In high altitudes is it necessary for the blood to have more or less hemoglobin?
In high altitudes the air is rarefied and oxygen concentration is lower than in low altitudes. In this situation the efficiency of the respiratory system must be greater and thus the organism synthesizes more hemoglobin (and more red blood cells) trying to get more oxygen. This phenomenon is known as compensatory hyperglobulinemia.
The compensatory hyperglobulinemia is the reason why athletes that will compete in high altitudes need to arrive in the place some days before the event so there is time for their body to make more red blood cells and they will be less affected by the effects of the low atmospheric oxygen concentration (fatigue, reduced muscular strength).