Suppose in a given area there are three power plants, each of which emits SO₂ with different intensities. The abatement cost functions for each firm j are:

(a) Set up the conditions for the socially optimal allocation. Can you solve it algebraically?

(b) Let a₁=a₂=a₃=1, b₁=1000, b₂=640, b₃=360, and d=1. Calculate the optimal emission levels for each firm using a numerical software program (i.e. Matlab, Mathematica).

(c) Suppose the government sets an SO₂ tax such that τ=10. Is the size of this tax optimal?

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