The TwoParameter Model
We are now able to bring the components parts together to create an initial working model to simulate the commercial behaviour of a real innovative enterprise.
The market modelling assumptions are from: A Labour Theory of Value Creation:
 Value is recognised to varying degrees by a population of consumers
 Consumer perceived values follow a Gaussian (normal) distribution with zero mean and a nonzero standard deviation x_{sd}> 0
 The Consumer Product Interaction (CPI) is the key event at which a decision to acquire some goods is taken
 Consumers will acquire these goods when their perceived value exceeds the price set by the supplier
 Overall investment is used to create the CPIs in a consumer population and value perceived is proportional to overall investment
The assumed Gaussian distribution with zero mean and a nonzero standard deviation x_{sd} effectively defines the Value Surface for a consumer population. The height of the Value Surface increases with investments made by the producer.
Click image to enlarge

The stochastic viscoelastic model described in the The Viscoelastic Sale Event has adopted the above Gaussian distribution of the failure of the CPI units that signifies a saleevent in the commercial domain. With each such saleevent, a further q_{s} new CPI units are recruited to join those that have yet to fail. This sequence of CPI unit failure and recruitment with each time increment t_{r} is illustrated below.
The stochastic model with a Gaussian Value Surface and the equivalent viscoelastic model shown above are analogous, which enables the latter to be used as a mechanical analogue for the former to create a simple enterprise simulation as a dissipative mechanical system.
Following this mechanical analogue, it is assumed that investment is distributed evenly between each of the CPI units that comprise the simulated Value Surface. The different CPI units will be raised to different heights that are representative of the differing propensity of consumers to value the goods. This variation of individual preferences is captured by the simple equation: –
Val_{i} = x_{i} . E_{i} i = 1, …….., 100 (1)
Where E_{i }= E/100 gives the portion of the total investment E that is distributed to each of the population of 100 CPIs. Val_{i} is the height of point i on the Value Surface.
The x_{i} values here comprise a Gaussian statistical distribution with a zero mean and a set standard deviation x_{sd}, which recognises that the majority of CPIs register a low value that will barely appear on the Value Surface, and only a small minority of consumers will seriously desire the goods,
It is now possible to construct a Simple Enterprise Model as shown above. Firstly, values of x_{sd} , q_{s} and Price are specified. The price fixes the saleevent threshold as shown in “The Viscoelastic Sale Event”. At the first time increment (the first day of trading for example), a small ‘packet’ of investment is added to the model and the varying heights of the 100 CPI units can be estimated to meet the requirement that their standard deviation is x_{sd}. It is likely that few if any units will achieve instantly the height that indicates a saleevent will occur in this first trading increment, as the investment added is low. There will be little income or profit. On the next and subsequent increments as more investment is made, the new heights of the Value Surface are recalculated and the number of units sold determined. When the height of any of the 100 units exceeds the saleevent threshold, the set price of the goods is returned as income[1]. There will now be additional CPI units that are recruited to behave just as their predecessors and receive their share of future investment in the enterprise. At later times and with this additional incremental investment, further saleevents will occur, producing an increasing income with time that is dependent on the level of investment, the values of x_{sd} , q_{s} and the set purchase price. At each time increment, total investment can be deducted from the total income to provide a measure of profitability of the enterprise.
Such an iterative model evolves as the numerical algorithm that steps though the time increments. The model then becomes a computer program in which the calculation of saleevents lies in the numerical integration of the Gaussian distribution that describes how a population of consumers value the commodities in question.
The relevance of the above simulation of a commercial enterprise needs to be established by comparison with the real world. Innovation needs to follow on from model invention. This simulation requires that two parameters be specified so that numerical simulations can estimate such things as units sold, income, profit and so on. However, these simulated estimates are actually the information that should be already known within an enterprise. Realistic estimates for the parameter values, however, could be useful to provide a new insight into the enterprise. We need to run the model in reverse, so that the parameter values can be estimated from known commercial data. In this way the parameters become the link between model and real world, and their values provide information that is otherwise unavailable.
The estimation of the model parameters values x_{sd} and q_{s} for real innovative enterprises is the subject of the next part of this series: Two Parameters for Seven Companies.
Notes:
[1] The proportion of CPI units that fail with each incremental investment is calculated from the numerical integration of the formula that defines their Gaussian distribution. Hence, this proportion is continuous involving fractions of units rather than considering these as 100 distinct entities.
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