Marx’s transformation problem and Pasinetti’s vertically integrated subsystems
证明在资本主义制度下，生产价格与垂直超整合子系统的劳动量成正比，从而解决了马克思的转型问题，并推广了劳动价值论。
Pasinetti (1988) constructs a ‘complete generalization of Marx’s “transformation problem”’, in the context of a non-uniform growth model, by proving that production prices are not proportional to the physical quantities of labour supplied to ‘vertically hyper-integrated subsystems’. Pasinetti therefore restricts the labour theory of value to a pre-institutional stage of analysis. In this paper I demonstrate that the transformation problem dissolves once we consider the vertically integrated subsystems induced by the specific institutional setup of a capitalist economy. I prove that production prices, both in steady-state and non-uniform-growth models, are proportional to the physical quantities of labour supplied to ‘vertically super-integrated subsystems’. In consequence the labour theory of value, suitably generalized, also applies at the institutional stage of analysis.