An Economic Trajectory

The product and the projectile

An Innovative Enterprise Simulation provides an analysis of a commercial enterprise as a dissipative physical system.  This earlier model is built upwards with the simulation of many individual Sale Events arising as transactions within a population of consumers.  Here we will take the analysis up to a macroscopic overview that can be conservative with respect to the energy transformations that are taking place.

We begin with the construction of an economic space through which an enterprise might pilot a product or service so that the resulting trajectory summarises the outcome of their commercial operations.  Fundamentally, this economic space arises by transforming the previously described Value Surface to a single point, the height of which represents an average perceived value across the population of consumers.

In a Labour Theory of Value Creation we have considered that the endeavours of the labourer may be uncoupled into two independent components: innovation that creates valuable information and production which replicates that information.  These two components can form orthogonal axes of the economic space so that a specific path describes changing combinations of innovation and production activity with time for the associated enterprise.

A companion post, What Goes Up Must Come Down, allows the opportunity to speculate on the origins of a potential field that might pervade this economic space.  This potential field operates to constrain the creation of value and makes the labour of innovation “hard”.  It fills the economic space through which, over time, products are born, mature and die, and this life cycle can be charted.

So let us now examine an economic trajectory using a physical analogy of the flight of a projectile through a potential field: a simple trajectory of a thrown ball under the influence of gravity.  Here two forms of energy are particularly relevant:-

  • Kinetic Energy (KE) that a moving object of mass m has on account of its velocity v. KE = ½mv2
  • Potential Energy (PE) that an object of mass m gains by being raised to a height h against the pull gravity. PE = mgh, where g is the strength of the gravitational potential field


The trajectory of the thrown ball is governed by the Principle of Least Action such that that Kinetic Energy minus Potential Energy (KE-PE) throughout the flight must be lowest of all possible values.  In practice this means over time a high initial kinetic energy diminishes as the height of the ball increases, potential energy reaches a maximum at the highest point, before being recycled back into kinetic energy as the ball falls faster back to earth.

First Bounce of Ball

The energetics of a thrown ball. For further explanation see Energy: Transformation and Conservation


To translate this behaviour to be relevant for an economic trajectory it is necessary to form economic equivalents for the physical kinetic and potential energies.


Economic Equivalent of Kinetic Energy

Kinetic energy in the mechanical domain arises in the movement of things that have mass.  In the analogous economic domain there is an equivalent energetic phenomenon that also is “kinetic” in nature and which is related to value.  This is information.  Value can be interpreted as a consumer response to information received through an encounter with a product or a service.  Indeed whether it is a direct encounter or via a marketing communication, a consumer may reach a perception of value that is fundamentally related to information received.  Furthermore, there is a dynamic nature to information.  Information can flow.

The relationship between energy and information appears in some famous paradoxes in physics, most notably in Maxwell’s Demon who can in principle convert pure heat to mechanical energy in contravention to the inviolable 2nd law of thermodynamics.

To resolve the Maxwell’s Demon paradox, the intelligent Demon must forget information (or at least have a finite memory).  In this act of deleting information, energy (heat) is released and entropy is thereby increased to remain compatible with the universal laws of thermodynamics.  This same concept appears in Landauer’s principle which has shown that the irreversible deletion of information in a computational operation must be accompanied by a minimum dissipation of energy as heat.  It is the heat that makes computer servers hot.  On the other hand, the replication of information does not necessarily require any additional energy input.  Such considerations lead to a physical theory of information.

To seek an economic equivalent to kinetic energy, an association can be made to the concept of an inertial frame of reference.  In this, the equations of classical mechanics are the same whether they are set according to a frame that is still or which is moving with a constant velocity.  In the absence of any opposing forces, such as gravity or friction, a mass will continue moving at a constant speed just as a stationary mass will remain stationary.  The effortless replication of information is equivalent to an unopposed mechanical motion at a constant velocity.

To transform a mechanical trajectory to an equivalent path for the commercialisation of commodities, information content (I) can be considered analogous to distance.  An equivalent velocity term would then be the rate that information is transferred (dI/dt).   We might then assume there is the equivalent to kinetic energy in an Information Transfer Function kit(dI/dt)2.  Where is a kit constant of proportionality that remains to be determined.


Economic Equivalent of Potential Energy

Next we will seek an economic equivalent of the transfer of energy observed in the trajectory of a physical projectile as shown above.  To complete this analogy we need to consider the nature of a potential field that confers an increasing value to commodities as they are developed, produced and commercialised.

This adding value to goods may be considered as increasing their energy content by moving the commodities higher in a potential field that pervades the economic space as described above.  As with the raising of a heavy physical object, it can take work and endeavour to create a perception of value.  Therefore, an economic potential field enables an appreciation of value to be considered as a form of potential energy, and as a transformation of the energies consumed to create this perception of value (see Bioenergetic Transformations).  Extending further the analogy with gravity, instead of this field being derived as a feature of the mass of the Earth, an economic potential field should be associated with the consensus of all consumers who are able to express an appreciation of the value of the goods, or more specifically their information content.  Essentially, value is in the eye of the beholder.

