Interactions between food demand, biomass energy and forest preservation are driving both food prices and land-use changes. This study presents a new model called Nexus Land-Use which describes these interactions through a representation of agricultural intensification. The model combine biophysics and economics to calculate crop yields, food prices, and resulting pasture and cropland areas within 12 inter-connected regions. The representation of cropland production systems relies on a biomass production function derived from the crop yield response function to inputs and a spatially explicit distribution of potential crop yields prescribed from the Lund-Postdam-Jena global vegetation model for managed Land (LPJmL). The economic principles governing decisions about land-use and intensification are adapted from the Ricardian rent theory, assuming cost minimisation. The land-use modelling approach described in this paper makes it possible to explore interactions among different types of demand for biomass, including indirect effects on land-use change resulting from international trade. Yield variations induced by the possible expansion of croplands on less suitable lands are modelled by using regional land area distributions of potential yields, and a boundary between intensive and extensive production. Idealized scenarios exploring the impact of forest preservation policies or rising energy price on agricultural intensification are presented.