What is a constrained market? How is it different from the “normal” market? How does it behave during the linking?
A constrained market is a market where all or part of a change in demand is not reflected in a corresponding change in supply but instead in a change in consumption elsewhere. Constrained market datasets include a conditional exchange with a direct activity link to the consumption activity that is affected by the change in demand. This exchange is activated only for specific system models that take into account market constraints, e.g. the consequential system model. When the system model Allocation at the point of substitution (former Allocation, ecoinvent default) is chosen, the conditional exchange is not activated and the constrained markets behave like any other markets. The following explanation is only relevant for consequential-type system models.
If a by-product that is exclusively produced as a by-product, i.e. not produced as a reference product by any other activity, and not treated in any treatment activity, its market will be constrained, i.e. its production volume is fully dependent on the production volume of the corresponding reference product which drives the production.
For example, fluosilicic acid is produced exclusively as a by-product of the phosphoric acid production.

Although there is a high demand for fluosilicic acid there will not be more supply, under the current market conditions, where the demand for fluosilicic acid would not be enough to drive the phosphoric acid production alone.

Fluosilicic acid is used as an input from technosphere for example in cryolite production, from fluosilicic acid. Cryolite can be also produced from hydrogen fluoride. Both productions supply the same market for cryolite.
During linking of the constrained market, the linking routine activates the conditional exchange with its direct activity link to the cryolite production from fluosilic acid, and as any other by-product the conditional exchange is shifted to the input side, its negative sign turned positive, i.e. representing an input from the directly linked activity.

The activity linked to by the conditional exchange is cryolite production from fluosilic acid. The direct link represents a reduction in consumption of the linked activity. But cryolite production from fluosilic acid has fluosilic acid as an input. In order for fluosilic acid to serve as an input to the constrained market, the consuming activity must have fluosilic acid as its reference product. The database service layer achieves this by moving fluosilic acid to be the negative reference product of "cryolite production from fluosilic acid" and moving the cryolite to be a by-product, thus quantifying the resulting reduction in consumption.

The market demand for the fluosilic acid from "cryolite production from fluosilic acid" thus translates into a reduction in the negative reference product output of fluosilic acid from "cryolite production from fluosilic acid". Note that the reduction in a negative output is a positive input namely the input required by the constrained market.
The demanded fluosilic acid thus effectively results in an increase in the supply of cryolite from hydrogen fluoride to cover the reduction in supply from the fluosilic acid route which is necessary to cover the demand for fluosilic acid. Likewise, a reduction in demand for fluosilic acid will release more fluosilic acid for the cryolite production this displacing cryolite from hydrogen fluoride.
The reason why the cryolite production from fluosilicic acid is the affected consumption activity is that it can be easily substituted by the alternative production route for cryolite (from hydrogen fluoride).
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What is linking and what happens during the linking process? Consequential System Model
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The ecoinvent database in Environmental Product Declarations (EPDs)
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APOS: why do I have carrots on my recycled aluminium?