The agriculture industry plays a critical role in the U.S. economy and various industry sectors depend on the output of farms. To protect and raise farmers' income, the U.S. government offers two subsidy programs to farmers: the Price Loss Coverage (PLC) program which pays farmers a subsidy when the market price falls below a reference price, and the Agriculture Risk Coverage (ARC) program which is triggered when farmers' revenue is below a threshold. Given the unique features of PLC and ARC, we develop models to analyze their impacts on consumers, farmers, and the government. Our analysis generates several insights. First, while PLC always motivates farmers to plant more acres compared to the no-subsidy case, farmers may plant less acres under ARC, leading to a lower crop supply. Second, despite the prevailing intuition that ARC generally dominates PLC, we show that both farmers and consumers may be better off under PLC for a large range of parameter values, even when the reference price represents the historical average market price. Third, the subsidy that increases consumer surplus results in higher government expenditure. Finally, we calibrate our model with USDA data and provide insights about the effects of crop and market characteristics on the relative performance of PLC and ARC. We provide guidelines to farmers for enrolling crops in the subsidy programs, and show that our guidelines are supported by farmers' enrollment statistics. We also show that if the economic and political frictions caused by running the subsidy programs is significant, the subsidy that benefits both consumers and farmers may actually result in lower social welfare.