In Shakespeare's The Taming of the Shrew, what is the purpose of Act IV, Scene ii, in the larger scheme of the plot?
In Shakespeare's The Taming of the Shrew, Act IV, Scene i, concentrates on showing how shrewd Petruchio is in not only taming his new wife, but also in punishing his staff in order to closer align her sympathies to the servants. He plans, it seems, to control Kate by lack of food and sleep—his final intent is to bring her around to his way of thinking. It is during this scene that, ironically, Curtis states that Petruchio may be more of a shrew in his behavior than Katharina.
As the plot moves along then into scene two, Shakespeare shifts the attention back to what is occurring in Padua with regard to Bianca and her "suitors." A lot of information is shared with the audience in a "I won't bore you with details," though even while in saying so, the audience is still overwhelmed with said details.
And while all this occurs...
Act IV, Scene ii is purely “connective,” or structural. It ties up loose ends and ensures the successful progress of the Lucentio-Bianca subplot.
As this scene progresses, one almost needs a score card to keep track of suitors who remain, those who depart, who is trying to trick another suitor to leave the "race," and even those who are willing to do what ever is necessary, honest or not, to get what they want.
For the most part, then, Act IV, Scene two, is primarily used as a structural device to connect the overlying plot of Petruchio and Kate, and the courting that now continues after Kate's marriage, over Bianca's hand.