Access to resources strongly constrains the decisions we make. While we might wish to offer every student a scholarship, or schedule every patient for follow-up meetings with a specialist, limited resources mean that this is not possible. Existing tools for fair machine learning ignore these key constraints, with the majority of methods disregarding any finite resource limitations under which decisions are made. Our research introduces the concept of ``resource-constrained fairness" and quantifies the cost of fairness within this framework. We demonstrate that the level of available resources significantly influences this cost, a factor that has been overlooked in previous evaluations.