A New Visual Representation of the Process of Economic Production and Consumption

February 12, 2018

 

 

 

Please Note: The version of the report below does not include diagrams.

 

A version with diagrams is available for viewing/download in a fully formatted PDF  HERE

 

 

 

A New Visual Representation of the Process of Economic Production and Consumption

 

Ian Brinkley

2/11/2018

 

Forward:

 

This report is intended to supplement my recently completed essay on economic theory titled “Economic Theory: A Contribution”. However, this report is not limited for consumption to those who have read that essay; the main points of connection between the two writings being the problematic issues with the bar-diagram model of economic production and consumption, as opposed to the positive elaboration of the new model presented in this report- a new model which overcomes those problematic issues to some extent. The reader is invited to skip to part II of this report if there is lacking a desire to read a summary account of the kinds of problems which this author found with the bar-diagram- problems which provided the impetus to develop the new model presented here, in part II.

 

In the future, I hope to furnish an essay on economic theory which brings together, in a single comprehensive elaboration, the model introduced in this report, with the essential content of the cited essay- that in such a way as to altogether avoid the necessity of addressing the problematic complications arising from the use of the bar diagram model.

 

Introduction

 

A visual representation of the process of economic production and consumption has been provided by those who have made use of “bar-diagram models.”

 

[Figure 1]

 

While variations in the specific characteristics of such models may be found to exist in presentations by different writers on the subject of economic production and consumption, the general characteristics of the models are the same. These general characteristics provide the models incorporating them with heuristic usefulness to the purpose of rationally considering economic consumption and production (or input/output). However, these general characteristics also, at the same time, limit the usefulness of those models to that purpose.

 

I have addressed some of these matters in a report which I authored earlier titled “Economic Theory: A Contribution.” The report can be found at the link in the footnote.[1]

 

 

I - General Characteristics of The Bar Diagram and Associated Problems

 

Below are listed the primary general characteristics of the bar-diagram representation, along with the problems which arise from them.

 

Quantization

The bar-diagram visual representation model of economic consumption and production can only represent the total production and total consumption as idealized over discrete intervals of time, as opposed to continuously. That is, the model can only correspond to a hypothetical situation in which a total aggregate of goods, say O1, available to a society at a point in time, say T1, is consumed and completely used up by a latter point in time, say T2, and that over that time interval (from T1 to T2) another aggregate of goods, say O2, is produced such that, at T2 the aggregate O2 is completely finished and ready for consumption, while none of O2 is consumed in the time interval T1-T2.

 

Problems

This creates certain conceptual problems when attempting to use the model to consider certain characteristics of the economic production/consumption cycle. For, over any interval of time in an economy, different goods will be produced and consumed at different rates. Thus, over almost any interval of time we choose to examine in a real economic process, many goods will need to be considered as both output and input- rendering the model inapplicable; while, many other goods, whose time of production and/or consumption is longer than the time interval chosen, will need to be omitted from consideration, which, again renders the model inapplicable, or at least reduces the usefulness of it.

 

Homogeneity

The bar-diagram represents the total economic output as a homogenous magnitude. How can this be done when the total produced goods of an economy over an interval of time is clearly not homogeneous, but is, actually, a highly differentiated collection of a large number of highly distinct articles? A provisional response to this question is as follows: We use the bar diagram to represent only a certain array of the total goods produced by a society. We define the goods in this array as those which are capable of being consumed in such a fashion as to result in the production of an identical array of goods of equal or greater size.[2]All other goods produced in the economy are excluded from being represented by the bar-diagram. Thus, although the array of goods so attributed to the bar diagram be highly differentiated, it is understood that each and every good in the array is causally/functionally connected to all of the other goods in the array as a whole by the coordinated labor (consumption) of a society, in such a fashion that the elimination of any single good from the array will reduce the ability of a society consuming that array to produce an identical array of goods with an amount of time and labor equal to that which was originally required to produce that array. Thus, provisionally, can be said this: The portion relative to a total economic aggregate O1 which a single good (or collection of goods) might be said to comprise, can be “measured” by the amount by which the total economic aggregate O2 (which is produced through the society’s consumption of O1- and with the same amount of time and optimal labor) is smaller than O1 as a result of the elimination of that good (or collection of goods) from the productive process of a society.

