I have a question about the use of the word "ransom". Ransom implies an exchange, someone makes a payment and another receives the payment.
If Jesus paid the ransom for us, who did He pay?
Good question. I don't think it's a complete cop-out to answer by quoting the NAB note on Mt 20:28 ("Just so, the Son of Man did not come to be served but to serve and to give his life as a ransom for many."):
Ransom: this noun, which occurs in the New Testament only here and in the Marcan parallel (Mark 10:45), does not necessarily express the idea of liberation by payment of some price. The cognate verb is used frequently in the LXX of God's liberating Israel from Egypt or from Babylonia after the Exile; see Exodus 6:6; 15:13; Psalm 77:16 (76 LXX); Isaiah 43:1; 44:22.
In other words, "ransom" doesn't necessarily imply an exchange. Who received the payment when the LORD ransomed captive Israel?
Let me propose an invented-for-this-post taxonomy: We can speak of the general act of freeing a captive, and call this liberation. We can go on to distinguish (at least) three specific types of liberation:
When the captor frees the captive himself; I'll call this manumission.
When someone in authority orders the captor to free the captive; I'll call this emancipation.
When a third party acts to secure the captive's freedom without invoking authority over the one holding him captive; I'll call this ransom or redemption. There are different means to securing a captive's freedom; e.g.:
forcibly removing the captive from captivity
effecting circumstances that cause manumission or emancipation
payment to the captor
exchanging places with the captive
According to the Scriptural accounts, the LORD's ransom of Israel from Egypt would be an example of forcibly removing the captives from captivity (once Pharaoh reneged on his promise of emancipation); the ransom from Babylonia would be more of an example of effecting the circumstances of emancipation, though the difference between effecting circumstances and direct removal didn't much concern the sacred writers.
And the ransom of the elect from the slavery of sin and death? Well, a price was paid, certainly, but not the kind of price that is paid to someone. It's the kind of price, or maybe "cost" is the better term from economics, that is an evil endured in order to attain some good.*
Generally, though, I think Christians speak of Jesus taking our place. (This may not sound to us like a plausible form of ransom, but the Mercedarians, for example, were founded with exactly this as their apostolate.)
How, and in what sense, was Jesus able to "take our place"? How did this effect our salvation? Good thing Holy Week's coming up.
* We often speak of people "paying the price" for some achievement -- you win the game at the cost of physical injuries, you meet deadline at the cost of a night's sleep. In ordinary matters, it's generally obvious how the achievement relates to the price; the other team isn't going to step aside while you score, the project will take nine hours to complete and it's due in ten hours. With the Atonement, it's more of a mystery (to say the least).