I am interested in analyzing the transfer from rentier sectors towards manufacturing sectors in Latin America, based on the reproduction schemes of Marx.
The model of Lowe, Adolph, "The Path of Economic Growth," (Cambridge, U. K.: Cambridge University Press, 1976) can do that for you. Before you get into Lowe's original work, which I think can be programmed with a spread sheet, I recommend that you look at some smaller hand applications as in the two references,
Halevi, Joseph, “Lowe, Dobb and Hicks,” Eastern Economic Journal, Vol. 10, No. 2 (Apr. - Jun., 1984), pp. 157-167.
Halevi, Joseph, Employment and Planning, Social Research, Vol. 50, No.2 (Summer 1983) pp. 345- 358.
How does this respond to the (non) transformation problem? As you may know, Kliman (2009) claims that previous attempts to quantify the theory suffers from physicalism and simultaneism. However, both are alien to the formulation of the law of value.
Kenneth, the traditional transformation problem (quantitative problem of relating values to prices) is the abstract direct solution to the transfers of value that happens in reality. So the solution to the problem becomes more concrete when we show empirically how value is being trasnfered between branches. Simultaneism and physicalism happens because the distinction between the abstract solution (of Sraffa type) and the concrete studies showing the transfers is still too weak.
Tiago, I agree with your point of view on the problem of transformation. In short, the problem of transformation is secondary if we wish to study is the transfer of surplus between branches into a concrete economy.