In the Pactum Salutis, the Covenant of Redemption, the three co-equal persons of the Godhead make a covenant, in which God the Father functions as the Lord of the Covenant who will send God the Son to die for the sins of the elect, through the power and surety of God the Holy Spirit. This covenant is the doing of God, and thus as a work, it belongs to the sphere of the economic Trinity. As God's work, it speaks of the persons of the Godhead as not timeless but everlasting. God the Father actually engages with His co-equals God the Son and God the Holy Spirit in this covenant before the world began. Thus, from eternity God the Son, though co-equal with God, has covenanted Himself to take the role of the servant, a role He would exercise during the incarnation.
What is important to note here is that because of the Covenant of Redemption, God the Son from eternity has put Himself in a lower role, otherwise known as "to submit," relative to the Father, taking the role of the Servant of the Covenant. Though equal with God in essence, equal to God in worth, value and honor in every way, though equal to God in the making of the covenant, yet He submits to the Father in the terms of the covenant. Nowhere in the making of this covenant did God the Son become subordinate in status, being honor, glory, or anything else. Neither does the Son become inferior just because He is the Servant in the Covenant.
It is typical for us to think of submission in terms of superiority and inferiority, but this is not necessarily true. Believers are called to submit to one another (Eph. 5:21), but this does not in any way imply that one believer is superior or inferior to another. Submission can of course imply a subordination of status, but as we have seen in Ephesians 5:21, it does not have to. Everytime a husband asks his wife for counsel when he is unable to make a decision and decides to follow through her decision, he has in some sense submitted to his wife on that matter at that instance. Of course, that He is the head means that he ultimately stands behind her decision and consciously chooses to follow it, but this does not imply that on that matter he has not submitted to her counsel at that instant.
Thus, to say that God the Son submits to God the Father in no way necessarily implies superiority or inferiority on any one party. In the covenant of redemption, God the Son obeyed the Father, taking on the lower role of the Servant, in order to save the elect for the praise of God's glory.
There is therefore an eternal economic obedience of the Son, a submission from eternity by God the Son, in light of the pactum salutis. The persons of the Godhead are not interchangeable, and thus it is fitting that God the Son took on a submissive role in the economy of salvation. To deny otherwise is to attack the Covenant of Redemption, and thus undermine the biblical doctrine of our salvation.