The utility function for hemoglobin is defined as the amount of oxygen transported by a single hemoglobin molecule per roundtrip from the lungs (the loading terminal) to the various tissues (the unloading terminal). Traditionally, the efficiency of transporting any ligand by a binding system has been inferred from the cooperativity of the binding process. The larger the (positive) cooperativity, the steeper the binding curve (the so-called binding isotherm), and hence the larger efficiency. This monotonic relationship between cooperativity and efficiency is indeed valid for some simple systems, such as a two-site system. It is also valid for more complicated multisubunit systems for which all cooperativities are pairwise additive. We found that when the binding process is nonadditive, efficiency does not follow straightforwardly from cooperativity. Hemoglobin is a typical, highly nonadditive binding system, for which efficiency should be studied in its own right and independently of cooperativity.