In theoretical land economics the existence of a competitive equilibrium with an additive price is considered problematic. This paper studies the exchange and allocation of a heterogeneous divisible commodity such as land, which is modeled as a measurable space. In a 'land' trading economy with unordered convex preferences, the existence of a competitive equilibrium with an additive equilibrium price is proved. This paper demonstrates also the existence of a weak core and a fair allocation. (C) 2010 Elsevier B.V. All rights reserved.