pork and poultry operations since they are the largest users of sub-therapeutic antibiotics by volume in the U.S., and explore the existing literature on the economics of sub-therapeutic antibiotic use for glimpses of heterogeneity in the returns to antibiotic use. Perhaps the most interesting source of heterogeneity in returns to antibiotic use may be heterogeneity in management and/or the use of potential substitutes for antibiotics, such as improved sanitation practices and more modern facilities. Productivity and use of technologies that substitute for STA use vary amongst producers, and likely by region and farm size. Thus, the marginal abatement costs of reducing STA use vary across industries, producers, production systems, and regions.