atheorist (atheorist) wrote,

bond graph modeling of businesses and economies

In bond graph modeling, the simplest way that two subparts of the whole can be connected is called a bond. The bond has a "typical power direction", pointing from one part to the other, represented by a arrowhead (traditionally, actually a half-arrowhead). It also has a "causal stroke", which can be on the same end of the bond as the arrowhead or the opposite end.

Someone called Brewer suggested that bond graphs could be used for economic modeling. The bond represents repeated sales of something from one entity to another entity. The arrowhead indicates which entity is selling and which is buying. The causal bond indicates which side is setting the price (the other side gets to set the order rate e.g. units per year). Brewer's papers are hard to find, but I think I understand essentially what was in them.

A simple model of a firm might have three "ports" - bonds piercing the envelope of the firm. One port is selling the finished product to customers. Another port is buying raw inputs from the raw market. The third port might be buying tools or machinery necessary to transform raw goods into finished goods. Internal to the firm, there might be stockpiles of raw and/or finished goods. The stockpile acts as a component that integrates order flow (or difference in order flow). That is, the raw stockpile contains the integral of the raw purchases minus the raw used up. The business might have a rule for setting the price based on the level in the stockpile. This kind of component is called a "C" component in bond graph modeling; in the electrical domain it would be a capacitor, and in the mechanical domain it would be a spring.

For simplicity, let's assume that we run the machinery continuously. That means that the machinery sets a work rate, how fast raw is transformed into finished. If finished is more valuable than raw, then the machinery accumulates profit. If we continuously reinvest the profit in more machinery, then the level of machinery is the integral of the difference in price between finished and raw. This kind of component is called an "I" component; in the electrical domain it would be an inductor, and in the mechanical domain it would be a mass with inertia.

If this firm starts buying a lot of raw (and possibly machinery), the raw and machinery markets may shift. If we simply model increased demand immediately causing increased price (via elasticity), then we can model the raw market as a curve that given a price, tells what the rate of supply be. In the opposite direction, we could model the machinery market as a curve that given a rate of purchases, tells what the price is. This kind of component is called an "R" component. In the electrical domain it would be a resistor, and in the mechanical domain it would be some kind of friction.

The bond graph that I'm discussing looks like this:

Doran and Parberry wrote an "Emergent Economies" paper, and Lars Doucet reimplemented it and published his code.

The example of "an economy" in that paper has essentially five sectors, farmers, woodcutters, miners, refiners, and blacksmiths, and five goods, food, wood, ore, metal, tools. Roughly speaking, the farmers produce food using wood as a raw material, and the woodcutters produce wood using food as a raw material, but both depend on tools being ambiently available. So given tools, the farmer-woodcutter loop is a over-unity engine of growth. Similarly, the miners produce ore, the refiners turn ore into metal, and the blacksmiths turn metal into tools, but all depend on food being ambiently available. So given food, the miner-refiner-blacksmith loop is another over-unity engine of growth.

It would be straightforward to duplicate the bond graph above five times and wire it together to form a bond graph model of the whole (tiny) economy. I think trying to "polish" the bond graph model against an agent-based simulation of that economy would be interesting; they're very different formalisms.

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