(This problem requires some knowledge of calculus.) Suppose there are two firms in a production economy, each using good 1 as an input to produce good 2. They are both located in the same town, and both are bad polluters, so each one's operation has a deleterious effect on the other. Firm 1's production set Y1 is given by y12y1143y22. Firm 2 's production set Y2 is given by y22y2143y12 Suppose the market prices of goods 1 and 2 are given by p=(1,1). Assume that each firm takes the other's output as given and fixed. a. Calculate the competitive equilibrium production plan for the economy. b. Show that the competitive equilibrium is not an optimum. (This problem requires some knowledge of calculus.) Suppose there are two firms in a production economy, each using good 1 as an input to produce good 2. They are both located in the same town, and both are bad polluters, so each one's operation has a deleterious effect on the other. Firm 1's production set Y1 is given by y12y1143y22. Firm 2 's production set Y2 is given by y22y2143y12 Suppose the market prices of goods 1 and 2 are given by p=(1,1). Assume that each firm takes the other's output as given and fixed. a. Calculate the competitive equilibrium production plan for the economy. b. Show that the competitive equilibrium is not an optimum