When all co‑products have alternatives
If all co-products of a joint production have an alternative production route, only one of these co-products can be the determining one.
If more than one co-product of the production system appears to be determining, then the two conditions below will be able to provide an unambiguous identification of which of these is the determining one.
The two conditions are:
1) To be determining, a co-product shall, either alone or as part of a combination of co-products, provide an economic revenue that exceeds the net marginal cost of changing the production volume.
2) To be determining, the product or product combination shall have a larger normalised market trend than any other joint product or combination of co-product that fulfil the first condition.
The reason why the normalised market trend plays such an important role here, is because we are studying changes in outputs of products that are produced in fixed quantities (from the co-producing activity).
When the demand for one of the co-products change faster than that of the other:
- the co-product (combination) with the largest change in demand will determine the output, when its revenue is adequate for the co-producing activity to change, and
- the co-product with the smallest change in demand will impose a constraint on the ones in higher demand, when the revenue from more co-products are required for the co-producing activity to change.
To identify the determining product when all joint products have an alternative production route, you can follow this stepwise procedure:
- First investigate if one or more of the co-products alone fulfil the first condition – namely that it provides an economic revenue that exceeds the net marginal cost of changing the production volume.
- Secondly, look at those co-products that do not alone fulfil the first condition, and identify all the combinations of co-products that do.
- Thirdly, compare the normalised market trend of all identified co-products and co-product combinations that fulfil the first condition. Note that the normalised market trend of a combination of co-products is equal to the normalised market trend of the co-product with the smallest normalised market trend within the combination, since the demand for this co-product imposes a constraint on the ability of the combination to change its output.
- Finally, identify the co-product or combination that has the largest market trend. If it is a single co-product that has the largest market trend, then this is the determining product. If it is a combination that has the largest market trend, the determining co-product is finally identified as the co-product with the smallest market trend within the combination, since the demand for this co-product imposes a constraint on the ability of the combination to change its output.
The other co-products (the non-determining ones) are referred to as by-products or dependent co-products.
It is not very often that more than one co-product can provide adequate revenue alone, but is quite interesting when it happens, since the high revenues of both co-products relative to production costs might have consequences for the entire market. Such a joint production has a large potential to outcompete other production systems. This situation can be illustrated with this hypothetical example:
Given two co-products A and B with revenues of 100 and 50 per simultaneous produced amount, respectively, as determined by the production costs of the alternative marginal production. If the co-producing activity has a net marginal production cost below 50 for the combined amount of A+B, the co-product with the largest market trend will provide enough revenue alone to be able to cover the cost of the combined production of A+B, and thus determine its production volume.
The situation where only a combination of products can provide adequate revenue can be illustrated with this hypothetical example:
Given two co-products A and B with revenues of 100 and 50 per simultaneous produced amount, respectively, as determined by the production costs of the alternative marginal production. If the co-producing activity has a net marginal production cost between 100 and 150, the revenue from both products are needed to fulfil the first condition. In a competitive market, the co-product with the largest market trend will be sold at the price of the alternative production cost, while the surplus co-product with the smallest market trend will – in order to clear the market – be sold at the lowest price necessary to cover the production costs. Since the price of the co-product with the smallest market trend cannot be lowered further without bringing the revenue below the marginal costs, the amount that can be sold of this co-product provides a constraint on (determines) the production volume of the co-producing activity and this co-product is thus the determining co-product.
- Further theory on marginal production costs For a co-product (or a group of co-products) to influence and be determining for the production volume of an activity, the revenue that it provides must exceed the marginal production costs.
- Further theory on adequate revenue If only one of the co-products from a joint production provide adequate revenue to cover the marginal production costs this is the determining product.
- Further theory on market trends It is the overall market trend which is of interest and not the direction of the change in demand implied by the specific decision studied, because it is the same suppliers that will be affected by an increase and a decrease in demand.
- Further theory on normalising market trends Before comparing the generic market trends of the co-products they have to be normalised to the relative outputs of the products from the co-producing activity.
- Soybean and oil co-product system An example on finding the determining product for the joint production of soybean meal and oil, where both products have alternative production routes.
- Revenue for molybdenum An example on identifying the revenue for the co-product molybdenum.
- Production costs of gold An example on identifying production costs of gold.
- Adequate revenue of copper An example were only one of the co-products from copper mining operation provides adequate revenue.
- Normalising market trends of sunflower oil and meal An example on normalising the general market trends for vegetable oil and protein meal to the relative outputs of sunflower oil and sunflower meal.