A factory produces jointly furniture and dust pollution. The pollution adversely affects a nearby cattle ranch . Both firms are price takers. is the market price of furniture. is the market price of cattle. (, )=2 +(2)2 is 's cost of producing units of furniture jointly with units of pollution. (, )=2 + is 's cost of producing units of cattle. = 20 and =5.

(Show all the steps and formulas that help you calculate a,b, and c) (a) If the two firms are operated independently, what is the profit-maximizing quantity of each firm? What is the profit of each firm? What is the total profit of the two firms? (b) If the two firms choose to merge, what is the profit of the merged firm? (c) Suppose the two firms didn't choose to merge and they are operated independently, and the government would like to impose a Pigouvian tax of dollars per unit of dust pollution generated by the factory, as a solution to negative externalities. How should the government set the tax? (Calculate the amount of the tax.)

Problem 9* A factory X produces jointly furniture and dust pollution. The pollution adversely affects a nearby cattle ranch Y. Both firms are price takers. Px is the market price of furniture. py is the market price of cattle. Cx(x, z) = x2 + (z -2)2 is X's cost of producing x units of furniture jointly with z units of pollution. Cy(y, z) = yz + zy is Y's cost of producing y units of cattle. Px = 20 and py = 5 (a) If the two firms are operated independently, what is the profit-maximizing quantity of each firm? What is the profit of each firm? What is the total profit of the two firms? (b) If the two firms choose to merge, what is the profit of the merged firm? (c) Suppose the two firms didn't choose to merge and they are operated independently, and the government would like to impose a Pigouvian tax of t dollars per unit of dust pollution generated by the factory, as a solution to negative externalities. How should the government set the tax? (Calculate the amount of the tax.) MacBook Pro * + a LO - O ~ O OO O