Economic Evaluation: The phase-out of fossil fuel vehicles

Question: The Danish government imposes registration taxes. Should it be counted as a social cost because it causes a deadweight loss, where it is relevant to use the MCPF? Or should it be categorized as social benefit, as the taxation decreases the negative externality (pollution) and hereby increases social surplus? 

Regarding valuing impacts in the input market, I am not sure how to handle this? Maybe the labor hired to administrate the taxations can be used elsewhere and hereby imposes an opportunity cost? 

The demand for non-fossil cars will increase, as the taxes are less than for fossil cars. The opposite is true for the fossil car market, thus is a social cost. As cars are a market good, the social benefit can be calculated by direct estimation. 

Answer: Taxes alone are not considered as social costs or social benefits. When taxpayers pay tax, it increases the government revenue (which can be used for public welfare).  Taxes are losses to the taxpayers but gains to the government, and at the level of the society as a whole, it is just a transfer. 

At the same time, as you correctly point out, taxation can lead to a distorted market, giving rise to a deadweight loss. This deadweight loss can be taken care of if we multiply all the government revenue and expenditure by MCPF. In other words, paying higher taxes itself is not a social cost, but it does lead to some deadweight loss, and this deadweight loss is accounted for by the MCPF coefficient. Note that the MCPF is the marginal cost of collecting tax revenue in general, which is not directly to the deadweight loss in the car market. In fact, appropriate taxes in the car market do not lead to a deadweight loss but increase efficiency, because it reduces pollution. However, when you reduce taxes in the car market, to keep tax revenue constant, the government has to collect taxes elsewhere, for example, by increase income tax or corporate tax -- because income tax or corporate tax lead to deadweight loss, making MCPF greater than 1. Let me know whether this is clear because it is not easy to understand the meaning of MCPF. 

The reduction in pollution (mostly carbon emission) should be calculated separately as a social benefit. This is probably the largest benefit of the policy, the main reason why the policy is implemented.

You do not need to calculate the input market for the tax collection. Because the government usually hires a fixed amount of employees related to taxation, even if there is some change to the employment, it is negligible compared to the impact (change in the consumer surplus and producer surplus, as well as the benefit from the reduction in carbon emission) caused by the number of fuel vs. electric vehicles.