Chaos rules at Baptista’s house the next morning as Katherine chases Bianca, cursing at her in a fury. Katherine has tied Bianca’s hands together and is trying to beat her sister because Bianca will not tell her which of the suitors she prefers. When Baptista comes in to try to break up the fight, he only angers Katherine more by showing that he favors Bianca. Both sisters leave in a huff, just before a group of visitors enters to see Baptista.
The group is composed of the gentlemen who were on their way to the pub at the end of the last scene: Gremio with Lucentio (dressed as a schoolmaster), Petruchio with Hortensio (likewise dressed as a schoolmaster), and Tranio (dressed as Lucentio) with Biondello (dressed as his servant). The introductions begin in a whirlwind of deception. Petruchio starts off, bluntly as always, by asking Baptista for the opportunity to see Katherine. In exchange, he offers a music instructor for her, the disguised Hortensio, whom he introduces as Litio. Baptista accepts the present and intends to tell Petruchio as kindly as possible that Petruchio must be crazy to want to see Katherine, when Gremio, who cannot stand being upstaged, interrupts him. Gremio presents his own schoolmaster, the disguised Lucentio, whom he calls Cambio, a master of classical languages. Baptista accepts the gift and then hears from Tranio, who, pretending to be Lucentio, presents his own gift of books and a lute, in exchange for the permission to see and woo Bianca.
The two phony schoolmasters leave to ply their trades on Bianca, while Petruchio presses Baptista further for information about Katherine. After confirming that a substantial dowry will accompany his successful wooing of Katherine, Petruchio assures Baptista of his abilities. Hortensio cuts him off by returning, his head now bleeding—apparently, when Hortensio attempted to teach Katherine how to play the lute, she promptly took the instrument and smashed it over his head. Undaunted, Petruchio waits for Baptista to send Katherine out to see him. He decides to adopt the tactic of calling her “Kate” and good-naturedly contradicting everything she says.
Abrasive as always, Katherine tears into Petruchio from the moment he sets foot in her room. Petruchio’s quick wit, though, proves equal to hers, and Katherine, used to skewering the slower-witted men by whom she is surrounded, finds his aptitude for sparring highly frustrating. They engage in a lengthy verbal duel with elaborate puns, each one constructing a new metaphor from the other’s comments—Kate’s puns generally insult or threaten, but Petruchio twists them into sexual innuendo. Eventually, she becomes so enraged that she hits him, but he continues the game just the same, saying that he will marry her whether or not she is willing: “will you, nill you, I will marry you” (II.i.263).
When Baptista, Gremio, and Tranio enter to check on Petruchio’s progress, he claims that they have already agreed upon Sunday as the wedding day. Kate, shocked, contradicts him, but he ignores her objections and insists to the other men that Katherine cannot keep her hands off him. Strangely, Kate remains silent after this remark, and when Petruchio again claims that they will marry on Sunday, she says nothing, and they both leave.
After recovering from the shock of the hasty arrangement they have just witnessed, Gremio and Tranio immediately move to the matter of Bianca, who suddenly will be available after Sunday. Baptista says that whichever of the suitors can best ensure that Bianca will be provided for when she is a widow—in other words, whichever has the greatest wealth—may have her hand. Having assumed the false, unknown identity of Lucentio, Tranio is able to claim that he has limitless funding and simply guarantees ten times whatever Gremio offers. Baptista agrees to award Bianca to Lucentio as soon as his father can guarantee the wealth that he has claimed. Tranio, confident of his ability to play the part of Lucentio, believes he can produce Lucentio’s father as well.