## From The Developing Economist VOL. 1 NO. 1## Efficient Pricing of Carbon in the EU and its Effect on Consumers## III. Computational ModelTo evaluate the efficacy of the carbon tax on the utilization rates of multiple generation technologies, a computation model was created. The model uses a Monte Carlo process in conjunction with a statistical tool known as the Dirichlet distribution to randomly create an array of portfolios, each with a different share of the various generation technologies. These energy portfolios were then evaluated based on their cost and CO ## Monte Carlo SimulationMonte Carlo simulations are often used in modeling in situations where a closed-form analytic solution is not readily available or exceedingly computationally intensive. A Monte Carlo simulation relies on repeated random sampling of input variables to obtain an optimal result. In the case of portfolio management (whether it be energy or equities), by randomly choosing the asset allocation percentages and calculating the costs repeatedly, the law of averages states that as the number of simulations approaches infinity, an optimal solution will be found. ## Dirichlet DistributionIn the proposed model, sampling was done according to the Dirichlet distribution, which ensures that some number of points in a set, ## Dispatchable Reserve RateAs mentioned in §2.2, grid operators maintain a reserve of dispatchable capactiy based on the fraction of total capacity generated from renewables. Since this is an The Dirichlet distribution first creates a portfolio consisting of the generation technologies listed in Figure 7 ## Qualification CriteriaOver 20,000 portfolios were generated and stored in a matrix. However, many of these did not meet certain the base load requirement, and were removed. With the remaining portfolios, matrix operations were performed to calculate the cost and emissions. The portfolios that had the highest and lowest cost and CO *Base Load If energy portfolios did not meet a predefined percentage of power generation from dispatchables (ρ), they were culled from the dataset. |