Why are Jesus' sayings about the poor concentrated in Luke?

Jesus' first person speech is almost entirely inside the gospels. The stated purpose of the gospel of John is that it is written to convince people to believe in him (John 20:30-31). It intentionally deals primarily with who Jesus was rather than primarily with Jesus' teaching. Mark is much shorter than the other gospels and may not include additional information from the proposed Q source present in Matthew and Luke.

As far as Matthew is concerned this question may be illuminating. If Matthew was primarily aimed at an audience of Jewish origin and Luke primarily at an audience of pagan origin the need to emphasise the message on helping the poor becomes clear. The Jews have an embedded culture of needing to care for the poor from the Old Testament (e.g. Ezekiel 16:49, Exodus 23:11, Proverbs 19:17, Isaiah 61:1... I could go on) which in Matthew Jesus has come to fulfill (Matthew 5:17). Whereas Luke needs to introduce his audience to and emphasis the importance of important basic aspects of Judeo-Christian morality that Jesus taught like the duty to help the poor. Likewise in Matthew there is a much greater need to emphasise points where Jesus' teaching is different from Old Testament tradition hence the increased frequency of Jesus presenting the anti-thesis ("You have heard... But I say unto you..." type quotes) found in the gospel of Matthew.

Attending to the interest in "what any scholar has to say" about teaching on poverty (and, necessarily I suppose, wealth -- the two themes tend to come together) in Luke...

1. For general context, see Martin Hengel, Property and Riches in the Early Church: Aspects of a Social History of Early Christianity (Fortress, 1998). Hengel was one of the foremost scholars of the Second Temple Judaism and nascent Christianity, but known as a New Testament specialist.

2. More specifically, the broad social context for Luke's writing is set in the volume edited by Jerome Neyrey, The Social World of Luke-Acts: Models for Interpretation (Hendrickson, 1991). None of the chapters are directly on poverty/wealth, but lots about social location which informs this theme.

3. And more directly yet, see Walter Pilgrim's recently reprinted book: Good News to the Poor: Wealth and Poverty in Luke-Acts (1981; reprinted Wipf & Stock, 2011). It has been widely cited by later scholars.

4. A published doctoral dissertation (Glasgow), covers this theme in some detail: Kyoung-Jin Kim, Stewardship and Almsgiving in Luke's Theology (Sheffield Academic Press, 1998).

5. In shorter compass, here are some articles and/or chapters that address this theme:

   • a starting point for many recent discussions was provided by J.R. Donahue's survey, "Two Decades of Research on the Rich and Poor in Luke-Acts", in Justice and the Holy: Essays in Honor of Walter Harrelson, ed. by D.A. Knight and P.J. Paris (Scholars, 1989), pp. 129-144. [no online sources I can find]
   • Joel Green, excellent orientation in a section on "The Economy of the Kingdom" in his (very readable) The Theology of the Gospel of Luke (Cambridge, 1995), pp. 112ff.
   • Peter Liu, "Did the Lucan Jesus Desire Voluntary Poverty of his Followers?", Evangelical Quarterly 64 (1992): 291-317.
   • Tim Kelley, "Renounce my Possessions? What does Luke 14.33 Mean?", Leaven 6/3.8 (1998): 131-135 [a more popular presentation, but still drawing on scholarly sources]
   • Thomas E. Phillips, "Reading Recent Readings of Issues of Wealth and Poverty in Luke and Acts", Currents in Biblical Research 1/2 (2003): 231-269 [this one would be a good place to start, in fact]

While that should be enough to provide an orientation to the scholarly discussion, the "Why?" question remains. And that's difficult to answer.

Many note the clear context of poverty out of which Jesus' ministry emerges: this is the clear signal of the offering of "two turtle doves" provided in Luke 2:24 (compare Leviticus 12:8). Not only does Luke use some distinctive Greek vocabulary for "poverty", he uses the standard Greek term (πτωχός = ptōchos, the "beggarly poor"), with ten occurrences, double that of either Matthew or Mark. And the general theme runs into Acts, too, so it is clearly a pronounced theme in Luke's writing, although obviously shared in many ways with the other gospels, Paul, and James in particular.