## 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?

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