Question

Consider two polluters (A and B) emitting a harmful chemical into the air. Let TAC-Total Abatement Cost, MAC Marginal Abatement Cost, and e-emission. A and B may be regulated for a standard of es 20 via the equiproportionate approach (10 "e" each) or the equimarginal approach (MACA MACB ). Their respective MAC curves are: MACA-20-ea and MACB l 5-0.75e. (a) Compute TAC subject to the equiproportionate approach. (b) Find x and compute TAC subject to the equimarginal approach. (c) Provide detailed graphs and offer a recommendation as to which approach would be more beneficial to society

Answer 1

a) TAC = TAC_A + TAC_B, MAC_A = 20 - e_A TAC_A = integral MAC_A de_A = integral (20 - e_A)de_A = 20 middot e_A - e_A^2/2 so when Equiproportionate, e_A = e_B = 10 so TAC_A = (20 times 10) - 100/2 = 200 - 50 = 150, TAC_B = integral MAC_B de_B = integral(15 - .75 e_B)de_B = 15 e_B - .75/2 (e_B)^2 = (15 times 10) - 75/2 times 100/100 = 150 - 75/2 = 112.5 so TAC = TAC_A + TAC_B = 150 + 112.5 = 262.5 Ans b) when EquiMarginal rightarrow MAC_A = MAC_B 20 - e_A = 15 - .75e_B & e_A + e_B = 20 so 5 = e_A - .75 e_B, put e_A = 20 - e_B so 5 = 20 - e_B - .75 e_B 1.75 e_B = 15 e_B = 8.5714286, e_A = 11.4285714] Ans so X = MAC_A = MAC_B = 20 - e_A^* = 11.4285 Ans c) Now TAC rightarrow in EquiMarginal Principle rightarrow TAC = TAC_A + TAC_B = 20e_A^*