Wednesday, April 25, 2018

The Curious Rhythm of the Productive Economic Sector

 \((1+k_k) n f_w \preceq c + g \pm k_p   \)
"It takes money to make money"  entrepreneur's adage

When I think of money, I make an immediate connection with property as in 'property of all kinds'. My mind wants to stop there, leaving property connected to money.  Period.

Perhaps the reader has the same narrow scope. If so, this article is designed to broaden that narrow perspective. This article will explore logical links between money, value, property, production, and time. It turns out that (in the actual world) they are all linked in a tight dance with a sensitive rhythm*.

Creating a mathematical envelope

Property has value, and money can buy property. Economist can all agree on that single connection.

Economist might not so easily agree that this single connection allows us to equate money with property in a barter fashion. I think we can say that one gizmo \(g_z\) has a value of \(x\) money units, denoted \(xM_u.\) We can write that as \[g_z=xM_u.\]This equation gives us two ways of describing one gizmo, \(g_z\) or \(xM_u.\) The math does not care what a gizmo or money actually represents. It only says that a link has been established between two symbols.

This connection between gizmo and money opens the possibility that money can be created by making gizmos. The reader's reaction to that statement is probably an objection that only banks can 'create money'. But think of the possibilities if someone with-no-money can bring together an organization to produce a product. If selling the product brings more money than the cost of production, the organization will 'make money'. Not 'make money' in the sense that banks make money, but 'make money' in the sense that money is transferred from others into the control of the organization.

One barrier to bringing this concept to fruition is the acquisition of initial capital. The old adage "It takes money to make money" holds true here. Money must be paid to workers and part suppliers during production. Preexisting money must be acquired before producing complicated items that take considerable time in production.

Is this concept micro-economic or macro-economic?

The productive firm must bring together more than preexisting money. Several macro-economic sectors must work together to accomplish a task of product construction and sale. We have a situation where a single entity (the micro-economic productive firm) is fractionally organizing the economy in a macro-economic way.

And let's face it--any member of any sector has the ability to disrupt or delay the workings of this prospective productive machine.

Let's make a gizmo (with a little math)

Let's think about producing a gizmo. Just to make the task easier, let's think about making a complicated gizmo that requires a lot of workers to make, and requires a lot of time to complete.

It is easy to see that we need workers to build a gizmo. These workers need to be paid on a regular basis, which explains the predicted need for preexisting money. Parts and a host of other things would also need payment with money. Money for this purpose, often called risk capital, can be borrowed (from a number of sources). The borrower will expect to pay a rent (often an interest charge) for any money borrowed. This rental cost is an ordinary expense for the productive organization.

Mathematically speaking, we can describe the cost of construction of our gizmo \(g_z\) in a very general way as \(g_z \mapsto k_b + n\) where \(k_b\) is borrowed money and \(n\) is hours of labor**. This description is not an equality. To build an equality that describes actual cost we need to adjust hours of labor into terms of money, thus fulfilling the worker's adage "Time is Money". We also need to adjust the borrowed money term using the rental rate to build-in the effective expense of capital. We define the labor adjustment rate as \(f_w\) and the rental adjustment rate as \(k_k\).

In a very general way, we can write our gizmo production cost as

(1)      \(g_z=(1+k_k) n f_w. \)    ***

We could make the equation more exact by including exact units and a limiting time period but that would go past the scope of this article.

Close the envelope with sales

 The goal of our productive firm is to 'make money'. Construction of the gizmo so-far has done nothing but cost money. This method of making money is obviously risky.

If we recognize this risk as a certainty, we can safely assume that expenses are very unlikely to equal income from sales. Rather than expecting sales to equal cost in general, the expectation should be for error between plans and reality. The challenge for the productive firm is to make this error favorable to them so that a profit \(k_p\) can be recorded and the firm can in reality make money.

We close the envelope by assuming that the general public \(c\) and government \(g\) will buy this product. [We make no assumption about where money for purchase will come from, only assuming that money is available.] Assuming that customers pay the price in money, we can almost complete our mathematical envelope. I say "almost" because it is not clear mathematically that production must precede sales if we simply equate income with expenses and profit. To make that time-sequential process mathematically clear, we will replace the equality symbol with the "proceeds or equals" symbol \( \preceq .\) **** The reader should understand that production proceeds sales and the final profit calculation. This is the sensitive rhythm previously mentioned. With all this in mind, we write

(2)       \((1+k_k) n f_w  \preceq c + g \pm k_p. \)

Equation 2 represents the flow of money for the construction and sale of any property. The actual physical property flows from left to right as does money used to finance construction. While the order of events is shown, the time required to accomplish all this activity is not represented here.

