A rich man’s approach to marriage

Baptista is a wealthy man who has two daughters. In an era when marriage was seen primarily as a financial and legal transaction, a way of securing assets and the security of a woman’s status, it is not surprising that the elderly father is most concerned with the economic advantages of his daughters’ matrimony. One daughter, Bianca is seen as being a valuable marriage commodity, while the other daughter, Katherina, is regarded as a liability because of her shrewish behaviour. Although Baptista does not want to prejudice Bianca’s hopes, in order to marry Katherina off quickly, he has decided that Bianca can only get married after Katherina has been betrothed. 
Faith, gentlemen, now I play a merchant's part
And venture madly on a desperate mart.
Act 2 Scene 1     
Hortensio, as a would-be suitor to Bianca, describes Baptista as the keeper of treasure:
Tarry, Petruchio. I must go with thee,

For in Baptista's keep my treasure is.

He hath the jewel of my life in hold,

His youngest daughter, beautiful Bianca,

And her withholds from me and other more.
Act 1 Scene 2     
According to Padua’s patriarchal society, Baptista is head of the family and he has the authority to decide when, and to whom, his daughters get married. See Religious / philosophical context > The faith setting of Shakespeare’s plays > The Ten Commandments. Much of the beginning of the play centres on his conversations with other men about dowries and marriage arrangements. In such conversations he ruefully recognises himself to be a trader negotiating the prices of his daughters’ dowries:

A caring parent

Baptista has done his best to bring up his girls to take an appropriate place in their society. He had educated both (by no means a universal accomplishment for females in that era) and pays good money to provide for their tastes in music and learning. Although he puts financial considerations first in his marriage negotiations with Petruchio, Baptista also considers Katherina’s feelings:
Ay, when the special thing is well obtain'd,
That is, her love; for that is all in all.
Act 2 Scene 1     
There is clearly affection for his elder daughter, as well as exasperation. Fearing how difficult Katherina (and doubtless everyone else around her) would find it for her to remain a spinster, Baptista is perhaps eager to be convinced by Petruchio’s confidence in his ability to woo Katherina: ‘I am as peremptory as she proud-minded’. In the face of Petruchio’s urgency, as well as the demands from Bianca’s suitors that she is no longer withheld from the marriage market, the marriage which everyone thought would never happen is organised in a very short time.    

Experience overturned

Baptista has had long experience of Katherina’s behaviour, which has led to fixed judgements about her. Once he understands the sincerity of Petruchio’s offer to marry her, he seems to have more concerns about his potential son-in-law than about Katherina and he warns him to be ‘arm'd for some unhappy words’ in their forthcoming marriage. In this sense, Baptista may be seen to represent the social and domestic conventions that shape and reinforce behaviour which labels a person as ‘shrewish’. In his role as father, he is unable to be the agent of change that Katherina needs.
Baptista’s judgement that Kate is a shrew is not shaken even when Bianca provides evidence of greater duplicity and cause for disappointment. Katherina’s father still thinks that she is ‘the veriest shrew of all’ at the end of the play (Act 5 Scene 2), even though it is an opinion held ‘in good sadness’. He demonstrates this conviction by backing Lucentio’s wager that Bianca will come when he calls for her, as opposed to his elder daughter. 
Yet Baptista seems genuinely delighted when Petruchio wins the wager, responding:
Now fair befall thee, good Petruchio!
The wager thou hast won, and I will add
Unto their losses twenty thousand crowns,
Another dowry to another daughter,
For she is changed as she had never been.
Act 5 Scene 2     
In Baptista’s world, there is no better achievement than to secure the security and happiness of a child, and this, it seems clear, has miraculously come true for both his daughters.
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