Now consider the continuum of firms model as suggested in section 11 3 The conventional and new technologies are again given by C 0 (e) (a 0 b 0 e) 2 2b 0 and C I (e) (a I b I e) 2 2b I with a 0 a I and a 0 b 0 a I b I The fixed cost is given by (a) Determine the socially optimal allocation, includ...

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Now consider the continuum-of-firms model as suggested in section 11.3. The conventional and new technologies are again

Question:

Now consider the continuum-of-firms model as suggested in section 11.3. The conventional and new technologies are again given by 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 fixed cost is given by:

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

(b) Determine the optimal emission tax and the number of tradable permits.
Assume now that the new technology is produced by a monopolist.

(c) Derive the inverse demand function for the new technology.
Determine the profit-maximizing price for the monopolist when the tax rate is given.

(d) Derive formulas for the optimal policy mix.

(e) Assume that the regulator may only use an emission tax. Derive a formula for the ex ante second-best-optimal tax rate.

(f) Alternatively, assume that the regulator may only issue emission permits, and derive a formula for the ex ante second-best-optimal number of emission permits to provide.

(g) Assume that the regulator may only set a tax, and she has to set the tax rate ex post. Determine a formula for the ex-post optimal tax rate.

Data from section 11.3