Back in Padua, Hortensio (disguised as Litio) leads the person he thinks is Lucentio (in reality Tranio) to spy on Bianca and the real Lucentio (disguised as Cambio). They see Bianca and "Cambio" flirt and kiss, and Tranio, pretending to be Lucentio, acts as if he is greatly upset by this. Hortensio reveals his true identity to Tranio and vows that he is done trying to woo Bianca. After seeing her with her teacher Cambio, he has decided that she is unworthy of his affections. Tranio promises also not to marry Bianca. Hortensio says that he will marry a rich widow instead and leaves.
While Hortensio thinks he has discovered a secret, he is still ignorant of the actual identities of Lucentio and Tranio. The instruction "Cambio" gives is again merely a pretense for Lucentio and Bianca to spend some romantic time together, for him to "teach" her to love him. Thinking that Bianca is attracted to non-noble men makes Hortensio see her as unworthy. He's looking for class and money in a wife—thus, the widow. At the same time, this shows that Hortensio's "love" for Bianca wasn't really love at all.
Tranio goes forward to Bianca and Lucentio and tells them the news about Hortensio. He also tells them that Petruchio is a master at taming shrews. Biondello arrives and tells Tranio that he has found a merchant who may be able to act as Lucentio's father, Vincentio. Lucentio and Bianca exit, as the merchant enters.
Hortensio sees Petruchio as a kind of teacher, who shows him how to "tame shrews." The merchant will become yet another character who disguises his real identity during the course of the play.
Tranio asks the merchant where he is from and the merchant responds that he is from Mantua. Tranio makes up a story that Mantua and Padua are in the middle of a political dispute and "'Tis death for anyone in Mantua / To come to Padua," (iv.2.86-87). Still pretending to be Lucentio, Tranio tells the merchant that he will do him a favor. Since the merchant resembles Lucentio's father Vincentio, he will allow the merchant to assume Vincentio's identity and stay with him. That way, no one will know that the merchant is from Mantua and he will be safe.
Tranio again displays his cleverness, tricking the merchant into wanting to dress up as Vincentio. Once again Tranio is, in a sense, the architect of the play's plot, despite the fact that he is a mere servant.
The merchant agrees and thanks Tranio for helping him. As Tranio leaves to find suitable clothes for the merchant, he mentions that he will need Lucentio's "father" to make assurances about his inheritance, in preparation for a wedding.
All that the merchant needs in order to assume a new identity and become a nobleman is a suitable set of clothes. Yet again, identity is established through performance, and that performance relies heavily on appearances.