Hello, I would like some help to solve this question please. Thank you

2. (40 pts) Suppose that you own a house along a river and like to swim and fish in the river every day after school. Suppose further that two factories open upriver from your house and begin to dump waste into the river. The two factories, namely A and B. produce the same product and face the following inverse demand function P = 300 - 6Q. Each factory has a supply function (marginal cost function) given by P = 30: + 30 for i = A, B. (a) Derive the aggregate supply function and calculate the level of output the two factories will supply (market equilibrium). What will be the market price? (b) Suppose that, due to the pollution being dumped in the river, you are catching fish with more than two eyes. A consulting firm estimates that this event imposes a marginal cost to you given by MOy = ;@ and a marginal cost to the ecosystem given by MCE = $Q. What is the socially efficient level of output that the two factories should supply? What will be the socially efficient price? (c) Graph the problem and calculate total social benefits, total social costs and total social surplus at the market equilibrium level of output and at the socially efficient level of output. What is the welfare gain from moving to the socially efficient equilibrium? (d) Assume that there is a technological progress that affects each factory's marginal cost function. Now each factory has a supply function given by P = ;Q, + 30 for 2 = A, B. Calculate the level of output the two factories will supply (market equilibrium). What is the level of output per factory? What is each factory's total cost to producing this level