function, before in Section 4 reporting the results from our analysis. As we discuss
in the concluding Section 5, the present paper should be considered a first effort
in combining recent advances in axiomatic theories of intertemporal social choice
(for a survey, see Asheim, 2010) with empirical evaluation of climate-change policies.
Nevertheless, we claim that our analysis is strongly indicative of the importance of
broadening the basis of climate-policy evaluation from DU to SDU and beyond.
2 What is Sustainable Discounted Utilitarianism?
In the empirical part of this paper we consider only consumption streams which
eventually become constant.2 This setting simplifies the presentation of SDU, and
we refer the reader to Asheim and Mitra (2010) for the more general treatment.
Let ct > 0 denote consumption in period t, and let tc = (ct, . . . , cτ , . . . ) be an
infinite stream of consumption, where there exists T ≥ t such that cτ = cT for all
τ ≥ T. A consumption stream tc is called egalitarian if cτ = ct for all τ ≥ 0.
Utility in a period is derived from consumption in that period alone. The utility
function U is assumed to be strictly increasing, strictly concave, continuous and
continuously differentiable for c > 0 with U0(c) → ∞ as c → 0. Clearly, any utility
function with constant relative inequality aversion satisfies these assumptions.
Let δ ∈ (0, 1) denote the utility discount factor. In the axiomatic analysis of
Asheim and Mitra (2010), time periods correspond to non-overlapping generations
assumed to follow each other in sequence. In the empirical analysis of this paper, time
periods are shorter, set to ten years (given by the time-step of the DICE model). As
long as the discount factor is properly adjusted to reflect a plausible trade-off between
present utility and future welfare, this choice of period length does not matter.
With overlapping generations, discounting from an ethical perspective between
different generations should be differentiated from the self-interested discounting that
people do within their own lifetimes, and our analysis - following most literature on
climate-policy evaluation - does not reflect the need to do such differentiation.
Given any δ ∈ (0, 1), the social welfare function (SWF) w defined by
w(tc) = (1 - δ)X∞ δτ-tU(cτ) (1)
τ=t
2 We use a modelling horizon from 2005 to 2395 and assume that consumption remains at the
2395 level thereafter.