the schedule of optimal emissions abatement corresponding to SDU and DU. It can
be seen, intuitively, that emissions abatement is at least as high under SDU as it is
under DU in every time period, and is considerably higher in some, specifically in the
latter half of this century and in the next (top panel). The bottom panel also brings
out the differences between the two sets of optimal controls, but it further shows
that, nevertheless, optimal annual emissions are increasing under SDU and DU for
at least the next one hundred years (albeit much less than under business as usual,
given the control rates). This is explained by our choice of ρ = 0.02, which favours
less aggressive strategies of emissions control, all else equal. Setting ρ closer to zero
would see the flow of emissions peaking earlier, under DU and especially under SDU.
5 Concluding remarks
In this paper we have introduced sustainable discounted utilitarianism (SDU) as an
alternative criterion to discounted utilitarianism (DU) for the evaluation of climate-
abatement policies and we have conducted a risk analysis with the DICE integrated
assessment model in order to find out how much the switch matters empirically. To
set the stage for this application, we first extended the concept of SDU to variable
population and uncertainty (specifically risk). On the back of recent controversies, we
also adjusted the climate sensitivity and damage function used in the standard DICE
model, as part of our wider risk analysis. The result is that, with our alternative
specifications, there is a non-negligible probability that some generation is better off
than its descendants due to the impacts of climate change.
In expectations and at an aggregate level, integrated assessment models like DICE
assume that the future will be much better off than the present, due largely to
the assumption of positive growth in total factor productivity. In our empirical
analysis we have exploited the possibility that in contingencies where the climate
sensitivity is large (so that the increase in atmospheric CO2 leads to a large rise in
temperature) and temperature rise leads to large damages, development of wellbeing
may not be monotonically increasing. When such circumstances are assigned positive
probability, SDU more than DU promotes present action against climate change,
decreasing everywhere (via an exponential penalty function when μt decreases between any two
time periods). Otherwise, the algorithm struggled to find a path towards the global maximum. As
a soft constraint, the penalty does not enter the welfare evaluation. We were able to verify that the
algorithm’s best solution satisfied the property of non-decreasingness in μt, and that no solution
was found which returned higher SDU/DU, where μt was decreasing at any point.
21