# Total Budget

First, we define the total amount of emissions to be allocated from 2000 until 2050 (Z). There are three different scenarios based on Meinshausen et al (2009) and similar to the pathways used by the Climate Equity Reference Calculator that restrict temperature increase to < 2°C at different probabilities. In light of the recent climate negotiations, we note that the strict budget would likely prevent temperatures from increasing more than 1.5°C.

Scenario Global 2000-2050 CO2 budget, Z Probability of temperature increase < 2°C
Strict 1000 GtCO2 75%
Medium 1440 GtCO2 50%
Soft 1600 GtCO2 > 33%

There are many different scenarios and pathways discussed by the IPCC and the above cited sources. We are aware that the budgets until 2050 actually depend on forecast until 2100, but we would like to focus on budgets until 2050, as it is important to start reducing emissions as soon as possible. The total budgets until 2100 are based on scientific calculations and do not focus on distributional and political problems, as we do.

## Total remaining Budget

Since we are interested in emissions after 2014, we determine a remaining budget, Z^\text{rem}, thus

Z^\text{rem} = \left(Z - E_{2000-2014}\right),
where E_{2000-2014} are the realized emissions from 2000 to 2014.

The method based on the equity proposal also takes account of previous emission up to 1990 so we add around 230 GtCO2 on top of the original budget.

# Subsets of Countries

Many argue that an international climate treaty focusing on a subset of countries would be sufficient to prevent climate change. This would reduce transaction costs, but still cover large amount of emissions, if the largest polluters were part of the agreement. In this calculator, you can choose the number of countries taking part of the treaty (n). Based on n we re-scale the total remaining budget (Z^\text{rem}) to obtain the budget corresponding to the n countries, using the following procedure:

1. Ranking countries according to their yearly emissions we calculate the percentage of emissions in 2014 (%E) corresponding to the n countries. For instance, if want to analyze the 60 largest polluters (n = 60), we obtain %E = 0.96, which corresponds to the emissions in 2014 of the 60 largest pollutants.
2. We re-scale the budget using %E, thus,

3. Z^\text{rem}_\text{scaled} = \left(Z - E_{2000-2014}\right) \cdot \%E,