Consider the following market demand and production cost functions.

(1) P = 10,000 - 2.5Q

(2) TC = 5Q

(1) (3 points) Derive the firms' quantity-response functions under Cournot duopoly. Show the derivation steps.Calculate firms' equilibrium quantities, market price, total market quantity, and firms' profits. These represent the pre-regulation market equilibrium.

(2) (3 points) A new regulation mandates cleanup. Now, each firm has to incur a marginal cleanup cost of $2.5 per unit produced. Note that the firm now has a marginal production cost as before, and a new marginal cleanup cost for each unit produced. Calculate the new equilibrium quantities, market price, total market quantity, and firms' profits. These represent the post-regulatory short-run equilibrium.

(3) (4 points) Next, the firms move to innovate and improve production efficiency to counteract the cleanup costs. These initiatives potentially result in reduction in marginal cleanup costs and/or marginal production costs. From the post-regulatory cost structure noted in #2 above, suppose the firms attain a 50% reduction in marginal cleanup costs, and another 25% reduction in in marginal production costs as part of their longer-run benefits from cleaner production. Calculate firms' equilibrium quantities, market price, total market quantity, and firms' profits. These represent the post-regulatory longer-run equilibrium.

(4) (2 points) Discuss the effects of the regulation on the two firms under Cournot competition, using the numbers calculated above. Be precise.