We develop a theoretical framework to analyse economically optimal GHG abatement strategies for a mixed farming system with crop and dairy production. Subsequently, it is implemented as a detailed bio-economic optimization model for mixed arable-dairy farms with non-linear crop and milk yield functions and a detailed accounting of Green House Gas emissions, and parameterized to Finnish agricultural and environmental conditions. Focusing on the role of sunk costs of investments and opportunity costs of labour, we analyse optimal farm management decisions under different CO2 tax levels, considering adjustments at the extensive and intensive margin, including changes in manure storage systems and application methods. We find that the amount of GHG abatement responds more strongly to the level of sunk and opportunity costs than the CO2 tax level which underlines the relevance of the planning horizon for that type of analysis. Our findings reveal that low cost abatement options in dairy production are limited. Our model can be easily adjusted to other locations, market and policy conditions and thus provides an interesting starting point for international comparisons. Acknowledgement :