Presentation of the group work on theoretical modeling

Today I would like to show you the next step in our theoretical model assignment. Just to give you a short recap, we want to find out the optimal amount of permits to regulate the needs to supply, given we have market power in the clean tech industry. We have different actors. In the clean tech industry, we have the firm with market power, and we have the other firm, both firms producing a given filter. Then we have the regulator and we have the polluting firms. So in the next step, we basically just created some equations.

The first equation or the first two equations show the production costs in the clean tech industry. The first equation shows the production cost for the firm with market power, and the second equation shows the production costs for the other firms. We assume that the firm with market power has market power because they can produce the filter at much lower costs than all the other firms. This you can see in the second equation where you can see that the production costs for all the other firms are higher by a share sigma. The third equation shows the emission cost function for the polluting firms. Here we have the abatement costs plus the cost of the permits.

The permit costs are multiplied by emissions, a function of the filters demanded by firm i and the number of permits initially distributed to firm i. The fourth and the fifth function show the market clearing conditions. Equation four shows the market clearing condition for the permit market. Here we have the total emissions must equal the total amount of the permits supplied on the market. In equation five, we have the demand for the filter and the supply for the filter. The supply for the filter is combined by the supply of the filters produced by all the other firms in the clean tech industry and by the firm who has market power.

With equation three, we would like to find out the optimal amount of filters demanded by the firms. And with the results from this equation, we try to go to this equation. After doing some maths, we try to get to our optimal goal, that is, to optimise environmental damage and to find optimal amount of permits to regulate the needs to supply.