3. The Demand for Pollution and the Social Optimum (14p) There are two firms (1 & 2) which use a guantity x of a polluting chemical. The total benefit B that each firm derives from the use of this compound (excluding the purchasing costs for the chemical) is given by: B, = 50x, 0.25x, and B, = 100x, x, The supply curve for the chemical is: p=10+4+0.75x where x refers to the total quantity supplied (x = x; + x,), and p is the price (marginal cost of production of the supplier). Please solve the following tasks both graphically and mathematically. a) Find the aggregate demand curve for the good, and plot it on an Excel chart. (4p) Hint: recall the relationship between demand curves (price ~ quantity) and benefit/utility functions b) Solve for the chemical's price and aggregate quantity demanded. How is this quantity distributed among the firms? (3p) Now suppose that the EPA levies a tax of $20 on the supply of each unit of the input. c) Solve for the new price and total quantity. How is this quantity distributed among firms? (3p) d) What is the change in producer and consumer surplus? How much revenue does the EPA receive in taxes? What is the deadweight loss? (4p)