Arranged marriages are alive and well, and the Internet allows apparently even this institution to flourish. Witness Marry our Daughter where underage daughter are proposed for marriage. This site features bride prices based on biblical justifications. But there can also be perfectly rational, economic justifications for a bride price.
The bride price is based on the idea that a family looses child-bearing services when it gives a daughter away. The argument is very similar to the one used to justify the high pay of prostitutes, especially young ones.
In this context, it may be puzzling that one can also have dowry, that is, a gift that a woman brings into marriage, typically from her parents. The usual justification is that she will not be able to use the services of her old family, in particular bequests (Maristella Botticini and Aloysius Siow). One can therefore understand dowry as an anticipated bequest. In fact, bride price and dowry can coexist, see Ted Bergstrom.