Multiple determining products from joint production
In the situation where a joint production has more than one product without alternative producton routes – and therefore more than one determining product – the markets for these products can only be cleared via changes in consumption of all the involved determining products.
For joint co-products that do not have any relevant alternative production routes, their prices will adjust until all the joint products have the same normalised market trend, since only then their markets will be cleared. In this situation, a change in demand for one of the joint products will influence the production volume of the joint production in proportion to its share in the gross revenue of the joint production. This is equivalent to the result of an economic partitioning (allocation) of the co-producing process. Furthermore a consumption adjustment will take place via constrained markets for the joint products, in order to maintain a balance in supply and demand (and thus in mass balances, which is otherwise lost in economic partitioning).
Thus, the changes resulting from a change in demand for one of the determining products can be modelled from the revenue provided by this product relative to the total revenue from all the determining products. This ratio is used as a scaling factor on the joint production activity, reflecting that a change in demand for one of the jointly determining products will only provide enough change in revenue to influence the production volume of the joint production in proportion to its share in the revenue from all the determining products.
The scaled joint production activity thus responds to a specific increase in demand for its determining products with a smaller output than what is needed to meet the increase in demand. Since there are no alternative production routes, the missing supply must be obtained from a reduction in consumption by other users of the demanded product, which in practice occurs due to the price signals resulting from the increase in demand. The users that reduce their consumption are identified as the marginal consumption activities in parallel to the way marginal suppliers are identified: The marginal consumption activities are those that have the least alternative costs from not using the product in question and therefore are the most sensitive to the change in price that is caused by the change in demand.
As a result, the market activity for the determining product is thus supplied partly by the joint production activity and partly by the input from the reduction in marginal consumption in the quantity necessary to compensate for the missing supply from the joint production activity.
Note that by this procedure the joint production activity is not partitioned, but only scaled to the change in demand, and it is therefore still a multi-product activity. Thus the outputs of the other co-products change proportionally to the change in the co-production activity. To obtain a single-output activity that only produces the demanded determining product, the other co-products are modelled as negative inputs instead of as positive outputs, i.e. by system expansion as described for by-products in general (see section by-products, recycling and waste).
For any dependent co-product this leads to the displacement of the alternative unconstrained supply, in exactly the same way as if the dependent co-product was an output of an activity with one determining product. But the remaining determining products (those for which there were no change in demand) do not have any alternative production routes to displace. Since the products do not accumulate and markets therefore need to be cleared through price adjustments, an additional output instead leads to increased consumption in the marginal consumption activities. The remaining determining products (those for which there were no change in demand), which are now modelled as negative inputs to the joint production activity, are therefore linked to their marginal consumption activities, thus representing the induced change in consumption.
It may occur that you during this deep investigation of consumption changes may realise that there is indeed an alternative production route for a determining product – well, that just means that you’re of the hook and can go back to normal procedures.
It should be noted that the consumption activities typically have the supplied products as an input. When modelling a marginal consumption activity, the supplied product instead becomes the determining product of the consumption activity (driving an additional consumption). The original determining output of the marginal consuming activity will then no longer be determining but will instead represent the resulting change in consumption, which may need to be defined as a social impact, unless it in itself can be modelled as a by-product.
Since the specific consequences of changes in demand needs to be investigated for each of the determining products separately, application of the above procedure to all the determining products of a joint production will require a separate dataset for each of the determining products. Each of these datasets will represent the consequences of a change in demand for one of the determining products.