This study was conducted within the context of providing an improved understanding of New Mexico’s food, energy, water systems (FEWS) and their behavior under variable climate and socioeconomic conditions. The goal of this paper was to characterize the relationships between production and prices of some forage crops (hay, grain sorghum, and corn) that can be used as feed supplements for beef cattle production and the potential impacts from a changing climate (precipitation, temperature) and energy inputs (crude oil production and prices). The analysis was based on 60 years of data (1958–2017) using generalized autoregressive conditional heteroscedasticity models. Hay production showed a declining trend since 2000 and in 2017, it dropped by ~33% compared to that of 2000. Crude oil production (R2 = 0.83) and beef cattle population (R2 = 0.85) were negatively correlated with hay production. A moderate declining trend in mean annual hay prices was also observed. Mean annual range conditions (R2 = 0.60) was negatively correlated with mean annual hay prices, whereas mean annual crude oil prices (R2 = 0.48) showed a positive relationship. Grain sorghum production showed a consistent declining trend since 1971 and in 2017, it dropped by ~91% compared to that of 1971. Mean annual temperature (R2 = 0.58) was negatively correlated with grain sorghum production, while beef cattle population (R2 = 0.61) and range conditions (R2 = 0.51) showed positive linear relationships. Mean annual grain sorghum prices decreased since the peak of 1974 and in 2017, they dropped by ~77% compared to those of 1974. Crude oil prices (R2 = 0.72) and beef cattle population (R2 = 0.73) were positively correlated with mean annual grain sorghum prices. Corn production in 2017 dropped by ~61% compared to the peak that occurred in 1999. Crude oil production (R2 = 0.85) and beef cattle population (R2 = 0.86) were negatively correlated with corn production. Mean annual corn prices showed a declining trend since 1974 and in 2017, they dropped by ~75% compared to those of 1974. Mean annual corn prices were positively correlated with mean annual precipitation (R2 = 0.83) and negatively correlated with crude oil production (R2 = 0.84). These finding can particularly help in developing a more holistic model that integrates FEWS components to explain their response to internal (i.e., management practices) and external (i.e., environmental) stressors. Such holistic modeling can further inform the development and adoption of more sustainable production and resource use practices.