page_title: Luigi Pasinetti
section_title: A mathematical formulation of the Ricardian system
hierarchical_section_title: Luigi Pasinetti / Theoretical contributions / A mathematical formulation of the Ricardian system
caption_attribution_description: English: Distribution of income in the Ricardian system Español: La distribución del ingreso en el sistema Ricardiano
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: Pasinetti's first major contribution to economics was probably "the mathematical formulation of the Ricardian system", published in 1960 in a paper now considered classical. In such work Pasinetti presented a very concise and elegant (and pedagogically effective) analysis of the basic aspects of classical economics.
  At that time, Piero Sraffa had just published The Works and Correspondence of David Ricardo, one of the most masterful editorial works ever to be published in economics; and scholars were wondering how Sraffa's remarkable work could clarify and enrich the interpretation of Classical economics. Pasinetti's mathematical formulation provided a rigorous and clear answer to that question, in particular with reference to two major Classical problems: the theory of value and the theory of income distribution.
  On this subject, a major stimulus came from a famous paper written by Nicholas Kaldor, in 1956, where Kaldor presented a review of the history of several theories of distribution, covering the period from Ricardo to Keynes. Although Ricardo's theory (in Kaldor's paper) was without equations, it was the starting point after which economists began to explicitly see the Ricardian model as a coherent whole, susceptible to mathematical formalization.
  Another influence came directly from Sraffa and concerned the relative prices of goods produced in the economic system made to depend only on the amount of labour embodied in them – the well known labour theory of value. In fact, an early draft of Pasinetti's paper was read by Sraffa, who gave his approval to almost the entire paper:
  I myself remember that, when I returned to my college after submitting to his attention an early draft of my mathematical formulation of the Ricardian system, a friend immediately asked me: ‘Have you now thrown it into the paper basket?’ At my answer, ‘I have, but only the first section; the major part of the work seems to stand’, the surprised reply was, ‘Well, if it has gone through Sraffa’s scrutiny, it will hold for good.
  — L. Pasinetti
  Pasinetti explains that“the more constructive approach is taken of stating explicitly the assumptions needed in order to eliminate the ambiguities” in the Ricardian model, hence, the reason for the mathematical formulation.
  In this view, the most straightforward mathematical Ricardian model that can be formulated, with minimal economic complications, is the one in which only one commodity is produced (‘corn’ for instance), and where there are three social classes: capitalists who earn profits, workers who earn wages and landowners whose income comes from the rent of land. This is the way to express Kaldor's model mentioned above. Although the Pasinetti model is more general and comprises two sectors (agriculture and manufacturing), it is illuminating to start with the simplest version –a one-commodity model expressed by the following equations:
  Equation (1.1) shows that output, Y, depends only on the number of workers, N, engaged to work on the land. Three conditions (1.1a) are necessary and help to restrict the meaning of (1.1). Specifically, the first displays that land, when workers are not employed, can produce something or nothing at all. The second condition shows that the marginal product to kick start the cultivation of land must be greater than μ, the subsistence wage; otherwise the system will never start working. The third condition shows the diminishing returns of labour.  The following equations show the determination of the quantities of different categories of income:
  where W are the total wages, x is the wage per worker, K is the capital of the economy, R is the total rents perceived by landowners and B are the total profits that go into the hands of capitalists. The latter are represented as a residual income once the rents and wages have been paid. In these models all the capital is working capital; it is assumed to be composed entirely of advances to workers as wages. Notice, moreover, that expression (1.4), supplemented by technical conditions (1.1a), expresses what still today is cal
caption: Distribution of income in the Ricardian system in terms of marginal product.
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