Climate Policy under Sustainable Discounted Utilitarianism



the probability of falling consumption increases significantly under business as usual,
while remaining broadly steady under the 2 CO
2 and 1.5 CO2 abatement policies.

4.1 Welfare evaluation of emissions cuts

Table 2 goes on to examine what these underlying estimates of consumption per
capita mean for SDU and DU welfare.

Before we explain the results, a few words are in order about our measure of
welfare changes. In computing social welfare according to SDU and DU, we obtain
the value of the two abatement policies compared with business as usual in terms
of social welfare, measured in utils. We need to express the change in social welfare
due to abatement in consumption-equivalent terms, in order to quantify willingness
to pay. However, matters are complicated by the very large changes in social welfare
we must contemplate as a result of the risk analysis (e.g. in a future contingency
where climate damage is severe under business as usual, but can largely be avoided
by abatement). We cannot simply normalise the change in social welfare using the
(inverse of the) marginal social welfare of a unit of consumption,
12 because the welfare
change may not be marginal, so that the first-order approximation of the utility
function may be poor. Therefore we turn to the stationary equivalent consumption,
a concept which, following Weitzman (1976), is a standard way of representing social
welfare in dynamic settings and which we have already discussed in Section 2.
13

Table 2 displays our estimates of the stationary equivalent consumption of the
2 CO
2 and 1.5 CO2 abatement policies, compared with business as usual, according
to both SDU and DU. We report the mean estimate, i.e. the expected change in
the stationary equivalent, and also indicate the nature of the underlying distribution
of the change in the stationary equivalent by reporting both the 5
th and 95th per-
centiles. The utility discount rate
ρ in these calculations is 0.02, thus the per-period
(i.e. decadal) discount factor is
~0.82, and the coefficient of relative inequality/risk

12Whereby u10W is our welfare change measure in consumption-equivalent terms, where W
is the change in social welfare according to either SDU or DU between one of the two abatement
policies on the one hand and business as usual on the other.

13We could instead have applied the balanced growth equivalent (BGE) introduced by Mirrlees
and Stern (1972). The BGE of a given amount of social welfare is the initial level of consumption
per capita, which, if it grows at a constant annual rate over all time, yields the same amount of
social welfare. However, as Anthoff and Tol (2009) show, the stationary equivalent consumption
gives the same result as the BGE (independently of the choice of growth rate), provided the utility
function exhibits constant relative inequality/risk aversion.

18



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