At Baptista's house, Kate has tied up Bianca, who begs her sister to let her go. Bianca says she'll do whatever Kate wants because she knows how to be obedient to her "elders." Translation: "You're an old maid."
When Kate demands that Bianca tell her about her favorite boyfriend, Bianca doesn't answer the question. Instead, she tells Kate that she can have all of her suitors, if that will make her happy. (Translation: "I have a lot of boyfriends and you don't.")
Kate slaps Bianca.
Baptista walks in and scolds Kate for being so mean to her little sis. Kate complains that Bianca refuses to dish about her boyfriends and she runs after Bianca to slap her around some more and pull out all her hair.
When Baptista steps in to protect Bianca, Kate complains that her dad loves Bianca more than her and she runs off crying.
Gremio, Lucentio (as Cambio the tutor), Petruchio, Hortensio (as Licio the tutor), Tranio (as Lucentio), and Biondello enter Baptista's house. (Whew. That's a mouthful.)
Petruchio the smart alec steps up and lays out his plan to Baptista. He wants to marry Kate, who he hears is a delightful young lady. He presents Licio the tutor (really Hortensio) as a gift to Baptista. Baptista accepts the bribe, welcomes Petruchio, and then warns him that his eldest daughter is a total pain, but he's welcome to woo her if that's what he really wants.
Gremio butts in and says he has a present for Baptista too—a schoolteacher named Cambio (really Lucentio in disguise).
Tranio (disguised as Lucentio) says he wants in on the action also and he too has a gift for Baptista—a lute (a guitar-like instrument) and a little bundle of books for Baptista's daughters.
Baptista thanks the guys for the great presents and lets the "tutors" into his house.
That being settled, Petruchio says he's a busy man and wants to get down to business with Baptista. "OK," says Baptista, "Kate comes with twenty thousand crowns, plus she gets half my lands and money when I die."
Sounds good to Petruchio, who promises Baptista that if he dies before Kate does, she gets a widow's share of his estate. (Basically, enough to live on. Their kids—assuming they have any—get the rest of the money.) Petruchio is ready to draw up the contract but Baptista says Kate needs to agree first.
Just then, Hortensio runs into the room crying about how Kate broke a lute over his head when he was only trying to teach her how to play.
Petruchio is really turned on by this and says Kate sounds hotter than ever—he can't wait to talk to her. Left alone, Petruchio tells us how he plans to deal with Kate—he'll contradict everything she says. If she says something snobby, he'll say she sings like a bird. If she refuses to speak to him, he'll say she speaks eloquently. (You get the idea.)
When our girl enters the room and Petruchio greets her as "Kate," she insists that her name is "Katherine." Petruchio retorts that her name is "plain Kate" or "bonny Kate" or "Kate the curst" and so on.
Kate and Petruchio go at it for a few rounds. Here's how it works: Kate insults Petruchio, then Petruchio contradicts her and twists her words, then she twists his words around, and then he twists her words around again until they become a dirty joke.
At one point, Kate smacks Petruchio after he makes a reference to his "tongue" in her "tail" (an oral sex joke). Petruchio threatens to beat her if she slaps him again.
They continue on this way until Petruchio decides they've had enough chit-chat. He informs Kate that Baptista has agreed to a marriage, the dowry has been set, and whether Kate likes it or not, he will have her as his wife. He's also going to whip her into shape because her whole shrew bit isn't going to fly when they're married.
Baptista enters to ask how things are going, and Kate yells at her dad for agreeing to let her marry a maniac.
Petruchio lies and tells everyone that Kate is as gentle as a pussycat, loves him, and has agreed to marry him on Sunday.
Kate grumbles that she'd sooner see him hanged.
The others are skeptical of Petruchio's claims, but he tells them that it's true: they're in love. They've just decided it's best if she pretends to hate him in public. But when they were alone? Kate was all over him.
Kate says nothing in response to this. (Note: It's not completely clear why she's silent here and the moment could be staged in a couple of ways. Kate could be too shocked or mad to say anything. Or, Kate could be resigned to the fact that her dad has already made a deal with Petruchio so she doesn't bother saying anything else. Or, Petruchio could intimidate her into remaining quiet. Or, Kate could be secretly pleased that she's engaged. Different directors have staged the scene in all of these different ways. How do you interpret Kate's silence?)
Petruchio announces that he's off to Venice, but will be back in Padua to marry Kate on Sunday. Petruchio skips out of the room and Kate storms out separately.
Baptista turns his attention to the business of marrying off Bianca and compares himself to a merchant who is embarking on a precarious venture.
Gremio and Tranio (as Lucentio) try to outbid each other and Tranio (as Lucentio) wins because he's the richest. There's a catch though: Tranio (as Lucentio) has to get his father to vouch for his wealth.
Gremio thinks he's golden since he can't imagine Lucentio's dad has really given him his inheritance already.
When he leaves, Tranio gets an idea. Since he's posing as Lucentio, all he has to do now is find someone to pose as Vincentio (Lucentio's father). Problem solved.
Baptista makes Tranio (as Lucentio) promise that his father will vouch for him and verify his cash flow.