Luigi Pasinetti
This is a very fine book that should be read by anyone who has a sufficiently strong background knowledge of linear algebra. Pasinetti is a fine writer who brilliantly exposits all aspects of the so-called "Sraffian" or "neo-Ricardian" theory using algebra and numerical examples. Pasinetti paces the book musically, showing how the concepts of Sraffian theory illuminate the problem of disaggregated production. Pasinetti makes it easy to understand what I call the Central Sraffian Theorem and why it may be wise to place it at the center of economic analysis.
Piero Sraffa
Pasinetti begins with a chapter on the precursors to the linear Sraffian system. Unlike most of these kinds of chapters, Pasinetti keeps things worth reading by using simple mathematical models instead of tedious linguistic analysis. Pasinetti expounds the basics of the old Ricardian system in aggregate and disaggregated along with its Marxian gloss. This chapter also distinguishes the production coefficients of Walras - which assume constant returns to scale - and the distribution coefficients of Sraffa which Pasinetti will work with. In the next chapter, Pasinetti moves to the simplest analyses of the so-called "Input-Output" method, going over the primary practical difficulties and introducing concepts he will use throughout the book.
The meat of the book begins in chapter three, where Pasinetti develops the linear theory of production in the mode of Sraffa, again pausing to explain how the coefficients are not necessarily the static production coefficients of Leontief-Walras. In chapter four, Pasinetti completes the analysis using both basic algebra, linear algebra and numerical examples of the Leontief-Walras case where the distribution coefficients are also the static production coefficients. This chapter introduces the conditions on which a distribution matrix may correspond to a stable productive economy: that the Perron-Forbenius eigenvalue should be less than unity. Economically, this means that the "quantity of input" should be less than the "quantity of output" with linear algebra providing precise meaning to the words in quotes even in the case of complete disaggregation.
With those four chapters as introduction, Pasinetti begins his wonderfully clear exposition of the Sraffian system. Where Sraffa's exposition was brilliant but mysterious, Pasinetti lets the theory free with it's assumptions and their reasons completely out in the open.
Essentially, Sraffa's system is a very large production network, which you can think of as a directed graph with positive weights. Sraffa tries out a few conceptual/topological assumptions about the nature of the network of production - it should be connected, the weights should positive, etc.. Assuming that the network is constant in time, Pasinetti & Sraffa can use the Perron-Frobenious theorem to find the amount of surplus production. The division of the surplus (between workers and capitalists) might seem - at first - a difficult problem. If we want to find the wages* in terms of some numeraire - gold, dollars, corn - then changing the wage rate must decrease the quantity that goes to capitalists, but not necessarily in a simple manner.
This is unpleasant, because it is not necessarily convex. This means that a Bergson–Samuelson social welfare function would not guide a social planner - not even the distributed one that we call "the market". (History of economic thought fans will recall the tie between convexity and general equilibrium was first noticed by Joan Robinson)
I had to draw this one, Pasinetti would never draw something with Samuelson in the name.
Pasinetti was able to spot an assumption even I managed to miss when reading Sraffa - that Sraffa's construction of the so-called "standard commodity" requires the physical own-rate of reproduction of the "basic commodities" that enter into the production of every good (labor, etc) must be less than the the physical own-rate of reproduction of all other commodities. I will put the Central Sraffian Theorem carefully: If the assumptions on the production network hold and prices (or wages, at least) are stated in terms of the standard commodity, then the relationship between how much excess production goes to the workers (wages) and how much goes to capitalists (profit) is linear.
Since a line is convex, Bergson–Samuelson social welfare is deterministic again. Woo. Further, Pasinetti shows that this unit for wages makes wages exactly equal to the labor commanded by the system - just as Adam Smith tried to tell you 241 years ago. If the distribution around the network really is stable for all time, as Sraffa assumes and Pasinetti assumes for now, then one can expand the distribution backwards as the sum of the history of splits of surplus product - as Marx might have told you. The Central Sraffian Theorem is sufficient to show historical materialism is coherent (though not necessarily correct).
Pasinetti then goes on to consider Marx's infamous "transformation problem" in a very helpful and unpretentious way. Pasinetti suggests that Marx's garbled account is due to to Marx's habit of moving parameters around that don't affect the production network, solving this special case and then lastly declaring the general problem solved. For instance, if we want to know the maximum level amount of excess output, it doesn't matter if we set wages equal to zero. Analyzing the system with great care, Pasinetti is able to reformulate the Central Sraffian Theorem in this way "The rate of surplus value is inversely related to the wage." (well, Pasinetti is more precise, but this gives the flavor). If all the excess production of the economy is given to the workers, the surplus value is exactly zero. This makes sense of Marxist political economy (if Sraffa's assumptions hold).
Joan Robinson
Unfortunately, no book from this school is complete without the inevitable chapter on "reswitching". Reswitching is all about taking seriously the concept of a function - is A a function of B or is B a function of A. A breezy theory where everything is linear makes everything a function of everything else - but life is not so breezy.
Pasinetti is characteristically scintillating, spreading light over this darkened field. He starts by considering three sets of worlds, which adopt three different production networks for the creation of a product. The rate of profit for a capitalist is uniform across industries (remember how Pasinetti defines profit), so the capitalist would like to be in the world with the production network that minimizes cost. However, which world that is depends on the profit rate. Therefore, profit rate determines choice of technique but choice of technique does not determine profit rate. This is the only theoretical fine point in reswitching. Pasinetti goes on to consider special cases and the general case in turn, but the result is the same, choice of technique is a non-invertible function of profit.
The upshot of all this is that the solution to the problem implicit in the Central Sraffian Theorem is the fundamental problem of the economy. If you want to know how an economy is structured, you have to know how it divides its product between its people.
In the final chapter, Pasinetti considers exogenous growth in a disaggregated Sraffian growth network. Expressing the system in terms of a standard commodity, Pasinetti finds a linear trade-off between current consumption and growth rate - just as Irving Fisher et. al. would have told you. The level of discussion is not quite as high as the well known DOSSO textbook (esp. Chapter 12), which made the knife edge transversality problem of a growing economy rather clear (of course, this was for Leontief-Walras fixed coefficients case, not the more mysterious Sraffa case). One could look at the above picture and think - with Irving Fisher - that all you need is an indifference curve. Pasinetti closes his system instead with a hypothesis on savings rates - which, obviously, are the reverse of present consumption. The hypothesis is this: workers cannot save but capitalists can. So Marxist political economy is not quite saved in the Cambridge Neo-Ricardian system. Workers have more to lose than their chains - capitalists are their bank accounts. In general, any relation between current consumption and distribution of excess product will turn the analysis of the exogenous growth case back into the static case.
This book is short, clear and eye-opening. Anybody who reads this will come out with a better understanding of economics than when they went in - no matter how much they know now. The only two flaws of the book are: 1) sometimes vital assumptions are put in footnotes and 2) there is a bit too much point-scoring against Paul Samuelson for my taste. Also, I still find the meaning of the constants in the Sraffian distribution matrix mysterious in a growing economy, but this may be just me.
A+, ten stars, book's alright.
* Pasinetti calls "wages" and "profit" the distribution of the excess product to workers and capitalists respectively.
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