Unravelling the dynamics of land-use change is key to assess the environmental and socioeconomic impacts of land-based strategies regarding climate or energy. In this prospect, this paper proposes an analytical decomposition of land-use change resulting from a shock in agricultural demand which takes into account indirect effects from price signals. This analytical equation is numerically estimated using a global model of land-use combining biophysics and economics. While being relatively simple, this model captures the main processes of land-use change: change in the intensive and extensive margins, international trade, change in intermediary demand and possible by-products. At the global scale, our results show that yield losses due to the conversion of marginal land amount approximately to half of yield gains due to fertiliser use. At the regional scale, patterns of yield and area responses are depicted by assessing the potentials for intensification (yield gaps) and extensification (areas of extensive pastures) given the future pathways of agricultural demand.