In real world accounting, Equation 2 is computed by taking data from a time period, usually one year. This practical practice hides time sequential dependency and plays havoc with theoretical models. We will not discuss the consequences of this theoretical gap here but will keep the possibilities in-mind for future discussion.

Rehashing sectors

Five commonly defined economic sectors have been included but their location in the equation may be obscure. Household \(c\) and government \(g\) are easy to locate as is a very stylish version of labor \(n.\) The entire equation is about the productive entity making a gizmo but only the profit term \(k_p\) is mathematically present.

The pure capital owning sector, denoted  \(K,\) is represented by the interest term \(k_k\) and is nearly invisible. Hidden is the risk capital that this sector provided to pay labor. Hidden is the decision to take a risk and build our gizmo. Hidden is the discontinuity that a negative decision by a capital provider introduces into beginning the process. Whether privately owned or government owned, upfront risk capital proceeds all production.

We can sum the sector rehash with a math function. I think we can say that a single productive firm \(P\) can be described with a macro-economic function \[P = F(c,g,K=k_k,n,P=k_p) \]scaled to single firm size.

Should we call this a "five sector rhythm model of production"?

Confirm expansion of the envelope into macro

Equation 1 was clearly developed by using micro-economic thinking using macro-economic interactions. Equation 2 expands the model to include the flow of money during both production and consumption. There is no reason that the equation can't be expanded to the pure macro-economic level by adding product production of all kinds. The equation should apply to both privately and publicly owned productive firms. The only difference between the two ownership models is the emphasis on who owns what and who makes decisions.

A Thought for the Future

The "proceeds or equals" symbol is potentially very useful to the study of economics. It enables an ability to mathematically show time sequences or mutually interacting flows, and even circular flows if we begin and end the equation with the "proceeds or equals" symbol. For example, to show symbolically a circular money flow in Equation 2, we could write

(3)      \(\preceq  (1+k_k) n f_w \preceq  c + g  \pm k_p \preceq.  \)

In text, we could indicate whether the intent was to focus on macroeconomic money flows or micro-economic flows.

This example mathematically expresses a money flow from production to consumer and back to production. It does not carry any indication of the velocity of the flow. It worth mentioning again that this circular flow is very sensitive to the decisions of sector members, any one of whom can disrupt the flow to the extent of his abilities.

[This flow of money back to production is VERY important. It it this return flow that allows the production sector to repay the initial loan that enabled the entire productive effort. If we think about it, we can see that a speedup in the velocity of production and money flow allows multiple items to be produced and sold for the same amount of startup money. This can be considered as an increase in the efficient use of capital, thereby reducing overall cost of production. This is one factor favoring mass production.]


We found that we can create a symbolic representation of the micro-economic or macro-economic productive event with five united sectors. The productive event takes place over time with a sequential rhythm.

It is tempting to overlay the five sector rhythm model with the hyperinflation occurring in Venezuela. While little confirmed data is available from Venezuela, it appears that government has preempted production decisions, causing disruption in the profit learning sequence. Government may be acquiring money for purchases not by working at productive effort (through taxes), but by borrowing money as if government was, in itself, a producing firm. This practice distorts the balance between customer need, willingness to work, and relative perceived value of natural resources. This harmful practice may be more obvious to foreign economies than to the borrowing economy, triggering sharp decreases in currency value.

The commonly used equality symbol \( = \) does not give any hint of the time-sequence-dependent relationships typically found in the study of economics. Economic discussions may be enhanced with increased use of the "precede equals" symbol.

Mainstream economist often mistakenly claim that profit is the reward of capital. The reward of capital is interest. Profit is the reward of the productive firm for acting to organize production.


* This article, emphasizing the importance of circular money flow, is a follow-up to a previous article on the same subject and includes several enhancements. Neither article would have been written but for a series of articles written by Brian Romanchuk. His "Curious" series of four articles explored the logic behind DSGE models in an unflattering way.

** The reader may not be familiar with the mapsto \( \mapsto \) symbol. The intent is to indicate that there is a relationship between the left and right side of the equation but no reason to expect equality.

***  \(g_z=nf_w + k_knf_w =(1+k_k) n f_w. \)

**** When we write \(x \preceq y,\) we intend that \(x\) precedes or equals \(y.\) TeX and LaTeX symbols can be found here.

(c) Roger Sparks 2018

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