Rare earths, classified as critical elements by the European Commission, are of high importance to the automotive, chemical, and pharmaceutical industries. They are produced simultaneously and therefore can be referred to as joint products. In this paper, an approach is presented to analyze the drivers behind supply and demand changes of joint products to reveal cross-industry relationships between rare earths. The approach is based on a techno-economic analysis and includes economic, market, and technological evaluations. The heavy rare earth Gadolinium is analyzed in detail to give insights into applications, capacities, the rare earth industry, estimated growth rates, and strategy recommendations.