Consider the model from section 11.3. Assume now that the cost of new technology is C'(e, v) with C^l _v (e, v)> 0 C^l _vv (e, v) > 0 and -C^l _ev (e, v) > 0, where v is a technology parameter impacting the variable abatement cost function. Assume further that [e_º(t)-e_v, (T)] is decreasing in τ, where e_v, (T) is firm ν’s optimal emission choice with the new technology.

(a) Show that all the results from section 11.3 follow through under this assumption.

(b) Alternatively, assume that the old technology depends on ν and is written as C^o (e, v), with C^l_v(e, v) l _vv (e, v)>0 and -C^l_ev(e, v) v, (t)-e_l, (T)], is decreasing in τ, where -e_v, (t) is firm ν’s optimal emission choice under the old technology. Proceed as in (a).

Section 11.3

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Thus far we have interpreted private investment either as private R&D with deterministic outcomes, or as the degree of adoption of some existing technology. In many cases, technology adoption is a yes/no discrete decision involving fixed investment costs. Since large fixed costs are involved in such investments, the question is not how much an individual firm should invest to lower its abatement costs, but rather how many firms should adopt the cleaner, but costly new technology. In this section, we first investigate the investment decision made by a single firm, and then look at the optimal adoption rate as it depends on fixed costs. We also examine how different policy instruments perform under different circumstances.