The Sustainability Limit

Exploring the Boundary between Profit and Loss

Commercial organisations are frequently likened to other kinds of organisms and their survival can be understood using evolutionary principles originally applied in biological and zoological sciences.  Here we would like to run this metaphor in reverse to indicate how other organisations and organisms may be understood from the behaviour of commercial organisations, which the overarching goal of survival through profitability makes relatively simple to understand.  So we will extend the dissipative viscoelastic systems analysis we have used to explore commercial enterprise to understand fundamentally what it means to be sustainable.

Previously, we have created a two-parameter Enterprise Model and then linked this to the real world by fitting the model behaviour to commercial activity for seven multi-national companies.  This approach uses the convenient separation of real Cost of Goods Sold (COGS) and real Operating Expenses (OPEX) in public company income statements to match respectively with a simulated energy dissipation and a potential energy retention in an elevated Value Surface following a simulated Sale Event sequence.  Commercial organisations exist to make a profit, where income should exceed investment, but what do Cost of Goods Sold and Operating Expenses mean for organisations or indeed organisms whose primary purpose is to sustain their own survival in a natural rather than a capital accumulating environment?  We need to translate these conventional accounting terms into something more generic and abstract.

Just as an enterprise requires investment, all organisations and organisms must receive an equivalent supply of energy to maintain their vitality.  Indeed survival may be defined in terms of throughput of energy in a diverse set of physical, biological and economic systems across a wide range of scales as considered in Writing the Information.

Survival a minima arises from equality between the supply of input energy or investment and income arising from the activity, so that income can be recycled for a sustainable input[1].  Cost of Goods Sold might sensibly be equivalent to the costs of the energy needed for daily sustenance: food, heat, light.  Operating Expenses then comprise the energy retained as stocks, knowledge, networks and generally whatever might be regarded as attributes that make an organisation or an organism valuable.

This sustainability principle is translated into the data presented below in which seven scenarios are derived with equality of investment and income, but with differing levels of Operating Expenses[2].  As the Operating Expenses are increased from negligible in OPEX(1) to high in OPEX(7), a Value Surface can be defined through estimates of qs and xsd  by fitting the two-parameter Enterprise Model to the data again using the Least Squares Method.   These estimates of qs and xsd for each sustainable scenarios are also shown below.

Data and associated parameter estimates for seven sustainable scenarios where investment equals income and which differ only in their Operating Expenses (OPEX).

Sustainable Enterprise Simulations

Furthermore, for each of these scenarios the qs and xsd parameters can be estimated when income is either below or above the level needed to sustain further investment, representing non-sustainable and profitable scenarios respectively.  In each case, as shown in the table below, the qs parameter is unaffected by this change of income.  It is the xsd parameter that rises and falls in proportion to the rise and fall of income in the profitable and non-sustainable scenarios.

Data and associated parameter estimates for different  scenarios where income varies between non-sustainability and profitability for the case of OPEX5.

Mixed Enterprise Simulations

Bringing together the above observations we can conclude thus:-

  • Parameter qs is only sensitive to the balance of COGS and OPEX in the Total Investment. The higher qs values correspond to the higher OPEX and lower COGS.
  • Parameter xsd adjusts the income returned to the enterprise through the simulated Sale Events

In a Labour Theory of Value Creation we have sought to uncouple in principle labour deployed on innovation (creation of value) from that expended on the replication of that value in production activities.  Now we have a means quantitatively to assess these two independent components of labour.

  • Parameter qs is a marker of production with lower values indicative of a higher proportion of investment directed to Cost of Goods Sold, and consequently a greater emphasis on information replication through production.
  • Parameter xsd is a marker of innovation, as one might expect where higher values of this standard deviation indicate a higher valuation for the associated commodities in their consumer population. The creation is value is needed for an organisation to become sustainable and still higher values of xsd lead to profitability.

These observations are summarised in the figure below.

Sustainability Limit

Estimates of qs and xsd for the sustainable scenarios establish a Sustainability Limit that separates the chart formed by these parameters into two regions defining the profitability of an enterprise.  Logarithmic scales have been chosen to better visualise these findings.


Finally, we can add into the above chart the parameter values estimated for seven commercial organisations to produce a template for the comparative performance of these organisations in terms of their Innovation and Production activities.

Commercial Orgs and Sustainability Limit 2

Parameter estimates for the commercial organisations appear in relation to the Sustainability Limit that divides the parameter space into profitable and non-sustainable regions.


This template formed by the parameter space from the two-parameter Enterprise Model also provides a common template to consider both commercial and other organisations and organisms in terms of their sustainability.  By referring to a Value Surface of a surviving organisation or organism as defined by the two parameters qs and xsd , we are adopting the concept that their Value Surface is being raised in a potential field just as if the organisation or organism were a commodity.  This commoditisation of non-commodities requires a wider interpretation of the concept of value, which engages with additional factors other than those which can directly command a commercial exchange value.  In all instances, the notion of value is a key attribute for both organisations and organisms to acquire, and which the efforts of acquisition can be portrayed in their raised Value Surface.



[1] Reserves as chemical energy in fat or as capital in bank accounts are useful in periods where energy usage temporarily exceeds its supply.

[2] As Operating Expenses take an increasing share of the same Total Investment (COGS + OPEX), Cost of Goods Sold must necessarily decrease by the same proportion.



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