Tranio, disguised as Lucentio, and the Pedant, disguised as Lucentio's father Vincentio, have come to see Baptista Minola about the dower. When the Pedant speaks with Baptista, he eloquently confirms the dower's availability. Tranio, delighted the plan is working so well, quickly suggests all parties involved draw up the binding agreements straightway. Tranio also suggests sending Cambio to tell Bianca the news. Cambio re-enters as the stage clears, and Biondello informs him of Tranio's plan to arrange a fake wedding so Lucentio can marry Bianca himself for real. In light of this new arrangement, Cambio hurries off to inform Bianca they are to be wed that very night.
As with other small scenes of the subplot, this one contains little action but does advance the play in a few crucial ways. First it helps to indicate the passing of time, a necessity if we are to believe the action of the primary plot. Further, we need to see the importance of the disguised father so that we can be prepared for the play's resolution.
This scene also reinforces how much marriage is a matter of economics. Baptista has, in effect, sold his youngest and most beloved daughter to the highest bidder. The joke is on him, of course, since in being so concerned with money he has been duped by a servant and an old man who haven't much money between the two of them together. In Baptista's greed, he seems to have worked his daughter right out of a suitable husband (whether that's true or not will be resolved in Act V). All Tranio had to do was give the appearance of being a gentleman, and he was afforded every advantage a gentleman should have, even beating out the competition by invention of a make-believe fortune.
Likewise, the Pedant's ability successfully to fool Baptista projects interesting light on the socially accepted concept that people of rank were distinguished by their birth. As we see in Shakespeare, time and time again, such is not always the case. Shakespeare, in fact, often uses his disguises to show the foolishness of the nobility who insist on taking people at face value and who are certain gentlefolk are different from commoners. As we see here, given the proper disguise, landed gentry have a hard time discerning who is authentic and who is an imposter.
In addition, Tranio's presence in the scene reinforces the economic side of marriage. When Baptista is quick to agree to put the marital negotiations in writing (thereby making them binding), he shows his primary concern is a legal one. In fact, Baptista's preoccupation places him in an almost pathetic light. When he innocently offers comments such as sending Cambio to tell Bianca "how she's like to be Lucentio's wife" (66), we cannot help but laugh at his foolishness. Bianca, of course, will become Lucentio's wife — but not in the way Baptista thinks.
"hold your own" (6) "play your part."
right (12) genuine, real.
tall (17) fine.
"set your countenance" (18) "put on the expression of an austere father."
"with one consent" (35) unanimously.
curious (36) unnecessarily inquisitive; prying.
lie (56) lodge.
pass (57) transact.
slender pittance (61) scanty banquet.
counterfeit assurance (92) pretend wedding.
"cum privilegio ad imprimendum solum" "with exclusive printing rights."
"against you come" (103) "in anticipation of your arrival."
roundly (107) vigorously, bluntly, severely, etc.