This dissertation is to study the competition of biofuels to meet the U.S. renewable fuels standards (RFS) and its impact on biofuel and corn prices, and the impacts of weather and soil moisture on corn yield in the Midwest. Chapter 2 illustrates the hierarchical competition of U.S. corn ethanol, Brazilian sugarcane ethanol and biodiesel to meet the RFS mandates and explained the evidenced two-way trade of ethanol between the U.S. and Brazil using a computable trade model of ethanol related markets between the U.S. and Brazil. And we estimate the impact of RFS on biofuel prices, agricultural commodity prices using a stochastic partial equilibrium model. Chapter 3 develops a linear spline fixed effect model to estimate the impact of climate variables on corn yield by adding in soil moisture as an explanatory variable. Recent two drought years 2011 and 2012 are included that facilitates estimation of corn yield response to extreme conditions. Daily soil moisture data in the Upper Mississippi River Basin Area from 1980 to 2012 is simulated from the crop model EPIC, which has very comprehensive interactions between hydrology, weather, soil, crop and plant environment controls. Bayesian Markov Chain Monte Carlo approach is applied to estimate the parameters and the thresholds simultaneously. Including recent two drought years 2011 and 2012 to have more drought observations in the modern eras, Chapter 4 revisits previous literature using the our extended data and then constructs yield response functions allowing the yield deviation from weather variables to change over time. Null hypotheses that the marginal and total weather impacts of adverse weather conditions remain constant are then tested.