Hello, I need help with this assignment. I have already solved question a)

Take Home Assignment 4, part 1 A steel plant is situated by a lake used by a sherman. Steel plant production is 5, sh production is f, and the quantity of pollution being led into the lake by the steel plant, and decided by steel plant management, is 3?. The cost functions for the steel plant. and the sherman respectively are given by (',(s. 1') = 32 + (:r s)2 (:f(f,.'r) = f2 +f;r: The steel plant sells its steel output on a perfectly competitive market, and the market price of steel is 8. Similarly, sh is sold at the market price 6. (a) Identify the prot-maximizing production levels for the two producers, the level of pollution Chosen by the steel plant, and the prots obtained by each producer, when they act. individually. (b) Verify that if the two producers were jointly owned, this owner would choose 3 = 3 and f = 2. (c) Identify the level of pollution chosen by a joint owner and the maximum level of profits obtained. ((1) Now, assume again that. there is separate ownership, and imagine you are to implement an optimal tax on pollution in this case. Identify the right. level for this tax