Sunday, June 30, 2013

Corporations And The Theory Of The Firm

I think the following are fairly typical aspects of a large corporation:

  • Operation of more than one plant.
  • Production of more than one product.
  • Use of large amounts of capital goods with fixed costs.
  • Production and sales in more than one country.
  • Provision of stock (also known as shares) that are traded on a specified stock exchange.

I suggest the indicated work of the following economists1 are useful to read2 in attempting to understand such organizations:

  • Joe Bain and Paolo Sylos Labini on Industrial Organization3.
  • John Maurice Clark, especially Studies in the Economics of Overhead Costs4.
  • John Kenneth Galbraith, especially his book The New Industrial State
  • Michal Kalecki on mark-up pricing.
  • Robin Marris' on managerial theories of the firm.
  • Gardiner Means and Adolf Berle, especially their book The Modern Corporation and Private Property5
  • Edith Penrose, especially her book The Theory of the Growth of the Firm.
  • Herbert Simon on the theory of administration.
  • Josef Steindl, who, as I understand it, was a follower of Michal Kalecki and did much work in Industrial Organization.

The theory of the firm, as taught to undergraduates, does not cover modern corporations and these economists. I do not claim that the theory cannot be expanded. Important issues include knowledge, organization, and competencies needed to expand into adjacent products and to expand the number of plants.

  1. Some of these authors or their works I only know of through secondary literature.
  2. Bruno Rizzi's 1939 book, La Bureaucratisation du Monde, occasioned an internal debate among followers of Trotsky and supposedly foretold some of the themes in some of the following works.
  3. Franco Modigliani's 1958 paper, "New Developments on the Oligopoly Front", reviews an important book by each member of this pair of authors.
  4. I do not want to claim Piero Sraffa showed how to correctly account for overhead costs; do corporations have sufficient data to set up his equations in their full generality? Do they not commonly adopt heuristics that sometimes, but not always, deviate from his equations?
  5. As I understand it, this book deals with, among other issues, the separation of ownership and control.

Monday, June 24, 2013

Two Systems Thinking Models: Mind Your Ps and Qs

Figure 1: A Market Mediated By Quantity
1.0 Introduction

I have been examining John D. Sterman's textbook, Business Dynamics. Sterman is a chaired professor at the Sloan School of Management and director of the System Dynamics Group at the Massachusetts Institute of Technology (MIT). The System Dynamics Group was founded by Jay Forrester, and the group is continuing research in his tradition.

This systems thinking approach provides tools for visualizing the hypothetical causal relationships and structures of dynamical systems. They show models in which hypothetical causal relationships, the distinction between stocks and flows, and temporal lags can be postulated and displayed. Software for specifying model structures provides capabilities for simulating dynamical behavior. These tools are directed towards managers who may not fully understand complex dynamical systems. The diagrams are intended to package and facilitate informal discussions about models, including desired system states. Simulations for the resulting models give some understanding of possible dynamics.

Sterman's diagrams and associated tools are one approach. Researchers in related disciplines have proposed other visual languages, with varying degrees of formalism for the syntax and semantics of the elements of such diagrams. I think of system block diagrams and the Unified Modeling Language (UML), for instance. Likewise, a number of tools exist (for example, Steve Keen's Minsky system, MathWorks' Simulink, Berkeley's Ptolemy system, and tools supporting Model-Driven Architecture and Model-Driven Development) for processing corresponding system specifications for various purposes.

2.0 "Tell Me What the Wires Do"

I might as well explain a bit about selected components of what Sterman calls Causal Loop Diagram (CLD). CLDs contain curved arrows connecting variable names. The arrowheads in CLDs are annotated with either a plus or a minus sign. Arrowheads indicate causal relations. Suppose an arrowhead points from the variable X to the variable Y:

  • Positive Link: If the arrowhead is labeled with a plus sign, Y increases when X increases, all else equal. In other words, ∂Y/∂X > 0.
  • Negative Link: If the arrowhead is labeled with a minus sign, Y decreases when X increases, all else equal. In other words, ∂Y/∂X < 0.

A CLD may contain circles with arrows, where each circle contains either the letter B or R, indicating, respectively, either a negative (balancing) or positive (re-enforcing) loop. The dynamical behavior of a system containing a single balancing loop is to approach an equilibrium point. On the other hand, a system containing a single re-enforcing loop exhibits exponential growth. The dynamical behavior of a system containing a combination of interacting balancing and re-enforcing loops, especially if it is non-linear, is more difficult to predict without simulation.

