which of the pilgrims was to tell an exemplum?

The Pardoner tells the exemplum. The purpose of his tale is to make a moral point.

All the Pilgrims, to some point, tell an exemplum. An exemplum is a tale told to prove a point. I suppose to the pilgrim it might be a moral but often the story is crass, silly or allegorical. In any case the two pilgrims with definite exemplums in them would be the Pardoner's and Wife of Bath's tales. The Pardoner's point is that greed is the root of all evil. So his modus oprerandi is to take people's gold and I suppose free their soul. The Wife of Bath likes to justify her having five husbands. She is kind of a medieval feminist. Virgins were all the rage but the Wife of Bath argues that to make more virgins, women must have sex. So the Wife of Bath sits on her donkey and quoting scripture to prove her points.