Papers by Fischer et al. (2004), Williams (2011), Slechten (2013), and VogtSchilb et al. (2014), all study the optimal accumulation of clean capital but do not investigate formally implications for existing polluting capital. Here we discuss the pacing of abatement efforts over time and the impact of different policy instruments on the price of existing capital.

Our analysis builds on a Ramsey model with two types of capital: “polluting” capital, which creates a negative externality (greenhouse gases emissions), and “clean” capital, which does not. Investment is irreversible, meaning that capital can only disappear through depreciation. Firms may however underutilize existing polluting capital, so that abatement efforts can be divided out between two qualitatively different channels: (i) long-term abatement through accumulation of clean capital instead of polluting capital (e.g. people buy electric cars); (ii) immediate abatement through the underutilization (or early-retirement) of polluting capital (e.g. people drive less).

We start from a _laissez-faire_ economy, in which marginal productivities of polluting and clean capital are equal. We compare two strategies (carbon price and investment-based instruments) to maintain the concentration of greenhouse gases in the atmosphere below a certain threshold, corresponding to an exogenous policy objective such as the UNFCCC 2<sup>_◦_</sup> C target.

We find that mitigation costs decompose as a technical cost — using clean instead of polluting capital — and a transition cost due to the irreversibility of pre-existing polluting capital. This irreversibly cost quantifies the regret that society has because of excessive past investment in polluting capital (e.g. having built a coal power plant before the climate mitigation policy has been announced). In the long run both strategies lead to the same steady state, in which most installed capital is clean and GHG concentration is maintained at a constant level. The carbon price and investment-based instruments however induce different trajectories and costs over the short run.

A carbon price maximizes inter-temporal welfare. It redirects all investment towards clean capital until polluting capital has depreciated to a level compatible with the long-term climate ceiling. The carbon price also induces a shortterm decrease in the market price of existing polluting capital. This market price has three functions. It values polluting assets, it reflects the demand for new polluting capital and it signals the profitability of polluting capital to investors. If the climate constraint is stringent with regards to past polluting capital accumulation, the market price of polluting capital can even reach zero, and part of this capital is decommissioned. These assets that loose all their value because of the policy are often referred to as “stranded assets” (Goulder et al., 2010; Carbon Tracker, 2013). The underutilization or early retirement of polluting capital allows high short-term abatement but has significant impact on production.

In contrast, investment-based instruments neither create stranded assets nor provide an incentive to underutilize polluting capital. Quite the contrary: by inducing a scarcity effect on polluting capital, these instruments increase the market price of existing polluting capital (i.e. generating “windfall profits” as in Goulder et al., 2010, when emission allowances are grandfathered instead of auctioned). Investment-based instruments yield a higher irreversibility cost than the carbon price as society keeps using obsolete polluting capital until the end of their lifetime instead of early-scrapping it – as if refusing to recognize that past accumulation of polluting capital was a mistake. Thereby, they are 2