Masters and Husbands/ Wives and Servants: The Ideals of Renaissance
The relationships between servants and masters closely reflect the gender relationships in Shakespeare's The Taming of the Shrew. Lucentio and Tranio's relationship as master and servant is an ideal of the Renaissance era according to "An Homily on the State of Matrimony." Tranio risks taking the place of his master because of his love for him and Lucentio always treats him with kindness and respect, almost like an equal. Though they are not involved romantically, Lucentio and Tranio fulfill these ideals better than any marriage in The Taming of the Shrew. Lucentio's relationship with Bianca reflects his role with Tranio: Bianca shows respect for Lucentio as he cherishes her and treats her with kindness, however Bianca fails to complete her role as an ideal wife by obeying her husband. Petruchio and his servant, Grumio, have a much different relationship, however. Grumio often disobeys his master, while Petruchio insults and even beats him. These roles are echoed in Petruchio's relationship with Katherine.
Shakespeare uses Lucentio and Tranio's relationship in the play as an ideal for both the master and servant relationship as well as gender relationships. Though Lucentio is the master, he always treats Tranio with respect and kind words. When the pair arrives in Padua, Lucentio tells Tranio that he his happy that he is with him: "And by my father's love and leave am arm'd with his good will and thy good company, my trusty servant well approv'd in all."  Rather than abusing his power over Tranio, he is grateful for him. In return Tranio refers to Lucentio as "gentle master mine" and "good master." 
Tranio demonstrates his obedience in part because he is a good servant, but mostly due to the fact that Lucentio treats him so kindly. Though Tranio takes great risk in putting on the apparel of his master, he takes it in order to please Lucentio: "In brief, sir, sith it your pleasure is, and I am tied to be obedient- for so your father charg'd me at our parting: ÔBe serviceable to my son' quoth he, although I think Ôtwas in another sense- I am content to be Lucentio. Because so well I love Lucentio."  Though it is partly due to his obedience to Lucentio's father that he serves Lucentio, Tranio knows that Vicentio did not mean for him to switch places with his son, but he does anyway due to the respect he holds for him.
It could be that Tranio is just taking on this disguise in order to have the chance to play the part of a master and noble. However, Shakespeare constantly reminds the audience that Tranio's intentions are pure and all for the love of his master. When Biondello exclaims how he wish he could play the master, Lucentio replies: "So could I, faith boy, to have the next wish after, that Lucentio indeed had Baptista's youngest daughter. But, sirrah, not for my sake but your master's, I advise you use your manners discreetly in all kind of...