"Corresponding ransom" was lifted almost bodily out of the Greek reference works as the definition of the word used at 1 Tim. 2:5-6, when Paul wrote under inspiration,
"For there is one God, and one mediator between God and men, a man, Christ Jesus, 6 who gave himself a corresponding ransom for all—[this is] what is to be witnessed to at its own particular times."
The ransom was paid by God, to God, to satisfy, not God, but justice coupled with mercy.
Why it was needed is shown by Romans 6:23:
"For the wages sin pays is death, but the gift God gives is everlasting life by Christ Jesus our Lord. " (NW)
That it was paid to God is shown by Psalm 49:6-9:
"Those who are trusting in their means of maintenance,
And who keep boasting about the abundance of their riches,
7 Not one of them can by any means redeem even a brother,
Nor give to God a ransom for him;
8 (And the redemption price of their soul is so precious
That it has ceased to time indefinite)
9 That he should still live forever [and] not see the pit. (NW)
So humans could not come up with the price necessary to "live forever and not see the pit."
It is also shown by Hebrews 9:22-26:
"Yes, nearly all things are cleansed with blood according to the Law, and unless blood is poured out no forgiveness takes place. 23 Therefore it was necessary that the typical representations of the things in the heavens should be cleansed by these means, but the heavenly things themselves with sacrifices that are better than such sacrifices. 24 For Christ entered, not into a holy place made with hands, which is a copy of the reality, but into heaven itself, now to appear before the person of God for us. 25 Neither is it in order that he should offer himself often, as indeed the high priest enters into the holy place from year to year with blood not his own. 26 Otherwise, he would have to suffer often from the founding of the world. But now he has manifested himself once for all time at the conclusion of the systems of things to put sin away through the sacrifice of himself."
Notice that Jesus had to "appear before the person of God for us."
A perfect human, Adam, got us into this mess, and it would take a perfect human to get us out, thus, a "corresponding ransom." Our parent, Adam, lost the right to perfect, eternal human life, and so did not have it to pass on to his children. Jesus offers to became our adoptive parent, sacrificing his right to perfect, eternal human life to make up for Adam's loss. Romans 5:18-19 puts it:
"So, then, as through one trespass the result to men of all sorts was condemnation, likewise also through one act of justification the result to men of all sorts is a declaring of them righteous for life. 19 For just as through the disobedience of the one man many were constituted sinners, likewise also through the obedience of the one [person] many will be constituted righteous."
Who, then, paid the ransom to God to satisfy justice? Man couldn't, according to Psalm 49 above, because there could never be another perfect man "corresponding" to Adam, per Romans 5 above. So God paid the ransom, Himself, at great sacrifice to Himself, to satisfy justice and not have to pay the wages of sin--death--to all imperfect, sinful humans:
"For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life." (John 3:16 KJ/AV)
"For all have sinned and fall short of the glory of God, 24 and it is as a free gift that they are being declared righteous by his undeserved kindness through the release by the ransom [paid] by Christ Jesus. 25 God set him forth as an offering for propitiation through faith in his blood. This was in order to exhibit his own righteousness, because he was forgiving the sins that occurred in the past while God was exercising forbearance; 26 so as to exhibit his own righteousness in this present season, that he might be righteous even when declaring righteous the man that has faith in Jesus." (Romans 3:23-26 NW)
Someone perfect had to come to earth as a perfect human corresponding to Adam, and sacrifice that right to life to make up for Adam's loss. God sent his own Son, and Jesus came willingly:
"No one has love greater than this, that someone should surrender his soul in behalf of his friends." (John 15:13 NW)
Best regards,
Mike