Consider J−1 small polluting firms with abatement cost functions C_j(e_j)=(a_j−b_je_j)²/2b_j and one large firm indexed j=1 with market power and abatement cost function C₁(e₁)=(a₁−b₁e₁)²/2b₁. Let ē₂,…,ē_J be the initial permit endowment for the small firms and ē₁ be the endowment for the large firm. The damage function is D(E)=dE²/2.

(a) Determine the socially optimal allocation.

(b) Consider the case where the initial endowment of the large firm is larger (smaller) than socially optimal. Determine the permit trading equilibrium.

(c) Investigate the comparative static effects of increasing the large firm’s initial permit endowment.
Assume now there are two large firms j=1 and j=2.

(d) Consider the case where the initial endowments of the large firms are larger (smaller) than socially optimal. Determine the permit trade equilibrium.

(e) Consider the case where the initial endowment of one large firm is larger and the initial endowment of the other large firm is smaller than the socially optimal allocation of abatement. Determine the permit trading equilibrium.