Growing demands for meat and dairy products (MDP), biofuels, and scarcity of agricultural land are drivers of global land use competition. Impacts of policies targeting demand for MDP or biofuels have only been analysed separately. We use the computable general equilibrium model DART-BIO to investigate combined effects, since MDP and biofuel production are closely related via feestock use and co-production of animal feed. We implement four scenarios: (a) a baseline scenario, (b) halving MDP consumption in industrialised countries by a tax; (c) abolishing current biofuel policies; and (d) no exogenous land use change. We find that a MDP tax and exogenous land use change have larger effects on land use and food markets than biofuel policies. International trade is affected in all scenarios. With respect to combined effects of a MDP tax and biofuel policies, we find decreasing biodiesel but increasing bioethanol production. In addition, the MDP tax decreases the impact of biofuel policies on agricultural markets and land use. Our results highlight the importance of a detailed representation of different vegetable oils used in biodiesel production and related by-products. Finally, since the MDP tax increases the use of fossil fuels, the net climate mitigation potentials of such a tax should be further investigated.