4. An economy consists of five firms. These are the only polluters in this economy. The...

  

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4. An economy consists of five firms. These are the only polluters in this economy. The total cost of abatement of each firm are given below. TC(Z) = 20Z1 + 5Z TC(Z2) = 20Z2 + 2.5Z2 5 Z TC3 (Z3)=20Z3+32 TC4(Z) = 20Z4 + 1.25Z TC5(Z5)=20Z5 + Z a. Derive the marginal cost of abatement for each firm, MC; (Zi). The aggregate marginal cost of abatement is given by MC(Z) = 20 + Z where Z = Zi. The aggregate marginal abatement benefit function is MB (Z) = 300 - Z. b. Find the optimal level of abatement. Also, calculate marginal benefit (or marginal cost) at the optimal level of Z. This is the shadow price of pollution at the socially optimal level. 4. An economy consists of five firms. These are the only polluters in this economy. The total cost of abatement of each firm are given below. TC(Z) = 20Z1 + 5Z TC(Z2) = 20Z2 + 2.5Z2 5 Z TC3 (Z3)=20Z3+32 TC4(Z) = 20Z4 + 1.25Z TC5(Z5)=20Z5 + Z a. Derive the marginal cost of abatement for each firm, MC; (Zi). The aggregate marginal cost of abatement is given by MC(Z) = 20 + Z where Z = Zi. The aggregate marginal abatement benefit function is MB (Z) = 300 - Z. b. Find the optimal level of abatement. Also, calculate marginal benefit (or marginal cost) at the optimal level of Z. This is the shadow price of pollution at the socially optimal level.