Sraffa was born in Turin, Italy, to Angelo Sraffa (1865–1937) and Irma Sraffa (née Tivoli) (1873–1949) a wealthy Italian Jewish couple. His father was a professor in commercial law and later dean at the Bocconi University in Milan. Despite being raised a practicing Jew, Sraffa later became an agnostic. He studied in his home town and graduated at the local university with a work on inflation in Italy during and after World War I. His tutor was Luigi Einaudi, one of the most important Italian economists and later a president of the Italian Republic.
From 1921 to 1922 he studied at the London School of Economics. In 1922, he was appointed director of the provincial labour department in Milan, then professor in political economy first in Perugia and later in Cagliari, Sardinia. In Turin he met Antonio Gramsci (the most important leader of Italian Communist Party). They became close friends, partly due to their shared political views. Sraffa was also in contact with Filippo Turati, perhaps the most important leader of the Italian Socialist Party, whom he allegedly met and frequently visited in Rapallo, where his family had a holiday villa.
In 1925, he wrote about returns to scale and perfect competition, underlining some doubtful points of Alfred Marshall's theory of the firm. This was amended for British readers and published in 1926 as The Laws of Returns under Competitive Conditions.
In 1927, Sraffa's yet undiscussed theory of value—but also his friendship with Antonio Gramsci, a risky and compromising endeavor in the context of the Italian fascist regime, considering Gramsci had previously been imprisoned (Sraffa supplied the material, literally pens and paper, with which Gramsci would write his Prison Notebooks)—brought John Maynard Keynes to prudently invite Sraffa to the University of Cambridge, where the Italian economist was initially assigned a lectureship.
Together with Frank P. Ramsey and Ludwig Wittgenstein, Sraffa joined the so-called cafeteria group, an informal club that discussed Keynes's theory of probability and Friedrich Hayek's theory of business cycles. (Sraffa–Hayek debate) In 1939, Sraffa was elected to a fellowship at Trinity College.
John Eatwell wrote of Sraffa's work on Ricardo:
[Sraffa's] reconstruction of Ricardo's surplus theory, presented in but a few pages of the introduction to his edition of Ricardo's Principles
, penetrated a hundred years of misunderstanding and distortion to create a vivid rationale for the structure and content of surplus theory, for the analytical role of the labor theory of value, and hence for the foundations of Marx's critical analysis of capitalist production.
Sraffa's Production of Commodities by Means of Commodities was an attempt to perfect classical economics' theory of value, as originally developed by David Ricardo and others. He aimed to demonstrate flaws in the mainstream neoclassical theory of value and develop an alternative analysis. In particular, Sraffa's technique of aggregating capital as "dated inputs of labour" led to a famous scholarly debate known as the Cambridge capital controversy.
Economists disagree on whether Sraffa's work refutes neoclassical economics. Many post-Keynesian economists use Sraffa's critique as justification for abandoning neoclassical analysis and exploring other models of economic behavior. Others see his work as compatible with neoclassical economics, as developed in modern general equilibrium models, or as unable to determine a long-period position, just like the Walrasian approach. Others still argue that the importance of Sraffa's economics is that it provides a new framing for how we understand capitalist economies that does not fall back on the arguably unrealistic assumptions of neoclassical economics.
Nonetheless, Sraffa's work, particularly his interpretation of Ricardo and his Production of Commodities by Means of Commodities (1960), is seen as the starting point of the Neo-Ricardian school in the 1960s. His approach has been described as serving "to help judge Ricardo's editor and to illuminate the unity in [his] scientific vision, from before 1926 until death in 1983."
As stated above, Sraffa is known also for his close friendship with Italian Marxist thinker Antonio Gramsci and for being instrumental in securing Gramsci's prison notebooks from the Fascist authorities after the latter's death in 1937. Titled “Problems of today and of Tomorrow” Gramsci published 1924 a letter from Sraffa (without signing, signed S.). In the letter Sraffa emphasizes the function of bourgeois oppositions in the struggle against fascism and the importance of democratic institutions for the social and political development of the proletariat. In view of the weakness of the Communist Party, Sraffa recommends collaboration with the bourgeois opposition to fascism. In his answer Gramsci rejects this suggestion but followed Staffa’s advice several years later.
Norman Malcolm famously credits Sraffa with providing Ludwig Wittgenstein with the conceptual break that founded the Philosophical Investigations, by means of a rude gesture on Sraffa's part:
Wittgenstein was insisting that a proposition and that which it describes must have the same 'logical form', the same 'logical multiplicity'. Sraffa made a gesture, familiar to Neapolitans as meaning something like disgust or contempt, of brushing the underneath of his chin with an outward sweep of the finger-tips of one hand. And he asked: 'What is the logical form of that?'
In the introduction to Philosophical Investigations, Wittgenstein mentions discussions with Sraffa over many years and says: "I am indebted to this stimulus for the most consequential ideas in this book". In 1946, however, Sraffa broke off his weekly conversations with Wittgenstein over the latter's protests; and when the philosopher said he would talk about anything Sraffa wanted, "'Yes', Sraffa replied, 'but in your way'".
Both Sraffa and Wittgenstein influenced each other deeply. They continually corresponded and discussed each other in their journals and notebooks. Both authors were dealing with a form of positivism dominant in their respective disciplines, economics and philosophy. While Wittgenstein made his famous turn from the Tractatus Logico-Philosophicus to the Philosophical Investigations wherein he jettisoned the previous idea that the world comprised an atomistic set of propositional facts for the notion that meaning derives from its use within a holistic self-enclosed system. Analogously, Sraffa was rebutting the Neoclassical paradigm which was similarly atomistic, individualistic and derivational (see Criticisms of neoclassical economics). While there are disputes about how to interpret Sraffa—falling primarily into the neo-classical camp of Paul Samuelson and the Neo-Ricardian of Pierangelo Garegnani—none dispute Sraffa's influence and it can be argued that Sraffa's critique of neo-classical economics is analogous to that of Wittgenstein's of philosophy, in that Sraffa sought to replace the individualistic and positivistic account of price as the result of an equilibration of supply and demand, for instead as price serving a social function, namely to reproduce a stationary or expanding economy given a distribution of income.
Sraffa was described as a very intelligent man, with a proverbial shyness and a real devotion for study and books. His library contained more than 8,000 volumes, now partly in the Trinity College Library. A popular anecdote claims that Sraffa made successful long-term investments in Japanese government bonds that he bought the day after the nuclear bombing on Hiroshima and Nagasaki. Another version of this is that Sraffa bought the bonds during the war, when they were trading at distressed prices, as he was convinced that Japan would honour its obligations (Nicholas Kaldor, pp. 66–67).
In 1961, when the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel had not yet been created, he was awarded the Söderströmska Gold Medal by the Swedish Academy. In 1972, he was awarded an honorary doctorate by Sorbonne, and in 1976 he received another one from Madrid's Complutense university.