2. (60 points) Consider a factory which is producing plastic bags. The factory production process causes some pollution in form of toxic suspended solids which can be transformed into a nontoxic particle and stored. The cost of producing x kilo of plastic bag is 0(1) : 10 + 0.7532. The factory produces 1 kilo of toxic solids for each kilo of x. If the factory captures the toxic solids it will cost them an extra amount of $5 for each kilo of z where z is the amount of captured solids in kilo. If they do not capture the solids then the toxic solids will pollute the products of a nearby farm and cause the farm an extra cost of C(t) = [1.5/3)t2 where t is the amount of released toxic solids in kilo. Therefore, t = :r z. The production cost of producing y kilo of crops for the farm is C(y) : 5 + (D.5/2)y2. Let us assume that P; = $15 is the price of each kilo of x and Pg 2 $10 is the price of each kilo of crops in market. (a) In a competitive equilibrium what is the values of x, y, and t? (10 pm) (b) In this case how much the rm spend to protect the environment? (6 DtS) (c) What is the externality cost imposed on the farm? (7 pts) (d) If the socially optimal outputs are resulted from maximizing the sum of the rm and the farm prots, what is the socially optimal level of x? (10 pts) (e) Why the competitive equilibrium is inefcient from a social perspec tive? (10 pts) (f ) If the factory buys the farm now what are the values of x, y and t'? (10 pts) (g) How much the united rm pays for protecting the environment and how much the pollution costs it? (7 pts)