In Padua, Tranio (still disguised as Lucentio) brings the merchant, who is dressed up as Vincentio, to Baptista's house. Biondello arrives, as well, and Tranio reminds him to act as if the merchant is Vincentio. Baptista enters with Lucentio (disguised as Cambio) and Tranio introduces the merchant to him as Vincentio. The merchant tells Baptista that he approves of the marriage between Lucentio and Bianca.
Nearly every character on the stage is in a disguise, highlighting the very performance of Shakespeare's play itself. After all, Baptista is merely an actor in a costume, too. Furthermore, we are still supposed to imagine that all of this is being staged for the entertainment of a beggar dressed up as a noble lord (Christopher Sly).
Baptista is convinced that the merchant is Vincentio. Baptista, the merchant, and Tranio decide to go to Lucentio's lodging to discuss the financial particulars of the marriage in private. Before they depart, Tranio tells Baptista to send "Cambio" to inform Bianca that the marriage has been approved. "Cambio" (that is, Lucentio) goes to find Bianca. Baptista, Tranio, and the merchant leave to discuss their financial matters.
Here, the marriage between Bianca and Lucentio seems to be less a romantic matter between those two and more a financial or economic matter between the various men arranging it. Of course, the real Lucentio and Bianca aren't even in this scene (except for "Cambio" being used as a messenger).
Lucentio returns and Biondello informs him of their plans. Baptista has asked for Cambio to bring Bianca to a banquet, agreeing to marry her to the person he thinks is Lucentio (actually Tranio). Before going to the banquet, Lucentio will elope with Bianca to a church and get married in secret.
In asking for "Cambio" to bring Bianca to the banquet, Baptista unwittingly sends Lucentio to Bianca. Lucentio and Bianca's elopement may be the only way for them to have a marriage that is (potentially) more about love between two people than economic exchange between two families—at least, until Baptista and Vincentio find out.