Density is a factor because larger aircraft used on dense legs lower per passenger costs.
Shaded areas show cost decreasing with increasing density. On very short and very long distances marginal cost rises as density increases. Very long legs are usually covered by large aircraft whenever density justifies a direct flight, so there is little opportunity to reduce costs on these routes. On the demand side, we allow for heterogeneous customer preferences. On the cost side, we allow economies of density to vary across routes of different lengths.