Controversy has been raging on the other side of the Pond over whether we may rightly speak of the eternal submission of the Son to the Father. See here for my thoughts on the matter. But I've had some second thoughts. Kind of. For one, would it not be better to speak of the submission of the Son to the Father in eternity, rather than the eternal submission of the Son? The latter expression may be taken to imply the eternal subordination of the Son to the Father, which strains homoousios almost to breaking point. The Son is of the same divine being as the Father and God in his own right. Any talk of subordination is therefore inappropriate.
That the Son submits to the Father in eternity, concerning his role as mediator and Saviour of sinners is less open to objection. Now we are talking about 'God for us' (or the economic Trinity), rather than 'God in himself' (the ontological Trinity). Besides, Scripture itself speaks of the elect being chosen in Christ before the foundation of the world (Ephesians 1:4) and of grace being given us in Christ before time began (2 Timothy 1:9). In eternity the Son submitted to the divine purpose that he should become flesh, die and rise again to save his people from sin (Galatians 4:4-6, Philippians 2:5-11).
But this was a divine purpose to which the Son was also party. As Calvin showed, Christ is both the electing God and the One in whom we were elected (see here). Calvin's successor at Geneva, Theodore Beza also grasped this point clearly. Richard Muller summarises his teaching, "Beza denied the charge that speaking of Christ as the executor of election he lost sight of Christ as the foundation of the decree. Beza resolved the issue of making a distinction between Christ as mediator and Christ considered according to his divinity as eternal God:
On the one hand, therefore, Christ is considered as the efficient cause of predestination with the Father and the Holy Spirit; on the other hand as being the first effect of predestination itself, on account of the servants mercifully elect in him." (Christ and the Decree, Richard Muller, Baker Academic, 2008, p. 82).
The Son no less than the Father was involved in the decree to save via his mediatorial work. In eternity the Son submitted to the triune decree that he would be sent into the world by the Father and through the power of the Holy Spirit. And so it was that in the fullness of time he came to seek and save the lost.
Stressing the co-equality of the Son with the Father and the Holy Spirit as the efficient cause of predestination in no way compromises the order of persons in the Trinity. The Three are not interchangeable. Each has his own distinguishing personal characteristics. As to their persons, the Father is unbegotten, the Son is begotten of the Father and the Holy Spirit proceeds from the Father and the Son. That is why it was singularly appropriate that the Father sent the Son to accomplish the work of salvation by the Holy Spirit.
The divine persons do not jostle for position, with one seeking to force the others into subordinate roles. The Three are One in being, will and acts. The Son seeks the glory of his Father, the Holy Spirit the glory of the Son and the God the Father is glorified when the whole universe acknowledges that Jesus Christ is Lord. It was in line with this attitude of 'other-seeking-glory' that in eternity the Son willingly submitted to become man and die for his chosen people. Before he went to the Cross, Jesus prayed to his Father who sent him into the world, "Father, the hour has come, glorify your Son that your Son also may glorify you." (John 17:1).
The cause and effect of the decree to save are the will and actions of the triune God; all for the glory of the One God who is Father, Son and Holy Spirit.