 

Problems

This seems very satisfactory upon first impression. However, there are significant complications which arise from this. Firstly, due to the synergistic characteristics[3] of the coordinated consumption of goods, it is not possible to measure, by the method above described, the portion which a single good (or collection of goods) comprises in a total economic aggregate. For, as is demonstrated in the above cited report, this method of “measuring” the portion of the total economic aggregate of a single good (or collection of goods) -the method which seems to be the only one which can enable us to sensibly say that a good can be measured as a portion of the total aggregate- does not produce consistent values for the same good under different instances of the elimination of goods from the total aggregate.[4] That is, the very causal/functional relationship adhering between the goods in the total economic aggregate, as defined above, which initially lead us to reckon that each good in the aggregate could be measured as a definite portion of the whole, (and that, thus, the whole aggregate could be represented as a homogenous magnitude in the bar-diagram), is the very characteristic which makes such a measurement dependant upon the total consumption pattern. .

 

Further, as also mentioned in the cited report, it is not possible to put a consumed economic aggregate O1 into quantitative relation with a produced economic aggregate O2, unless, (and only when), the goods in O1 and O2 are identical, and present in identical proportions. The elimination of certain goods from the process of production, can lead to the loss of a capability to produce the same goods, even in lesser quantity than were previously available. Thus, the elimination of certain goods (or collections of goods) can result in the production of an economic aggregate O2 which is not capable of being put into quantitative relation with the aggregate O1 which was consumed in producing it. In such a case, no quantitative portion of the total aggregate O1 could be attributed to any good or collection of goods by the method above described. This leads to certain complications in the consideration of other questions in economic theory, such as the buy-back problem, the diminishing rate of return, and the technological improvement of the goods which a society produces- complications which are illustrated in the cited report.

 

II - A New Representation of Economic Input/Output

 

The way in which the difficulties arising out of the quantized and homogenous characteristics of the bar-diagram model can be overcome, is to produce a model without those characteristics. That is, a model, or visual representation, of the process of economic input/output, should be created which represents the process over time continuously, and which represents every single qualifying good available to the society individually (as opposed to representing the entire aggregate as a homogenous whole).

 

Such a representation is provided in the following diagram:

 

 

[Figure 2]

 

The horizontal axis represents time. The bar A, perpendicular to the time axis, represents the population of the represented society. The motion of bar A to the right represents the motion of the population of the society through time. The line B is not actually a continuous line, but represents the termination point of the shaded region Z. What is the shaded region Z? Perpendicular to and extending to the right of bar A are very thin bars. Each bar represents a single good in the economy. The length of each bar, from bar A to its termination point at the right, represents the total use-time (under a certain mode of consumption)[5] of a good in the society. These bars are arranged such that the shortest are on the top, and the longest are on the bottom- lengths corresponding to the use-lifespans of the goods they represent. For example, the bars closer to the top of A represent goods with shorter use-lifespans such as food products, or toiletries, the use-lifespans of which range from a few seconds to a few days; while the bars closer to the bottom of A represent goods with longer use-lifespans, such as basic economic infrastructure- bridges, roads, railways, etc.- which have use-lifespans of decades.[6] 

 

[Figure 3]

 

The thickness of each bar is arbitrary. In this diagram, it is simply determined by dividing the total height chosen to draw bar A on paper divided by the number of qualifying, or relevant goods[7] in the society the economy which is being represented.[8]The motion of A to the right and over the “good-bars” represents the consumption over time, by the population, of the relevant goods in the society.

