Research Project Proposal: Bridging Keynes and Sraffa: the Z Function Grounded in Activatable Plants and Vertical Integration

Starting from the Keynesian reading of \(D(N)\) and \(Z(N)\) as \emph{value} magnitudes steered by expectations, we reconstruct \(Z(N)\) on classical--Sraffian foundations, avoiding the identification \(MPL=w/p\). The key idea is to model aggregate supply as a \emph{piecewise linear frontier} of branches/plants (\emph{vintages}) evaluated at administered \emph{normal--cost prices}, with slopes given by the \emph{value per unit of vertically integrated labour}. This lets us treat capacity and technique changes as \emph{switches} between segments without intra--period repricing, while preserving additivity of values. In the medium run, we \emph{re--benchmark} to production prices consistent with distributive closure and the updated production structure; this rotates slopes and may generate \emph{reordering} and \emph{reswitching}. We show how the equilibrium condition \(D=Z\) determines the active segment \(j^\star\), and we provide comparative statics (local, across periods, and global), including distributive implications for the wage share and the real wage. We extend the analysis to non-uniform rates/mark--ups, wage advances, and changes of \emph{numéraire}; existence conditions remain governed by the spectral radius of \(\mat A\). The framework integrates Input--Output (Pasinetti--Leontief) accounting with the Keynesian employment determination, offering a theoretical and operational basis for empirical and policy analysis.