The primary production of rare earth elements (REE) used in neodymium-iron-boron (Nd-Fe-B) magnets is associated with environmental impacts from both mining and processing. It has been suggested that recycling of scrap Nd-Fe-B magnets would reduce primary production of REE, and thus environmental impacts. However, existing studies on environmental effects of recycling based on the methodology of Life Cycle Assessment (LCA) do not take into account the so-called balance problem, which accounts for the fact that all elements co-occuring in the ore are jointly produced, resulting in either an excess or a shortage of individual elements. We develop a two-part approach to incorporate this issue into LCA. In the first part, we investigate the effects of introducing large-scale Nd-Fe-B recycling to the global rare earth market. A production model is presented that quantifies the potential market effects of secondary production (recycling) on the balance problem. Results show that primary production could partly be avoided when introducing a secondary production route to the rare earth market, whilst still meeting demand for joint (non-magnet) REE, only produced from the primary route. The production model will be used for a consequential life cycle assessment study which will be published as a separate paper (Part II). In addition, we show that our approach may also be interesting for other LCA studies, where effects of market changes on a co-production system are investigated.