To what extent did Sraffa assume constant returns to scale in PCMC?

[Kotze]

The question is about Piero Sraffa's model in Production of Commodities by Means of Commodities. I have access to the German translation and in the translator's introduction [EDIT MORE THAN A YEAR LATER for anybody who might read this: it was actually the introduction by the publishers] it says the text assumes constant returns to scale, right after that Sraffa starts by saying he doesn't assume constant returns to scale...

After poking around for a bit I figured the model is weird (to the traditional counterfactual assumption of equalised profit rates he adds the idea of the real wage being entirely variable to "simplify" the analysis, which is exactly the kind of simplification that gives economists a bad name, surely the subsistence wage is an important constraint on real-world economies) and the writing style is atrocious, so I probably won't read it, but I do have a question.

Sraffa had written very critical about the neoclassical assumption of increasing marginal costs playing a big role in determining prices before, so did he have some implicit assumption of constant returns to scale in that book, despite his claim to the contrary?

From what I heard about PCMC it distinguishes between basic goods and non-basic goods, basic goods are those that are a direct or indirect input in the production of all goods. I heard Sraffa derives a composite standard good by ignoring all non-basic goods and mentally scaling back production of some basic goods so that the ratios that go into the composite standard good get exactly replicated, the increase of that hypothetical standard good is then considered the growth limit of the economy.

If that's a fair description: How can you make sense of mentally scaling back the production of basic goods into stable ratios of a composite standard good if your model doesn't assume constant returns to scale at least in producing basic goods?

EDIT: Derp. >_< I guess for "mentally scaling back" you can keep production as it is and just mentally throw away some of the output. Remember kids, it's harder to write about something when you haven't read it.

[ar734]

Would you mind translating that into non-econospeak?

[Kotze]

Most of the jargon is about the cost per unit between scenarios where you produce different quantities of a thing. To make sense of the terms consider that economists are used to looking over graphs which have average cost on the vertical axis and quantity on the horizontal axis, moving their eyes from the left to the right.

When economists say "constant returns to scale" or "constant average cost" or "constant marginal cost" or "costs that change proportionally" they mean the production cost per unit is the same in the compared scenarios where different quantities are produced. When economists say "increasing returns to scale" or "economies of scale" or "falling average cost" or "falling marginal cost" they mean the cost per unit is lower in the scenario(s) where a bigger quantity is produced. When economists say "decreasing returns to scale" or "diseconomies of scale" or "rising average cost" or "rising marginal cost" they mean the cost per unit is higher in the scenario(s) where a bigger quantity is produced.

The economists don't just use many words for the same concepts to make it more complicated, these actually have somewhat different usage, marginal this or that has a more short-term flavour and blahblah to scale refers to more long-term stuff usually, but that difference doesn't matter here.

Neoclassical economics refers to the mainstream introductory econ model that explains product prices and quantities by the intersection of rising supply curves and falling demand curves. How common is it in the real world that your production cost per unit goes up as you produce more? One can find examples with bottlenecks when it comes to the supply of a certain needed ingredient, so it does get very hard to produce a higher quantity, but having that as the usual assumption seems unrealistic. Sraffa was one of those who pointed that out. (I believe the reason for continuing to use the unrealistic usual assumption is indoctrination. If one's default assumption is decreasing returns to scale, one thinks less about developments towards monopolies.)

Sraffa's text Production of Commodities by Means of Commodities has that title because it doesn't present a model where materials of one category are made into a completely different set of consumer goods and that's the end of it, instead you have inputs that are made into outputs and many of these outputs are again used as inputs. Instead of supply-and-demand diagrams everywhere the text has input-output tables. An idea is presented how to identify some processes as being more important for the whole than other processes and how to mentally isolate this more important part from the rest — and it would be really handy to assume constant returns to scale here if we want to mentally fiddle with the quantities produced in that more important part. I asked for help without having read much because I suspect that the translation is poo (see first paragraph in first post) and that there might be some insights despite its unreality.

As far as the real world is concerned, I don't assume constant returns even if all inputs into producing something are varied in a way that their ratios are kept the same because we live in a three-dimensional world (http://en.wikipedia.org/wiki/Square-cube_law).

Did I miss any terms? Oh, real wage as opposed to nominal wage means the wage with effects of inflation or deflation filtered out. So when your wage goes up a bit measured in $, and there is a slight inflation so in effect you can buy the same amount as before with your wage, an economist would say that your nominal wage went up and your real wage staid the same. (In PCMC everything is counted in physical units.)

[ar734]

well, that cleared things up. according to wiki sraffa developed a neo-ricardian theory of value. it seems to me that the real issue is that mainstream economists, say, Bernanke, et al, have never accepted the original ricardian theory of value, that the value of a commodity is determined by labor.

[Kotze]

Found a paper by Ajit Sinha, who seems to be an expert on Piero Sraffa, claiming that Sraffa DID NOT assume constant returns in PCMC: Sraffa and the Assumption of Constant Returns to Scale: A Critique of Samuelson and Etula (2007) (http://cpe.oxfordjournals.org/content/26/1/61.full)