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CO2 tax and EQ_CombalM - LucasD - 29-07-2020

Hello all, I am implementing a CO2 tax on the TIAM-FR model. In a first attempt, I set a CO2 tax of 10$/ton for all regions and all periods until 2100, with the attribute COM_TAXNET for the commodity TOTCO2. There are no climate constraints. When I look to the EQ_CombalM attribute, I get negative values in the order of magnitude of -0,500 $/t (varying according the period). Both the negative value and the (low) value itself are quite mysterious to me. If I understand correctly, it means that increasing the production of 1 ton of CO2 will save 0,500$ on my objective function? Can you please enlighten me on the interpretation? Thanks a lot, Lucas

RE: CO2 tax and EQ_CombalM - Antti-L - 29-07-2020

If you want to be a good modeller, you might want to get acquainted with the mathematics of optimization.  The marginals are obtained from the duals of the commodity balances, as calculated by the solver. If you have a good solver such as Cplex, you can be confident that the values are correct. The duals give the amount of change in the value of the objective function per a unit change in the equation slack. For energy commodities the value is positive, because by increasing the slack from zero to a positive value would cause the supply becoming greater than the demand. The value can be interpreted as the (marginal) price of the commodity. But if you put a tax on the VAR_COMNET of CO2, increasing the slack would allow the emissions produced to be greater than the VAR_COMNET variable, and so it would allow emitting without paying that tax. Hence, the value of the objective function would decrease in that case. In an otherwise non-constrained case, you would thus get EQ_CombalM=−10 with a tax of 10.  I just tested it myself with a small test model, with a COM_TAXNET(r,t,'CO2',ANNUAL,CUR)=10,  and indeed I got EQ_CombalM=−10 in all periods.  In your case the tax/cost savings are smaller, which suggests that you have some other constraints causing your total cost savings to remain small even if you allow emissions to be higher than the VAR_COMNET variable, which is taxed. I am not able to tell why in your case the tax savings are so small, but anyway, if you have a good solver you can be confident that the values are correct.