In the parable of the prodigal son whom does the father, the lost son, and the eldest son represent?

Rembrandt, The Lost Son

“It was fitting to celebrate and be glad, for this your brother was dead, and is alive; he was lost, and is found.'" (Luke 15:32)

The key to understanding the story of the prodigal sons is the context in which Jesus told the parable, which was a crowd of tax-collectors & sinners who “were gathering to hear him” and Pharisees & teachers of the Law who were muttering about why he'd hang around such shameful people.

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• The Father – The father in this middle eastern family depicts God The Father, as the providential provider despite our foolish choices, even to the point of rebellious abandonment. The Father complies with our “I wish you were dead” claims, still empowering us to reap the fruits of our immoral sowing. Yet, The Father's love does not diminish. The Father is depicted as waiting for the lost son in order to see him “while he is still a long way off,” and then doing the unthinkable in middle eastern culture, “he ran to his son, thew his arms around him and kissed him.” “He celebrates the son's return with gifts of a robe of distinction, a signet ring of authority, sandals to distinguish the freeborn son from a slave, and a fatted calf, only sacrificed for special occasions (Howell, 241).
  
  
• The Lost Son – As most recognize, the lost son stands for the lost sinners of this world, whether those who have chosen a lifestyle of immorality or those who simply left the Father's presence. Even if the Father had sought out the son and dragged him home, it would not have changed the son's bent to squander all that the Father gave him on foolish living and short-term choices. It's not until reality sets in and the son recognizes the consequences of his choices that he repents of his actions and returns to once again live in the Father's house. The same applies to those who have wandered away from God today living for their own desires, but they can turn back to God at any time and He will take them back.
  
  
• The Eldest Son – While the parable's focus is primarily on the younger lost son (answering the religionists question), Jesus concludes by speaking about the second part of his audience, the Pharisees and teachers of the Law with the elder son. These are the people who have not left the Father, but due to their attitude are just as separated from the Father's presence. The eldest son is so put-out by the inclusion of his shameful brother that he cannot join the celebration in the Father's house. His complaint to the Father about “all these years I've been slaving for you...” reveal his works-based righteousness theology and his complete misunderstanding of grace. The same applies to those who have never left the faith, but feel that somehow God owes them for their loyalty, or that somehow they should be better off than those who left because of all their work for the church.
  

Combined with the parables of the lost sheep and the lost coin, Jesus clearly reveals that this parable teaches the “joy that fills the heart of God when a sinner repents...” and thus that the “Heavenly Father [has a ] yearning love for lost people” (Howell, 241). Jesus clearly illustrates that those who recognize their deviance from God and repent will be forgiven and brought into the Father's presence with great rejoicing, but those who do not recognize that they cannot earn God's love will be left in their wanderings. However, we must be careful about reading too much into the parable for it “does not teach that the atonement is necessary, for one cannot expect a parable's teaching to be exhaustive” (Elwell, 827).

• Elwell, Walter. A.. Evangelical Commentary on the Bible. Grand Rapids: Baker Book House. 1989.
  
• Howell Jr., Don N.. The Passion of the Servant. Eugene: Wipf & Stock - Resource Publications. 2009.