1. Consider the following numerical version of the manufacturing} shing externalitv problem that was discussed in class. Let: I gm, Pm denote the quantity produced and price of manufactures I of Pr denote the quantity caught and price of sh I 3: denote the amount of pollution created by the manufacturer. Let the technologies for the two rms he represented by the cost functions: I fanufactnring: leqm._r] = 29'3\" + (J: 2]2 I Fishing: Sil'ljeml = 2n; + 33: That is, Cpqp, r] is the total oost of producing om manufactured goods when the level of pollution is .12. Similarly: Cf{qf133) is the cost of catching 1}; sh when the level of pollution is 1'. Prot [which rms maximize] is dened as the difference between total revenue and total cost. Let Pm = T, F; = 8, and assume that pollution is generated through manufacturing production according to the mction : :r: = .qm. a. How much pollution, Jr", will be produced if the rms are independent enterprises? b. Hov.r much pollution will be produced if the rms merge? If your answer is different from that derived in part 3., what accounts for the difference? c. Find the Pigouvian tax, T1 that induces the independent manufacturer to produce the same amount of pollution as it would if it were merged with the shing rm.|