The Upstream Nukem Co. uses a technology that produces pollutants as a by- product. The company dumps these pollutants into Radiant River. The only way that Nukem can reduce pollution is by cutting output. Nukem's prots, expressed as a function of the amount x (in tons) of pollutants per day, is HN (x) = 100x 5x2 The pollution adversely affects the performance of Downstream Glowing Fisheries. Glowing's prot, as a function of the quantity of pollution, is given by HG(x) = K 5x2 where K is a constant relating to all factors other than pollution. (i) If there are no restraints on pollution and no negotiations between the two companies, how much pollution will Nukem produce per day? 35 =. 10 8 6 4 2 00000 (ii) What is the socially optimal quantity of pollution? x* = 00000 oa~u] 4:. Suppose Nukem has the right to continue to pollute, but Glowing can pay it a constant price per ton to reduce pollution. This price will be determined through (competitive) market negotiations between the two companies. Negotiation is costless. Let the price be represented by p per ton. Note that if the post- negotiation quantity of pollution is x