 

 

[Figure 4]

 

Obviously, as the population moves through time, and consumes the goods available to it in the process, there will be a gradual diminution of the amount of relevant goods which are available to it for consumption. However, this is remedied by the production of new goods during the process of consumption. The addition of more good-bars to bar A at different points in time in the diagram represents the completion of the production of goods by the population at those points in time. Thus, if we assume that the consumption of goods available to the society at T1 is required to sustain the EM of the society at a certain value over time, we admit that the EM value of the society will diminish over time if the rate of production, by the population, of the goods in the aggregate Z does not equal the rate at which those goods are consumed. We can see how, then, at point T2 the population will have consumed the goods in area Z1 and used up the use-lifespan of the goods in Z2. If the society is to have maintained its EM at the value indicated above over this time interval, it it would have had to produce functionally identical goods to Z1 in the amounts indicated by the area Z3. In short, to maintain economic equilibrium, the rate of production of the goods in Z must equal the rate of consumption.

 

Uncompleted goods which are still in the production phase (before they are completed and made available for consumption by society) can be represented in the diagram. By adding more good-bars to the diagram, also perpendicular to and beginning at bar A, but extending to the left of A (instead of to the right), we can represent the good in production. With an animation, the diagram can be shown with good-bars in production as growing as bar A moves to the right. The rate of growth can be calibrated to represent the average completion time for the production of the good. If this kind of animation is done, economic equilibrium will be represented as A moving through time, while the sum of the magnitude of the growing good-bars of goods in production and the magnitude of the shrinking good-bars of available goods being consumed will remain constant. If the sum is found to increase, this would correspond to an increase in the rate of production relative to consumption, which corresponds to an increase in total economic potential, or economic growth. A decreasing sum would correspond to a reduction in the total economic potential, or, economic contraction, (except in cases in which technological progress is altering the array of goods utilized by the society).

 

 

[Figure 5]

In this instance, we can say that the area Z5 is comprised of bars representing the goods still in production. The area Z6 is comprised of bars representing goods completed in the time interval T1-T2 and which are made available to the society for subsequent consumption. This instance, represented in Figure 4, corresponds to the case of “economic equilibrium” described above.

 

The representation of the goods consumed by a society in the past as in figures 4 and 5 can be left out, and region Z can be left to be altered as a function of time. Under fixed environmental conditions, and a fixed level of technological and scientific progress, the following would hold: An expansion of region Z would represent economic growth (of a certain type); shrinkage of Z would represent economic decay. An unchanging Z would represent economic equilibrium.

 

Horizontal growth of Z represents an improvement in the quality of goods leading to longer use-lifespans. Vertical growth of Z represents an increase in the number of relevant goods in the society, which means that an increase in a certain kind of relevant goods aggregate can be so represented.

 

Given these capabilities of representation, representations of disinvestment in certain categories of goods can be represented. For example, is a society is reducing investments in infrastructure and other long-term economic investments, this will be reflected in the diagram as a reduction, over time in the length of the lower portion of region Z. As all of the goods in the diagram represent relevant goods, it can be understood how the EM of the society, along with the goods producing capability of the society, will be reduced if any portion of Z is allowed to shrink to zero without being replaced (given a fixed level of technology, and fixed environmental conditions).

 

Correlating such changes with alterations in the MPEM and SPEM diagrams introduced in the cited report are also of interest.

 

Representing Distribution

 

With this representation of the economic consumption and production of a population of a society, the same distribution scheme as was used in the cited report can be used. The population sector can be divided into the categories found to be appropriate. However, we arrive at a problem respecting the representation, in this model, of the allocation of the available goods to the various population sectors. This problem derives from the lack of homogeneity of representation of the output which contributed to the usefulness of the bar-diagram. Because we are accounting for every good available to the society individually as opposed to as representing all of the goods as a homogenous mass, it would seem that the only way to represent the allocation of the goods to the various population sectors would be to draw a line from each individual good-bar to the population sector which consumes it. As the number if goods in a society is astronomical, this would not be representable visually, or usefull conceptually.

