Climate Policy under Sustainable Discounted Utilitarianism

and is equivalent to a few percent of output. Unfortunately, what the impacts of
climate change will be for larger amounts of global warming remains largely in the
realm of guesswork (Weitzman, 2009), due to possible non-linearities in the biophys-
ical and socio-economic response to changes in climate variables, as well as possible
singularities in the climate system itself (e.g. a collapse in the Antarctic ice sheet,
or a shutdown in the ocean circulation), all of which are very poorly understood at
present. This points the spotlight at the functional form for damages.

There has never been any stronger justification for the assumption of quadratic
damages than the general supposition of a non-linear relationship, added to the fact
that quadratic functions are of a familiar form to economists, with a tractable linear
first derivative (i.e. the marginal benefit function of emissions reductions). However,
when extrapolated to large temperature levels, the implications of a quadratic func-
tion have recently been cast in doubt. Both Ackerman et al. (2010) and Weitzman
(2010b) have shown that, with Nordhaus' (2008) calibration of eq. (7), 5^oC warming
results in a loss of utility equivalent to just 6% of output, despite such warming being
equivalent to the difference between the present global mean temperature and the
temperature at the peak of the last ice age, while it takes around 18^oC of warming
for losses in utility to exceed the equivalent of 50% of output.

There are various ways to remedy what is increasingly regarded as an implausible
forecast (Ackerman et al., 2010; Stern Review, 2007; Weitzman, 2009). Following
eq. (7), utility losses can be ramped up by increasing the coefficients α1 and α2 ,
but only at the expense of unrealistically large losses in utility for the initial 3^o C
warming. Conceptually, much follows from the specification of the utility function.
Working with a standard utility function whose sole argument is consumption of the
composite good, we can introduce a higher-order term into the damage function to
capture greater non-linearity, as Weitzman (2010b) does.⁹ We specify the following
function:
where α₃ is a normally distributed random coefficient with mean and standard devi-
ation reported in Table 1. The remaining coefficients α1 and α2 are as in Nordhaus
(2008). If α₃ takes its mean value, 5^oC warming results in a loss of utility equiva-
lent to around 7% of output, while 50% of output is not lost until the global mean

⁹ The alternative is to specify utility as a function not only of consumption but also of environ-
mental quality directly, for example indexed by global mean warming.

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