The Wand is made rather than bought in every tradition that specifies it. The Key of Solomon directs that the rod be cut from a hazel or nut tree in a single stroke, at sunrise, from wood that has never borne fruit, and inscribed before use. The Golden Dawn replaced cutting instructions with construction ones. Its Fire Wand is a turned shaft with a magnetised iron core and a conical cap, painted in the flashing colours, and it belongs to the Philosophus grade, the grade of Fire.
That grade attachment is the part most often lost when the four weapons are listed together as a set. In the Golden Dawn system the aspirant does not acquire all four at once. Each implement is made and consecrated at the grade whose element it carries, so the Pentacle comes at Zelator, the Dagger at Theoricus, the Cup at Practicus, and the Wand last of the four, at Philosophus. Making the implement is part of the grade work, not a preparation for it, and a wand bought finished has skipped the exercise the requirement exists for.
Aleister Crowley, writing after his years in the order, kept the Wand for the will but shifted where the weight fell. In his treatment the Wand is the magician's own will given an object to live in, and its dimensions matter less than whether the maker can state what it is for. The Golden Dawn's Lotus Wand, banded in the colours of the zodiac and used for a different class of work, is a separate instrument rather than a variant of this one.