Is the theory of a falling profit rate valid?

Marx's theory of the falling rate of profit makes two main appearances in his work. The first is in Chapter 25 of Capital Volume 1, entitled: The General Law of Capitalist Accumulation. It is further developed in Part III of Volume 3 of Capital, entitled The Law of the Tendency of the Rate of Profit to Fall. In this paper I will outline the structure of the theory presented in these two volumes of Capital. Following that I will look at some criticisms that have been levelled at it. I will go on to argue that the criticisms are based on a misunderstanding of some of the dynamic causal mechanisms that Marx assumed. Following on from this I shall present a dynamic solution to the equations of accumulation and show under what circumstances these lead to a falling rate of profit. The dynamic model will then be used to analyse the trajectories of some contemporary capitalist economies and to help understand the current structure of the world economy

Marxian Reproduction Prices Versus Prices of Production: Probability and Convergence

I shall argue two main points. The first is that although Marx is conventionally taken to have formulated two different theories of price in the the three volumes of Capital, labour values in volume I and prices of production in volume III, there is actually a third theory, hidden inside the reproduction schemes of volume II. This theory is not explicit, but can be logically deduced from the constraints that he presents on simple reproduction. It is not a theory of individual prices, but a theory of relative sectoral prices. I will go on to argue that this theory of sectoral prices allows us to make probabilistic arguments about the relative likely-hood that either production prices or labour values will operate at the level of reproduction schemes. This paper provides a measure on the configuration space associated with Marxian prices of production and labour values. By use of random matrix techniques it shows that the solutions space associated with prices of production is similar to that associated with classical labour values. In the latter part of the paper, a sample of reproduction schemes is simulated over time, under assumptions of capital movement, to see whether such systems dynamically converge on prices of production. It is found that some converge, and some fail to converge

Mises, Kantorovich and Economic Computation

An article that reviews the work of Kantorovich in the light of von Mises claim that rational calculations were impossible without markets. It gives a tutorial introduction to the use of Kantorovich's methods, compares his approach to that of Dantzig. An assesment is given of the extent to which new interior point methods of linear programming strengthen or weaken Kantorovich's claims.Kantorovich, Linear-programming, von-Mises

Humans, robots and values

The issue of machines replacing humans dates back to the dawn of industrialisation. In this paper we examine what is fundamental in the distinction between human and robotic work by reflecting on the work of the classical political economists and engineers. We examine the relationship between the ideas of machine work and human work on the part of Marx and Watt as well as their role in the creation of economic value. We examine the extent to which artificial power sources could feasibly substitute for human effort in their arguments. We go on to examine the differing views of Smith and Marx with respect to the economic effort contributed by animals and consider whether the philosophical distinction made between human and non-human work can be sustained in the light of modern biological research. We emphasise the non-universal character of animal work before going on to discuss the ideas of universal machines in Capek and Turing giving as a counter example a cloth-folding robot being developed in our School. We then return to Watt and discuss the development of thermodynamics and information theory. We show how recent research has led to a unification not only of these fields but also a unitary understanding of the labour process and the value-creation process. We look at the implications of general robotisation for profitability and the future of capitalism. For this we draw on the work of von Neumann not only on computers but also in economics to point to the {\em real} threat posed by robots

Array languages and the challenges of modern computer architecture

There has always been a close relationship between programming language design and computer design. Electronic computers and programming languages are both 'computers' in Turing's sense. They are systems which allow the performance of bounded universal computation. Each allows any computable function to be evaluated, up to some memory limit. This equivalence has been understood since the 30s' when Turing machines (Turing 1937) were shown to be of the same computational power as the λ calculus

Optimising Simulation Data Structures for the Xeon Phi

In this paper, we propose a lock-free architecture to accelerate logic gate circuit simulation using SIMD multi-core machines. We evaluate its performance on different test circuits simulated on the Intel Xeon Phi and 2 other machines. Comparisons are presented of this software/hardware combination with reported performances of GPU and other multi-core simulation platforms. Comparisons are also given between the lock free architecture and a leading commercial simulator running on the same Intel hardware

Heinrich's idea of abstract labour

The article reviews Heinrich’s An Introduction to the Three Volumes of Karl Marx’s Capital. It questions three main features of Heinrich’s work: its defence of teleology, its view that no empirical proof is needed of the labour theory of value and its particular monetary interpretation of the theory of value. This approach, it argues, is anti-scientific

Can we meaningfully speak of changes in price under the regime of changes in techniques?

This paper presents a simulation exercise on Sraffa's system under various types of technical changes to show that the direction of changes in prices of commodities is contingent on the choice of the numeraire. Thus, such a comparison of prices in two systems turns out to be meaningless. This result points to the arbitrary nature of the neoclassical supply functions, as they inevitably compare prices across several Sraffa systems on the basis of an arbitrarily chosen numeraire. We anticipated such a result from our reading of Sraffa as part of his 'prelude to a critique of economic theory'