(P&I) The Process Discordant

Liberty 1789

Essay. We know quite a lot about the The Process in which the Company A, B, C and D “harmonize” with their trading connections and exhibit the E-conditions with the same modality; and we know how Company A and Company C can be absorbed into the Company B modality in-process (The Food Chain).

But what if the “company” and its trading connections don’t harmonize and exhibit different modalities such as a×log(a) = α×log(b) and b×log(b) = β×log(a) with α≠β which we might expect in economies in which self-interest and the societal norms of risk aversion and bargaining practice with which we are familiar and in-accord, so to speak, are trumped by some other factors such as armed force? Or a”ruling class” whose interests and values are not the same as ours? And how far can they stretch the string (or noose) that binds us until it breaks or snaps-back and they might loose everything?

For the down-trodden we select Company A which is persistently in debt and has a modality 0<α<1/e; and for the “ruling class” we select Company C which always has lots of money but not necessarily the enterprise to earn it and exhibits a modality of 1<β. However, we cannot compare Company A or Company C within themselves because their trading connections allow and accept that modality and it is a common modality which they share and have developed in-process.

Berg Hohenburg, Germany 13th-15th Century

For example, the trading connections in Company A might not be “poor” nor necessarily are the “owners” of a Company A modality “poor”; nor is everybody in a Company C modality “rich” and we have the “castles” to show for it.

What we need to discover is when Company A can no longer deal with Company C in the sense that there is no “profit” and dealing with Company C is impossible in-process; and vice versa, when does Company C find no benefit in dealing with Company A or more poignantly is unable to derive a benefit in dealing with Company A in-process.

Company A In-Process At End-Of-Process

Figure 1: End of Process α=0.2

If Company A with modality α=0.2 < 1/e = 0.368… is in-process with its trading connections and they both exhibit the same modality, then the “profit” on the delivery of product by Company A and the receipt of the product by its trading connections is determined by the intersection of the 2nd E-condition with the N-condition; please see Figure 1 on the right.

There are more details (and proofs) in The Process End-Of Process but we can describe what happens.

“Profit” in-process is determined by the measure of Company A’s payables a”=p((a”)) and its receivables b”=p((b”)) after the “delivery of product” and the “receipt of product” both of which events occur in the “process space” of the E-conditions at a=1 and b=1 and which “co-ordinates” we need to interpret not as “co-ordinates” in the usual sense but as “an action” in the embedding space (and σ-algebra) (N) just as subtracting 1 twice from 1=p((N)) to leave 1=p((N)) needs to be interpreted as “an action” in the embedding space (N) which is implemented by the M-conditions but measured by the N-condition.

That’s All?

Moreover, the “delivery of product” is not the same as the “receipt of product” and (sensibly) the action of the first is not the same as the action of the second; for example, has anybody ever had a sense of “buyer’s remorse” or “seller’s regret” or do we just imagine these things?

Another way of thinking about that is that the money in-process is already spent and sits in “inventory” waiting for the buyer and the delivery of product and the receipt of product amounts to an exchange of payables for receivables.

On the delivery of the product, Company A would like to obtain the “maximum profit” which occurs at b=b(up) in the (b)-space which is defined by the M-condition log(a) = lim log(1+b^α)/(b^α) as b→0 but such limit does not exist in-process and a=p((a))=1/e is “pushed back” to a’ on the 2nd E-condition and the receivables set is reduced to b’ on the M-condition. But we’re not done.

To seal the deal, some of the receivables will be converted to receipts (cash) and some of the payables will be paid in order to remain in-process and that occurs at the intersection of the second E-condition and the N-condition at a” and b” respectively; and we note that in a world in which there are only payables and receivables, “cash” doesn’t count but all of these things can be calibrated to the “currency” of the balance sheet (please see The Theory of the Firm (Goetze 2006)) and even to what the stock market thinks about them (the Nash Equilibrium between “risk-seeking” and “risk-averse” investors neither of whom want to lose their money but will take a chance on a hopeful return above the rate of inflation).

Company A In-Process With Company C At End-Of-Process

Figure 2: Kleptocracy

With the same notation as in Figure 1 above, we can reduce the exchange to just a few lines and it’s noteworthy that the bottom-line is determined in the “client space”; please see Figure 2 on the right.

The N-condition which was below the M-condition in Figure 1 is now above the M-condition and although Company A might have hoped for profits at b(up) and a’, they will have to settle for profits at b” (too small to mark but in the lower right corner) and payables a” that are only marginally below the cost of the product at a=1 in the process space. Things could get worse if Company A has to buy at the “Company Store”.

Teach a man to fish. Feed him for a lifetime.

On the other hand, if we are a Company C, well-heeled and prosperous, and it is our intent or mission to “help” a Company A, the “bottom-line” is determined in the Company A modality no matter what we do; if they don’t want it or can’t use it and can’t migrate to a better modality affecting both them and their trading connections, it’s just a waste and in practice promotes “kleptomania” and corruption.

Or maybe we are the ruling class and want to get more for our money. Same story.

For more applications of these concepts please see our Posts which rely on a Theory of the Firm developed by the author (Goetze 2006) which calibrates The Process to the units of the balance sheet and demonstrates the price of risk as the solution to a Nash Equilibrium between “risk-seeking” and “risk-averse” investors within the societal norms of risk aversion and bargaining practice.

And for more on The Process, please see our Posts The Food Chain and The Process End-Of-Process.

Postscript

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