The airport problem is a classic cost allocation problem that has been widely studied. Several rules have been proposed to divide the total cost among the agents, attending to the characteristics of the problem or via game theory. The axiomatic approach provides a way to choose among rules. Our main goal is to provide some tools to evaluate how rules differentially treat larger airlines as compared to smaller airlines. We use the Lorenz and no-subsidy orderings to compare rules. We introduce some monotonicity and boundedness properties that imply a specific ranking with respect to the nucleolus and the Shapley value.