Climate Policy under Sustainable Discounted Utilitarianism

The stationary equivalent consumption c of a consumption stream ₀c is the con-
sumption level c, which if held constant yields the same welfare as the consumption
stream ₀c. By (w.2), the stationary equivalent consumption c of a consumption
stream ₀c under DU satisfies U(c) = w(₀c), or since U is strictly increasing:

c = U^-1(w(oc)) .

By (W.2), the stationary equivalent consumption c of a consumption stream ₀c under
SDU satisfies U(c) = W(0c), or since U is strictly increasing:

c = U^-1(W(oc)) .

We use the stationary equivalent consumption to express non-marginal welfare dif-
ferences in consumption terms (more on this in Section 4).

2.1 Variable population and uncertainty

Asheim and Mitra (2010) introduce SDU in a deterministic setting where population
growth is not explicitly discussed. Application of SDU to climate change, and indeed
to a number of other policy issues, requires explicit treatment of population growth
and uncertainty, however, and we turn to these issues now.

In Asheim and Mitra (2010, p. 150), consumption in period t is interpreted as “a
non-negative indicator of the wellbeing of generation t”. However, how do we compare
the wellbeing of the present generation with the wellbeing of future generations if
population size changes over time?

One possibility is to represent the wellbeing of each generation by the product
of population size and the utility derived from per-capita consumption. This is the
position of ‘classical utilitarianism’. An alternative position is to let the wellbeing
of each generation depend only on per-capita consumption; this is called ‘average
utilitarianism’. There is a substantial literature taking a stance in favour of classical
utilitarianism (see, e.g. Meade, 1955; Mirrlees, 1967; Dasgupta, 2001; Blackorby et
al., 2005). Moreover, this position is standard in the empirical literature on climate-
policy evaluation. Against this background we apply classical utilitarianism in this
paper, while carefully observing the need to make meaningful comparisons of present
utility with future welfare when developing SDU within this position.

Let ct = Ct /Nt be per capita consumption at time t, where population Nt varies
exogenously with time. Classical DU welfare at time t, wt , depends on

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