3.0 Two of Three Models

Since Sterman's textbook is directed towards business managers, he provides some examples from economics. In Section 5.5, he presents three models of a single market:

  • Demand and supply responding to price (Figure 5-26 in Sterman (2000), Figure 2 below)
  • Orders and production respond to queues (Half of Figure 5-27 in Sterman(2000), Figure 1 above)
  • Customer base and service quality interact (Other half of Figure 5-27 in Sterman (2000), not shown here)
Figure 2: A Market Mediated By Price

I think Sterman's model of demand and supply mediated by price mixes classical and neoclassical ideas. One should read "demand" and "supply" in Figure 2 as, by an abuse of language, actually referring to the quantity demanded and the quantity supplied. We see that this model postulates that firms increase the quantity supplied for industries in which profits are high, that is, when the price increases more above the cost of production. This is a classical idea, to be found in Adam Smith. The model also postulates that an increase in the quantity demanded puts upward pressure on price. I think how demand is conceptualized in this model, including the role of substitution in consumption, is close to how demand functions are presented in neoclassical textbooks.

Figure 1 shows a model in which firms respond more to increased demand by changes in the level of production, not by changes in price. If price were to be inserted into this model, price would be appropriately modeled by theories of administered, full-cost, or mark-up pricing.

I am not sure I agree with all of Sterman's economic examples. But the above picture of markets fits a Post Keynesian view, articulated by Michal Kalecki, that different microeconomic theories are needed to describe the prices and quantities for markets for raw materials, industrially-produced goods, and services. Do business schools provide a somewhat greater opening for non-neoclassical economics than supposedly leading economics departments?

  • John D. Sterman (2000). Business Dynamics: Systems Thinking and Modeling for a Complex World, Irwin McGraw-Hill

Wednesday, June 19, 2013

On "Substitutability"

"[The] validity [of the Cambridge Criticism of neoclassical theory] is unquestionable, but its importance is an empirical or an econometric matter that depends upon the amount of substitutability there is in the system. Until the econometricians have the answer for us, placing reliance upon neoclassical economic theory is a matter of faith. I personally have the faith; but at present the best I can do to convince others is to invoke the weight of Samuelson's authority." -- C. E. Ferguson (1969) [as quoted in Carter (2011)].
1.0 Introduction

In this post, I describe two different meanings of "substitutability", as used in the literature and economists' remarks on the Cambridge Capital Controversy1.

2.0 Joan Robinson's Criticism

Imagine two island capitalist economies, Alpha and Beta, each in a steady state and with access to the same technology. Suppose for some reason, the distribution of income happens to be different in the two islands. Then the capitalists on the islands will, maybe, have adopted different techniques of production and be producing a different mixture of commodities for final output. Consequentially, the structure of capital goods, both in composition and in quantities, will differ between the two islands.

An (illegitimate) thought experiment is to imagine the distribution of income slowly changing from as it is on one island to the distribution on the other. One might mistakenly consider the capital equipment slowly changing through the composition appropriate to imaginary intermediate islands. This claim ignores the reality of what Joan Robinson called historical time. One is treating a process occurring in time as if it occurring in space, ignoring that past bygones are gone, and assuming no difficulties exist in getting into equilibrium.

Neoclassical2 economists frequently ignore the structure of capital equipment and the plans of the entrepreneurs. One meaning of "substitutability" is the assumption that capital goods can be instantaneously taken apart and reassembled to be appropriate for whatever equilibrium is being considered. The tranverse from one equilibrium to another is abstracted from. Robinson satirized this meaning of substitutability by designating the capital good in, say, the Solow-Swan growth model with such names as "ectoplasm", "leets", and "mecanno sets". Post Keynesians, including Sraffians, are generally suspicious of this approach. (Any fans of Austrian school economists want to chime in in the comments?)

3.0 Substitutability and Smooth Microeconomic Production Functions

Another meaning relates to the smoothness of production functions. One might say substitutability exists when derivatives (including, second, third, etc. derivatives) exist for all production functions. That is, substitutability exists in these examples, but not in these ones. (But what would you say about this one, where the cost-minimizing technique varies continuously with the interest rate, and output and each capital good are produced with fixed-coefficients?)

As far as I know, capital-reversing, for example, is consistent with substitutability, in this sense of smooth production functions. I, too, will invoke the weight of Samuelson's authority, even though I reject it in the former case. I would like, however, to see an explicit numeric example.

4.0 Conclusion

I believe C. E. Ferguson was referring to my section 2 meaning of "substitutability". That is, when neoclassical economists claim that Sraffians rely on a lack of substitutability for their critique of neoclassical economics, they should not be objecting to a lack of differentiability of microeconomic production functions.

