||Price elasticity and Beta are cherished variables in Economics and Finance, respectively. Price elasticity is a measure of a percent change in the quantity of a good demanded divided by the percent change in its price. Beta is the covariance of a firm's return with respect to the market, divided by the variance of the market. Although they do not measure the same metric, as price elasticity is based against a price change, and Beta is based against a market return, there are suggestions that these variables like these could be related (Coles 1995). Data-driven statistical support is lacking, yet it is very common for Economists to generalize price elasticities of goods/services, based on the level of "need" intrinsic to the good. For example, a food store would have a more inelastic demand curve than a private yacht manufacturer. One could also postulate that an inelastic demand curve would result in a low Beta as well, and vice versa. One might expect that firms with low demand elasticity of its product would also have a low covariation of their returns with the market, and thus a low Beta. This paper seeks to test the connection between a firm's output demand elasticity and a firm's Beta, using the oil industry as a case study. Given its consistent use and demand, oil is a relatively inelastic good. Additionally, the copious price fluctuations and availability of data make this industry an easy subject for analysis. I hypothesize a direct correlation between price elasticity and Beta, such that a higher price elasticity begets a higher Beta, and a lower price elasticity begets a lower Beta. Using large sets of averages and indices as a benchmark for data collection and analysis, no such connection exists on any statistically significant level. Upon whittling the regression down to smaller parts, and dismissing outliers, I found a statistically significant connection between the price elasticity and Beta. However, because of these conflicting results, there is no truly conclusive evidence that such a connection exists.