Consider abatement cost curves of the type C₀(e)= (a₀−b₀e)²/2b₀ and C_I(e)=(a_I−b_Ie)²/2b_I with a₀>a_I and a₀/b₀>a_I/b_I. The social damage function is D(E)=d·E²/2 and the adoption cost for technology I is denoted by

F. The total number of firms is J, while J_I
denotes the number of firms adopting the new technology.

(a) Determine the socially optimal allocation, including emissions and the optimal number of firms adopting the new technology.

(b) Determine the boundaries  and F̅ of fixed costs for which complete adoption, partial adoption, and no adoption is socially optimal.

(c) For each case, determine the formula for the socially optimal emission tax rate and the optimal quantity of emission permits.

(d) Determine the second-best optimal emission standard.

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F