Systems based on machine learning may exhibit discriminatory behavior based on sensitive characteristics such as gender, sex, religion, or race. In light of this, various notions of fairness and methods to quantify discrimination were proposed, leading to the development of numerous approaches for constructing fair predictors. At the same time, imposing fairness constraints may decrease the utility of the decision-maker, highlighting a tension between fairness and utility. This tension is also recognized in legal frameworks, for instance in the disparate impact doctrine of Title VII of the Civil Rights Act of 1964 -- in which specific attention is given to considerations of business necessity -- possibly allowing the usage of proxy variables associated with the sensitive attribute in case a high-enough utility cannot be achieved without them. In this work, we analyze the tension between fairness and accuracy from a causal lens for the first time. We introduce the notion of a path-specific excess loss (PSEL) that captures how much the predictor's loss increases when a causal fairness constraint is enforced. We then show that the total excess loss (TEL), defined as the difference between the loss of predictor fair along all causal pathways vs. an unconstrained predictor, can be decomposed into a sum of more local PSELs. At the same time, enforcing a causal constraint often reduces the disparity between demographic groups. Thus, we introduce a quantity that summarizes the fairness-utility trade-off, called the causal fairness/utility ratio, defined as the ratio of the reduction in discrimination vs. the excess loss from constraining a causal pathway. This quantity is suitable for comparing the fairness-utility trade-off across causal pathways. Finally, as our approach requires causally-constrained fair predictors, we introduce a new neural approach for causally-constrained fair learning.