*This is the second part of the series started with this post. It is well worth it to begin by reading the first part, as it lays the foundational framework for the topics discussed in this post. If you would like to skip the math, scroll down to From Natural Systems to Economic Systems.*

Up to this point we have only outlined events *i* and *j* in vague terms. We will now narrow our focus to only transfers or transformations. Event *i* will signify that some quantum of medium is transferred or transformed from component *i*. Correspondingly with *j*. Aggregation of all quanta both leaving *i* and entering *j* during a unit of time — the transfer or transformation from *i* to *j* — will be signified by T_{i j}. Thus, T_{i j} might represent the flow of electrons from point *i* to point *j* in an electrical circuit; or the flow of biomass from prey *i* to predator *j*; or the the transfer of money from sector *i* to sector *j* in an economy.

T_{i.} will represent everything leaving *i* during the unit time interval, and T_{.j} will represent everything entering *j* during the same duration.

The above equation represents the total activity of the system, or “total system throughput”.

These definitions allow us to estimate all the probabilities defined previously in terms of their measured frequencies of occurrence. Thus:

You can then substitute these estimators in for *p* in all of the previous equations (H = X + φ), respectively.

Further, we need to impart physical dimensions to the measures using the scalar constant, *k*. Accordingly, we will scale each index by the total system throughput, T_{..}. We will give them all new identities.

The “capacity” for system development is given as:

The scaled mutual constraint, which we will call the system “ascendency” is given as:

And the scaled conditional entropy, named the system “reserve” is given as:

Uniform scaling does not affect decomposition, which now appears as;

**From Natural Systems to Economic Systems**

The above equations states that the capacity of a natural system to undergo change is given by it’s ability to both exercise sufficient power as to be able to sustain itself over time, and it must possess a reserve sufficient to allow flexible reactions to novel disturbances. In this model, these two features are literally complementary. Thus, we can see in the figures below^{[1]} that given an ecosystem with a total carbon throughput of 102 mg Cm^{-2}y^{-1} there arises multiple channels by which carbon flows through the ecosystem. These alternative channels give the system the reserve capacity needed to survive a shock to the most efficient transfer means.

**Figure 1:** Three pathways of carbon transfer between prawns and alligators.

**Figure 2:** The most efficient pathway in Figure 1 after elimination of other pathways.

**Figure 3:** Possible accommodation by turtles and snakes to the disappearance of fish as intermediaries.

In our graphical examples above, we can see that **Fig 1** represents the optimal balance of efficiency and robustness. We can see that carbon throughput is more efficient in **Fig 2** and less efficient in **Fig 3**. However, if **Fig 2** were to experience a catastrophe (like a disease affecting fish), all transfer between prawns and alligators would be affected in direct proportion. Given a robust population of snakes and fish, it is possible that these pathways would buffer the loss of fish in the ecosystem. In terms of the equations above; if snakes and turtles are present, rather than total system collapse, throughput falls modestly, ascendency falls marginally, and reserves (being the chief casualty) falls by almost half. Thus our system adapts to buffer performance (A) by expending reserves (ϕ).

This brings us to our current money system, which is a monopoly of state issued legal tender — with stiff barriers to entry to any complementary system. It is exemplified best by **Fig 2**; a widely used system which places utmost importance upon efficiency. However — and of course this is not theory, both the Great Depression and Great Recession bear this out — in the event of any monetary disturbance, you have total system collapse. And because the monopoly of our money system has relegated all “second best” systems (like barter, or gifts in kind) to marginality, it lacks the reserve capacity to continue functioning at its previous level. In economic terms; assuming __no intervention__, if M*V in a given economy falls, then wages and prices must fall proportionately. The economy then begins growing again from the new, lower level of output. Much like our ecosystem (if it survived) would begin growing again at a lower level of throughput once the population of prawns was sufficiently high, and alligators sufficiently low.

However, given a robust complementary currency, an economy would be given the reserve capacity to weather a catastrophe in its most efficient throughput mechanism, as throughput and ascendency would not fall nearly as much — and the economy could fall back on its reserves. Again, this is not theory, but has been shown to work this way. Complementary currency systems around the world have likely (as I have not surveyed them) allowed people within certain communities to better weather the current global recession. Of course they did not get so lucky due to “keeping money in the community”, quite the opposite — complementary currencies buffer communities from a fall in M*V by supporting V, and thus sustaining an adequate flow of ‘legal tender’ through the community to sustain a certain level of aggregate demand.

In the recent recession, businesses throughout the economy faced a tough time due to a fall in M*V exacerbating problems in the financial sector, cutting off their supply of credit through traditional lending channels. Had the US a robust B2B currency (like the Swiss WIR), actively participated in by businesses throughout the economy, businesses could have turned to eachother to support the lending that they needed to continue growing — and our recession would likely have been much milder.

— — — —

**Note:** Our recent recession would also have been milder had the Fed kept NGDP growing at a rate consistent with previous trend as well. After all, a central bank has never failed to hit a nominal target. However, as is always the case, greater diversity would *still* have helped cushion even a the mild recession that would have resulted. Instead of grappling with 6-7% unemployment from 2007-2008Q3, we could have been dealing with 4-5%, which is not too shabby given we are stuck over 9% right now.

____

^{[1]}Ulanowicz et. al., 1996

Niklas, I cannot recall because you blog with others at Modeled Behavior: Are you on the Scott Sumner NGDP targeting bandwagon?

I ask because you’ve got the bit in here about the Fed keeping NGDP at a constant rate.

Tom, yes, I’m a proponent of NGDP level targeting.