Climate change poses a global threat to the sustainable development of human societies. If not controlled, its impacts can threaten a vast range of human life including economic, social welfare, and public health. Most of the human-made part of this phenomenon is caused by the excessive greenhouse gas emissions (GHG), particularly carbon byproducts. Several solutions have been proposed to reduce the carbon emissions. In this paper, we investigate the effectiveness of an Emission Trading System (ETS), with a case study on the European implementation of this approach.

Our approach is based on the system dynamics methodology. First, we perform a literature study on the main sources of carbon emissions, and investigate the key factors involved in the carbon cycle. Then, we extract the casual relations between the derived factors and parameters. On top of the casual model, we build a stock and flow model in which the stock variables are related to their rate variables through a differential equation whose coefficients are time-varying and determined in the model itself. The whole model is reduced to a system of differential equations with variable coefficients, and is solved numerically using methods such as Runge-Kutta. The mathematical relations between the main variables are derived using regression analysis on the available historic data which are used to train the model. For the set of variables where analytic relations cannot be derived or are not suited, look-up tables are utilized.

The main procedure involved in the ETS is providing an Emission Allowance (EA) trading system, by placing a price on the volumes of the emissions. Thereby, financially incentivizing the main entities that emit large amounts of CO2 (or other GHGs in equivalent volumes of CO2) to reduce their emissions. An economic model between the EA Price, Demand and Supply is derived, where the supply is determined according to the regulations (reduced by 1.74% annually), and the demand is proportional to the actual carbon emissions. All main sources of emissions such as the power sector (whose main player is the electricity demand), manufacturing industries and construction, transport sector, aviation, etc., are included in the demand side. For our case study, the data and reports of Eurostat are used and the model is simulated.

A system dynamic model to determine the relations between the emissions production, demand and allowance prices is provided, which implements the method described in the EU ETS. The European data is used to simulate the model. Our simulations show that the EA pricing system can be increasingly effective to control the emissions though the EA prices, by consistently covering more industries (currently only 45% are covered) and reducing the allowance allocations. The possible implications of such a system for the US are investigated.

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