The Necessity of Christ's Divinity for the Atonement

I have heard and often reasoned myself for the necessity of the divinity of Christ for the efficacy of the atonement. If Jesus were merely a man, and not God, then he could not pay for the sins of all who come. At best a perfect man could replace one other. I have never really seen this reasoning in Scripture, though, before this morning:

“Truly no man can ransom another, or give to God the price of this life, for the ransom of their life is costly and can never suffice, that he should live on forever and never see the pit. But God will ransom my soul from the power of Sheol, For he will receive me.” Psalm 49:7-9, 15