  1. Other usages are ignored in this post. For example, J. R. Hicks' "elasticity of substitution", as used in his mistaken Theory of Wages (1932), is not treated here.
  2. As far as I am concerned, "neoclassical" is a meaningful and appropriate word in this context.
  • Scott Carter (July 2011). C. E. Ferguson and the Neoclassical Theory of Capital: A Matter of Faith, Review of Political Economy, V. 23, N. 3: pp. 339-356

Monday, June 17, 2013

Elsewhere, On Neoclassical Economics

  • Noah Smith complains about the supposed overuse of the label.
  • Alex Marsh comments.
  • Matias Vernengo responds.
  • Lars Syll responds, including in pictures. Also, see here.
  • I wrote much of the wikipedia article, albeit not the introduction. And some stuff in it I now disagree with. I also wrote much of the Wikipedia article on Classical economics, and the subsection of that article is especially relevant to a Sraffian perspective on neoclassical economics.
  • Daniel Kuehn shares some thoughts.
  • David Ruccio comments.
Update: Added some links.

Friday, June 07, 2013


These have been written by authors who have not acknowledged their authorship. (I have written many of them myself.)

John Maynard Keynes
Created Bretton Woods system
The theory works

Michal Kalecki
Macro with markup pricing
Empirical success

Nicholas Kaldor
Nonlinear business cycle
Generates chaos

Lorie Tarshis
Elements of Economics
Met McCarthyism

Richard Goodwin
Tenureless at Harvard
Among best of the best

John Kenneth Galbraith
The world listened
Not economists

Joan Robinson
Predicted stagflation
Bastard golden age

John Hicks
Renounced IS/LM
Post Keynesianism

Nicholas Kaldor
Defeated Milton Friedman
Endogenous money

Paul Davidson
Explains historical time

Post Keynesians
Kicked out of Rutgers
Alfred Eichner died

Wynne Godley
Invents Sectoral Balances
Predicts Crises

The genius of Keen
His splendid model
Remains unrecognized

Post Keynesianism
Destroyed Reinhardt and Rogoff
No surprises here

Monday, June 03, 2013

A Continuous Time System Block Diagram For Nicholas Kaldor

A System Block Diagram For A Business Cycle Model

In this model of business cycles, two state variables, Y(t) and K(t), represent national income and the value of the capital stock, respectively. These state variables are each specified by a differential equation. In the above block diagram, I have adopted a notation from Steve Keen. The triangles in the upper-right and lower right equate the integrals of their inputs, over time, to their outputs. In other words, the following differential equations obtain:

dY/dt = α[I(t) - S(t)]
dK/dt = I(t) - δK(t)

You can compare and contrast this continuous-time representation of a dynamical system with its analogous discrete-time version.

This is a multiplier-accelerator model that allows for the economy to normally be out of equilibrium. An economic interpretation1 of the model is that entrepreneurs have some sort of common opinion about the level of economic activity they expect in this nation's economy. And they have an opinion about the total value of capital stock that they believe is needed to sustain that activity. When these expectations are realized, this dynamical system is in an equilibrium. The model shows that when the economy has more activity than expected, entrepreneurs tend to increase the capital stock more rapidly, and vice versa for when activity falls below the expected level. This tendency is a non-linear relationship. Maybe, the more extreme the difference between the actual level and the expected level is, the less likely entrepreneurs are to expect the actual level to continue.

Neither interest rates nor prices are modeled here. Such modeling might be justified by the claim that the income effects in the model overwhelm the effects of prices. At any rate, this model does not contain an aggregate production function. Capacity can be operated either above or below the rate that was desired when the capital equipment being evaluated was installed. If the value of the capital stock falls below the expected level, entrepreneurs tend to increase investment, and vice versa for when the value of the capital stock rises above the expected level. (I think of the depreciation of the capital stock shown in the model as an accounting heuristic, not a physical decay.)

I am not putting forth grand empirical claims. To me, this model is of mathematical interest. It illustrates how non-linear economic dynamics can be generated endogenously. A source of continuous external shocks is not needed2.

Unlike in the discrete-time case, I do not see how the continuous-time model given here can generate chaos. Trajectories in the two-dimensional state space are smooth, with no gaps. They cannot intersect. So, I think, this continuous-time model can generate cycles, but not strange attractors3. Another difference between discrete-time and continuous-time systems revolves around the details of stability analysis4.

Anyways, the graphical specification of the Kaldor model, given in this post, is suitable for numerical exploration in Steve Keen's software, as I understand it.

  1. As I understand it, mainstream macroeconomists currently reject the rough-and-ready microfoundations I provide here. They insist on formal microfoundations, even though their preferred formal treatments are just nonsense.
  2. Some more mainstream economists seem to be willing to make this points in Overlapping Generations (OLG) models. I am willing to explore the mathematics there, despite the absurdity of assuming investment is driven by intertemporal utility-maximization of consumption.
  3. The logistic equation is an example of a one-dimensial, discrete-time, chaotic dynamical system. Off-hand, I cannot think of a continuous-time chaotic system with less than three dimensions.
  4. In discrete-time systems, one analyzes the stability of a fixed point by analyzing whether the eigenvalues of the system, linearized around the fixed point, are inside or outside the unit circle in the complex plane. In a continuous-time system, one looks to see if the eigenvalues are to the left or the right of the complex axis, if I recall correctly.