||Marginal cost|Abat|ement potential|
|---|---|---|---|
||_γ_<sup>_′_</sup><br>_i_<sup>(1 GtCO2/yr)</sup><br>[ $/tCO2]| ̄_ai_|[ GtCO2/yr]|
|Waste|34||0.76|
|Industry|17.6||4.08|
|Forestry|15.9||2.75|
|Agriculture|11.9||4.39|
|Transport|11.6||2.1|
|Energy|10.3||3.68|
|Buildings|3.6||5.99|

Table 2: Assumptions on marginal abatement costs and maximum potential in seven sectors of the global economy. Numerical values derived from the abatement potential at a marginal cost below 20 $/tCO 2 in gure SPM.6, page 11 of IPCC (2007).

# 4 Illustrative examples using IPCC abatement costs

We use the two models (with and without economic inertia) to investigate the optimal sectoral abatements over the 2007-2030 period. We set a policy objective over this period only,<sup>4</sup> and use abatement cost information derived from the IPCC (2007). Because of data limitations, this exercise is not supposed to suggest an optimal climate policy (see also section 5). It aims at illustrating the impact of two extreme assumptions (abatement options are totally evanescent or totally permanent) on the optimal abatement strategy, using the same cost estimates and the same policy objective. We show that the optimal abatement strategy and in particular the choice of which sectors need to abate more and earlier depends on whether abatement actions are assumed permanent or evanescent.

## 4.1 Data

IPCC (2007) provides data on abatement costs and potentials until 2030, in 7 sectors of the global economy (Tab. 2). These abatement costs have two components that are aggregated in IPCC data. The rst component is the cost for evanescent reduction; it is captured by the model exposed in section 2. The other component is the costs of persistent reductions, it can be captured by the model exposed in section 3. From the same data on costs, potentials and carbon budget, we derive two optimal reduction strategies, one from the model with no economic inertia (section 2), and the other from the model with technical inertia and convex investment costs (section 3).

In this illustrative example, we assume abatable emissions _Eabat_ =<sup>�</sup> _i_<sup>_a_ ̄</sup><sup>_i_=24GtCO2/yr.</sup> Compared to the total baseline emissions in 2030 in the A1B scenario from Nakicenovic et al. (2000), 69 GtCO 2 /yr, this gives _E_ 0 = 45 GtCO 2 /yr. In this case, _E_ 0 cannot be interpreted as a denitive safe level for emissions, but rather as an emission milestone in 2030 in a pathway toward a sustainable longer-term target.

We call _T_ = 23 yr the time span from 2007 the publication date of IPCC (2007) and 2030. We set the discount rate to _r_ = 4% /yr. We constrain the cumulative dangerous emissions over the period as: The two models are solved with a numerical resolution, using a time step _dt_ = 0 _._ 1 yr.<sup>5</sup>

## 4.2 Calibration

We calibrate the two models (with and without inertia) such that the discounted costs of reaching the same target are equal in the two models (this methodology was rst used by Grubb et al. (1995)).

> 4 The theoretical, innite-horizon models exposed in sections 2 and 3 have to be modied; all the results exposed still apply.

> 5Data and source code are available at the corresponding author's web page. Computation and plots use Scilab

> (Scilab Consortium, 2011).

8