Extend the model of this chapter by assuming that the firm’s cost function has the form C(X,E) satisfying assumption 5.1.

(a) Derive the second-best optimal combination of an emission standard (no emission tax revenues) and labor tax.

(b) Assume now that an emission tax with revenue recycling is possible. Derive formulas for the second-best optimal combination of the emission and the labor taxes.

(c) Substitute C (X.E) = (aX-bE)²/2b+cX²/2 for the cost function C(X) = cX²/2 in the section 7.3 example, and assume all other functions are the same. Determine the second-best optimal formulas corresponding to (a) and (b).

assumption 5.1

Data from section 7.3

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Assumption 5.1 The cost function C(x,e) is twice continuously differentiable with C()>0, and for any production level x there is an emission level e such that C(x,e) = 0. Furthermore C.(x,e) <0 Ve