 

The question of representing economic distribution is a complicated one. When we speak of distributing the wealth of a society, we are speaking of distributing a certain kind of potential. That potential is economic potential, or, as mentioned before for the case of goods, the potential to be consumed in such a way as to sustain or increase the EM of society. As mentioned, “relevant goods” are those which are defined as having such potential. How then do we measure how much of this potential is consumed by an individual or a group of individuals which we choose to identify in society? The great difficulties and complexities involved in this question, additional to the ones already mentioned in this report and in the cited report, will not be discussed here. We must be content with the following: Understanding that in societies which use money to facilitate the process of goods distribution, it is generally the case that the greater is the amount of money spent by an individual, the greater will be the amount of relevant goods that that individual is responsible for consuming or using up. Thus, we can represent the distribution of the goods of a society in our diagram in a fashion similar to the way in which it is represented in the older bar-diagram: By dividing the population bar into the appropriate sectors, with lines from the sector division to the shaded region Z representing the allocation a portion of Z considered as a homogenous mass. The proportions of the mass allocated to each sector being determined, generally, by the money allocated to each sector.

 

[Figure 6]

 

Unfortunately this representation tends to convey that the population sectors in A are allocated thos goods in Z which correspond to the positions they occupy in the diagram. That is, the utmost sector in A seems to be solely responsible for the consumption of the goods near the top of Z- the goods with shorter use-lifes. But this is not what is intended.

 

This problem of representation can be overcome by making the diagram three dimensional, and dividing the volume of Z vertically amongst the population sectors. This would convey that each sector consumes, more or less a portion of the entirety of the array of relevant goods represented by Z, as opposed to only certain kinds.

 

 

[Figure 7]

 

Figure 7 would have been better if the population bar were also vertical to the time axis. The diagram is messy in other of its parts due to a lack of graphic design skills on my part. But, hopefully, the idea is conveyed as to what a proper three-dimensional version of the diagram could be.

[1] https://www.findingprometheus.com/single-post/2018/01/03/Economic-Theory-A-Contribution

[2] As discussed in the referenced report, the array of goods represented by the bar diagram is actually best understood as that which is capable of being consumed in such a fashion as to sustain or increase the “existence metric of a society”; or, the product of the average lifespan and the population density of the society.

[3] For more on “synergy” see the section in the cited report titled “The concept of synergy in economics”.

[4] For more on this see the section of the cited report titled “Paradoxes of Measurement [of Value]”. The same argument presented there, respecting the attempt to measure the value of a good by the effect of the elimination of that good from the economic process upon the EM of a society, can be equally applied to the case of attempting to measure the portion of the total consumed aggregate which a good represents by the effect of the elimination of that good on the total produced aggregate.

[5] Because the mode of consumption can change such that certain goods are used up faster or slower, the length of the bars representing each good are subject to change. For now, however, we will consider the simpler case in which those lengths do not change- the simpler case in which the characteristic mode of consumption of a society is relatively constant.

[6] Obviously, maintenance will affect the use-lifespan of goods. Such changes in use-lifespan by maintenance can easily be represented in the model by changing the lengths of the good-bars. Initially, for simplicity, we will not consider changes of the use-lifespan of goods by maintenance.

[7] Qualifying goods: As mentioned in the cited report, I define “relevant output” or “relevant economic aggregate, as all of the synthetic goods available to a society which are capable of being consumed in coordination with each other to the effect of sustaining or increasing the EM of a society. See the cited report.

[8] For example, on this piece of paper, the line is an inch or two tall. Thus, assuming that the economy we are representing has one quadrillion relevant goods in it, the thickness of each bar representing each good will be about one quadrillionth of an inch or two. Obviously, for bars that thin, to-scale representation is not possible. Thus, a shaded region is used to represent the area which all the bars cover.

 

Share on Facebook
Share on Twitter
Please reload

Recent Posts
Please reload

© 2017 Ian Brinkley