Petruchio claims he is ready to draw up the marriage contract, but Baptista insists he must first get Kate's love. As Petruchio and Baptista discuss the likelihood of Petruchio's wooing successfully, Hortensio re-enters with his lute hanging around his head, courtesy of Kate. When Petruchio and Kate are finally left alone, Petruchio insists Kate is the most demure, lovely woman on earth, but she is not drawn in by his rhetoric. They banter and exchange quips until Kate, having had enough, hits Petruchio. He does not strike her back but threatens he will do so, if need be. Petruchio remains undaunted in his quest for a wealthy wife, though, and vows to marry her despite her obvious objections.
When the men return to check on Petruchio's progress, he announces the wedding will be on Sunday. Kate raises her voice in protest, which leads Petruchio to make up a story about how in private Kate is coy and gentle but they have come to an agreement that "she shall be curst in company" (303). Baptista agrees to the match and Petruchio exits.
Baptista then turns his attention to Bianca's suitors. Gremio and Tranio vie for her by outlining for Baptista all they can offer her. Whatever Gremio offers, Tranio offers more, until Baptista has no choice but to accept Tranio's dower, provided he can provide proof that he does, in fact, possess the riches he claims. Tranio now realizes that he must get someone to impersonate Vincentio, Lucentio's father, in order to continue the masquerade and win Bianca for his master.
