This is an interesting question because before we can focus on a character study of Pakhom we need to pay particular attention to the type of short story that "How much land does a man need?" is. Because this tale is a parable or an allegory, the character of Pakhom is not fully developed into a round character. Rather the details we are given serve to establish him as a type instead of an intensely interesting pscyhological phenomenon.
Pahom is shown from the first to be a poor peasant, who desires more land to have an easier life. He resents being treated badly by other landowners and is clearly preoccupied with providing for his family. However, envy begins to enter him when he hears of other peasants buying their own land, which leads to his own purchase of land. Having bought his own land, Pahom now finds that he is treating other peasants the same way that he was treated by landowners - the ownership of land has resulted in a change of his character. This is something that continues throughout the tale, until his attitude to land is juxtaposed harshly with that of the Bashkir chief: the more land Pakhom receives, the less he will share, wheras the Bashkirs treat land as something to be shared and something that is held in common. Throughout the story, however, Pakhom's desire to own more and more land grows with intensity until it finally results in his own death, and the grimly ironic possession of 6 feet of land - all that is needed to bury him.
Therefore, Pakhom as a character is not fully developed - he is rather a medium through which Tolstoy conveys his concerns about the impact of land ownership on peasants and suggests that they might not actually be better off after their emancipation in some ways.