The merchant poses as Lucentio’s father, and Baptista agrees to the match.
Characters: 
Tranio

Disguised as Lucentio, Tranio introduces the merchant as his father Vincentio.

Merchant

The merchant successfully presents himself as Lucentio's father.

Biondello

Biondello helps Lucentio and Tranio pull one over on Baptista. 

Baptista

Baptista is reassured by the promises of the merchant, disguised as Vincentio, and agrees to a marriage between Bianca and Lucentio.

Lucentio

Now that Baptista has agreed to a match between Lucentio and Bianca, he hopes that Bianca will go along with it. 

Scene Summary: 

Back in Padua, the fake Lucentio (Tranio) is taking the fake Vincentio (the Merchant) to Baptista’s house to guarantee the money for the dower so that Baptista will let Lucentio marry Bianca. Biondello shows up to say that he’s told Baptista that Lucentio’s father is in town. Then Baptista shows up, accompanied by Lucentio, who is still disguised as the tutor, Cambio, and the fake Lucentio gets right to the point, asking the fake Vincentio to promise his wealth for the marriage of Lucentio and Bianca.

The fake Vincentio makes his pitch, and Baptista agrees to the deal. To make the engagement official, they decide to go to Lucentio’s place to draw up the contracts and celebrate. Baptista sends Cambio to bring Bianca to Lucentio’s place. Then Tranio, the Merchant, and Baptista leave, followed by Biondello. Left alone, Lucentio tells the audience that he hopes Bianca will go along with the marriage.