It would be convenient at this point to imagine that the economic value of a product can be hoisted progressively higher by the dedicated exertions of its creators, to stand aloft attracting potential acquisition like a huge advertising balloon.  This, however, must be too simple an image.  Adding value is not a simple incremental process such as filling a bucket.  Many influences not directly related to the product itself impact upon its perceived value.  A more subtle and realistic interpretation of value-adding activity is necessary.

Two things will determine the evolution of consumer perception of value.  Firstly there is the purposeful deployment of energy from the economic efforts of the innovators and producers through a supply chain.  Secondly, external events will continuously disturb the orderly creation and replication of value through innovation and production.  Although the precise properties of an economic potential field that describes the relationship between value and information content remains to be defined, this can be specified generically by an Innovation Function through which the  value (V) of the goods depends upon their information content (I) and also which can be seen to vary with time t.  That is: V = V(I,t).[1]


A Simple Trajectory

We are now able to translate what the mechanical Principle of Least Action might mean when applied to an equivalent economic trajectory.  It should be emphasised that this analogy need not be taken to imply economic analysis should inherit the absolute deterministic nature of a mechanical system.  It is a geometric transformation to examine how mechanical analysis might inform its economic counterpart.  The human element is retained in the time-dependent nature of the economic potential in the Innovation Function V(I,t). 

Now we must understand what this means for the trajectory of commodities as they are launched through an economic potential field.  Whilst we cannot readily formulate and solve the economic equations, we should assume these solutions are analogous to the flight of a mechanical projectile, in which case we can use the characteristics of a mechanical trajectory to inform what could be expected in the economic domain.

Some external energy is needed to launch a physical projectile, perhaps originating in the muscular contractions of the thrower.  In the economic domain some initial investment is needed to launch the activity.  This initial investment does not instantly transform into commodity value, but begins a transfer of information into the goods that takes time to be complete.  In the mechanical analogy an initial kinetic energy over time is transformed into a potential energy.  The same is assumed for an equivalent economic trajectory, as the value of a commodity increases and the rate of information transfer should naturally decrease.

Let us consider what would happen without any potential field.  In this case, the Innovation Function V(I,t) = 0 at all times.  The initial deployment of investment would begin with the same rate of information transfer, but this would have no associated value and the information replication should then continue perpetually at the same rate.   In other words kit(dI/dt)2 = constant at all subsequent times t.

One could speculate that such a constant transfer of information must take place by automatic continuous replication.  We have already associated this behaviour with the invariance of mechanical dynamics to an inertial frame of reference.  In an abstract sense it represents the continuous production of a product that has no value.

Next we can explore an opposite case in which there is no replication of information, only value creation.  The commodity would then be exemplified by the economic trajectory of a single item such as a sculpture.  Such activities that are devoted to the creation of a single unique item could be considered as pure innovation.  The Innovation Function V(I,t) increases with time, through conversion of kit(dI/dt)2 that signifies the transfer of information to the item.  Importantly, there is no replication of this information, just value creation in the production of a single item.  In the mechanical analogy, the ball would be thrown vertically upwards.

If the same mechanical analogy where to be applied to a mass-produced commodity, such as a reproduction of the above sculpture, value creation is accompanied by the replication of the original information.  There will be balance between innovation and replication, which in the mechanical analogy can be shown as an inclination of the trajectory to the horizontal.  Pure innovation is vertical and pure replication is horizontal.  Combinations of the two appear in the trajectories as shown in the figure below.


E-Trajectories from Zero

Economic trajectories for several different initial inclinations


If the goal of the commercial organisation is to gain income through product sales, then income depends on the productive reach of the economic trajectory, which is furthest at an inclination of 45 degrees.  We can note that in Two Parameters for Seven Companies some organisations operate in this region with a balanced investment in innovation (OPEX) and production (COGS).  It appears that profitability (and sustainability) might be more easily achieved with an economic trajectory with the greatest productive reach.  Other companies operate with relatively greater COGS (e.g. Apple) or OPEX (e.g. Microsoft).  In these latter two cases the representative product needs raised higher in a weaker potential field (as indicated by higher values of the xsd parameter) for the organisations to be profitable.  There is more to be said on this interesting point later.

This paper has introduced the concept of an economic trajectory that is highly idealised.  In Flightpaths and Forgetful Markets we will make this more realistic and consider some of its practical implications.



[1] Whilst the nature of the economic potential field as specified by the Innovation Function V(I,t) remains to be determined, some practical evidence indicates that this should include an element of diminishing returns.  That is, the value of commodities is not simply proportional to information content.  It seems likely that diminishing returns might apply as information content of goods is further increased, the consequent incremental increase in value becomes progressively less significant. The economic potential field could thus differ from its gravitational analogue.



Back to Foreground Contents

Comments are closed.