Question: Teter the Gnat at one time levied a tax upon beads. He held that the beard was a superfluous and useless ornament The tax is said to have been proportional according to the length of the beard and progressive according to the social position of its possessor" [Groves, 1946, p. 51]. Evaluate Peters beard tax from the standpoint of optimal tax theory and from the standpoint of horizontal equity.