page_title: Luigi Pasinetti
section_title: The Cambridge equation and Pasinetti’s theorem
hierarchical_section_title: Luigi Pasinetti / Theoretical contributions / The Cambridge equation and Pasinetti’s theorem
caption_attribution_description: The west end of King's College Chapel seen from The Backs. Clare College Old Court is on the left. A group of people punting along the River Cam can be seen in the foreground.
context_page_description: Luigi L. Pasinetti is an Italian economist of the post-Keynesian school. Pasinetti is considered the heir of the "Cambridge Keynesians" and a student of Piero Sraffa and Richard Kahn. Along with them, as well as Joan Robinson, he was one of the prominent members on the "Cambridge, UK" side of the Cambridge capital controversy. His contributions to economics include developing the analytical foundations of neo-Ricardian economics, including the theory of value and distribution, as well as work in the line of Kaldorian theory of growth and income distribution. He has also developed the theory of structural change and economic growth, structural economic dynamics and uneven sectoral development.
context_section_description: Kaldor's 1956 article already mentioned above (“Alternative Theories of Distribution”) was at the origin of another ‘seminal’ paper written by Pasinetti. Kaldor had reviewed the major theories of distribution throughout the history of economics from Ricardo to the Marginalists and even to Kalecki. But then, he added a theory which he named the Keynesian theory of income distribution. This was a surprise because these issues were never treated by Keynes in an explicit way. Kaldor baptized his theory as ‘Keynesian’ because it succeeded in catching a few important concepts both from Keynes's Treatise's widow's cruise allegory and from Kalecki's profits equation.
  In any case, in this paper Kaldor reached remarkable results. Starting from a closed economic system, without government, and in which there are capitalists and workers, starting from the saving-investment identity, Kaldor came to the following identity between investments and savings:
  where Y is the national income, P is the volume of total profits, sw is the workers propensity to save, sc is the capitalists’ propensity to save and I is investment. If we suppose that workers do not save (sw=0), divide both members by K and remember that in dynamic equilibrium I/K = gₙ, we get:
  where gₙ is the natural rate of growth and k is the capital/output ratio. Finally, note that these two expressions only have economic significance in the range:
  This interval excludes equilibrium with negative shares, either by the workers (first inequality) or by the capitalists (second inequality).
  The expressions (3.1) and (3.2) are those that have subsequently formed the core of the post-Keynesian distribution theory; but only after an extremely hard-fought debate. Equation (3.1) shows that the share of profitsin total output depends positively on the natural rate of growth and the capital/output ratio and negatively on the propensity to save of the capitalist class. The second of these relations, (3.2), better known as the “Cambridge equation”, shows that the profit rate is solely determined by the ratio of the natural rate of growth and the propensity to save of capitalists.
  
  The importance of these expressions became clear only after an intense debate. These expressions were achieved with an additional assumption that was heavily criticized. Kaldor's assumption was that the workers propensity to save was zero. 
   Specifically, if you eliminate this assumption, the above formulas lose their conciseness, depending on the propensity to save of workers. This assumption was explicitly criticized because, whatever justification it might have had in the early days of industrialization, it appeared to have no sense in contemporary times. If you eliminate this assumption, the above formulas lose not only their conciseness, but also their applicability to the industrial systems of our own days.
  Pasinetti went into this debate with his 1962 paper. With his now famous Pasinetti Theorem, he achieved the result of re-stating Kaldor's original equations without the need to rely on Kaldor's much criticized assumptions. It is worth quoting the first time that Pasinetti presented his views about these issues to an audience:
  I dared, while being the youngest member, to present the results of my work on income distribution (Pasinetti, 1962) to a session of the so-called ‘Secret Seminar’ in King’s College (a post-war version of Keynes’s more famous Circus)-a unique experience for me. I presented my results as a criticism of Kaldor’s theory. The members of the audience were stunned, or suspicious, or disbelieving, with one exception: Nicky Kaldor. He was extraordinarily quick in grasping the gist of the idea and in seeing that the concession of his having fallen into a ‘logical slip’ led to a generalization of the post-Keynesian (in fact of Kaldor’s) theory of income distribution and moreover to a new, long-run, Keynesian theory of the rate of profits.
  — L. Pasinetti
  In his 1962 paper, Pasinetti showed that Kaldor had fallen into a "logical slip". He implicitly assumed that the total profits only came from t
caption: King's College, University of Cambridge.
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