Disclaimer: this book uses math as a way to build an argument. Unfortunately, I have lost most of my mathematical intuition along the long humanities road which is famously allergic to quantative methods.
Nonetheless, this book is persuasive enough for those like me who will not be able to get the full reasoning behind the arguments. It has been written for a marxist public, as it tries to summarise the insights of post-Keynesian and Ricardian economist Piero Sraffa, and how it forms a challenge to the value theory of Marx.
The basic insight is quite easy: Marx utilises a concept of "value", which hoovers over his more concrete analyses of capitalism as a social system, and is used as a metatheoretical concept to explain exploitation. Famously in Marx's theory, value is only created by concrete labour embedded in capitalist commodity production, but this is beside the point. It is from his concept of value that he later "puts it down" in more concrete, actually observable variables in capitalism, such as prices of production, rates of profit, real wages etc. Because, obviously and as Marx himself acknowledges, capitalists and workers do not care about their "value" production, they only care about profits and wages. What Sraffa shows, so argues Steedman, is that you can determine all these important variables from solely the conditions of production and real wages. To be sure, this does not say anything about how the conditions of production and real wages are historically determined, and what kind of class struggle is behind those changing positions.
Importantly, this is, in principle, fully consistent with what Marx wanted to argue with his concept of value. You can also "plug" value into a Sraffian model, but it wouldn't be necessary to say something meaningful (Ockham's razor!), and perhaps more stronger, along the way Steedman does show how Marx's attempt to allign value with his more concrete concepts sometimes fail to produce consistent models (in determining prices and profits, for example). But, this does not refute much of other parts of Marx analysis, nor does the model produce a conclusion that stands at odds with Marx. But it still seriously questions the function and merits of "value". For those who have struggled their way through Volume 1 of Capital, a serious blow to the theory.
Two things I find missing. First: Steedman shows that Sraffa's book "Production of Commodities by Means of Commodities" was written as a perfection of the classical model of political economy, to function as a basis for a critique of the marginalist school. Steedman then continues to use the insights to criticise Marx's value theory solely, while I would've been interested in how it debunks neoclassical thought as well. I guess the model allows, similarly to the analytical status of value, to make a determination of all the important factors in a capitalist economy without having to rely on the concept of "utility", which has been raised by Joan Robinson as equally metatheoretical as the concept of value. Indeed, Steedman makes the point that there is no "transformation problem" at all, in line with Shaikh's argument that all economic schools have a transformation problem (also the neoclassical one). But a more explicit summary of the goals of Sraffa, instead of a direct hyperfocus on the implications for Marx, would have been welcome.
Second, and more importantly, there is no engagement whatsoever why this is politically relevant. The most important intervention seems to be his refutation of the tendency of the rate of profit to fall. Steedman argues that Marx indeed made such an argument, and that it, within the Marxian value theory, is internally consistent to make. However, he then argues that it relies on the dysfunctional notion of value, and that it is unable to overcome the bridge between the concept and the real variables. And indeed, the TRPF has increasingly been used since the 70's as an important aspect of Marx's theory of crisis, and I agree that it barely has any contribution to make to an analysis of capitalism's current crisis (I'm sorry Michael Roberts). But I mean... the link with the current state of affairs is really thin.
This book is highly abstract, it can often be quite easy to get lost in Steedman's abstractions. As a result, a reread of some pages may be necessary. All in all this book can be seen as a more Heterodox approach towards the economic phenomena in which Marx proposes. Although Sraffa's critique of Marx brings with it significant changes to the way we view Marxian economics, it is not a complete rejection of the overarching edifice. If anything, Steedman poses views with challenge some notions put forth by authors such as Paul Sweezy. Steedman establishes that the rate of surplus labor is a function of the rate of profit. He operates off of the claim put forth by Michio Morishima that the rate of profit can only be positive if, and only if, surplus labor is positive. Completely rejecting the traditional notion that technological progress serves to aid the rate of profit.
Good summary of how to do sraffian analysis. Not a convincing argument that Sraffa disproves value theory or renders it obsolete.
**Edit- there's like three lines in here about international trade and how to measure labour embodied in imports that have me thinking sraffian analysis is impossible unless you have every single country's input output table...