Hello, I would like some help to solve this question please!

3. (35 points) Suppose there are two firms, namely firm 1 and firm 2. In the course of their operation, they burn fossil fuels releasing greenhouse gases into the atmosphere. The abatement cost function for each firm is given by MAC, = 180 - 0.4E, and MAC2 = 160-0.4E2, where E; for i = 1, 2 is tonnes of CO2 emission per month. The damages caused in the atmosphere can be described by MD = 0.18E. (a) Derive graphically and algebraically the aggregate marginal abatement cost func- tion and find the socially efficient level of emissions. (b) Assume that the regulator sets uniform emission standards to the two firms in order to achieve the socially efficient level of emissions. Find the uniform standard per firm and calculate the total compliance cost per firm. (c) Assume now that the regulator applies a transferable emission permit (TEP) system to control pollution. They issue permits for a total emission level equal to the socially efficient level of emissions. Each permit gives the holder the right to emit one tonne of emissions per month. They allocate (i.e., free-of-charge) all the permits to firm 1. (i) Find the price of the permits in the market and the optimal allocation of the permits. How many permits are traded in the market? (ii) Calculate the total compliance cost per firm at the initial allocation and at the optimal allocation. What are the private cost savings for each firm due to trading? (iii) If the regulator allocates initially all the permits to firm 2, what do you expect to be the effect on the price of the permits, on the number of the permits that are traded in the market, and on the total social compliance cost at the optimal allocation? Justify your answers