The Impacts and Costs of Climate Change Page: 38
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The Impacts and Costs of Climate Change
With a utilitarian social welfare function, each person's utility counts equally. It is generally accepted that each
additional unit of consumption provides diminishing marginal utility.
That is, giving 1 Euro to a rich person produces less Utility functions for different a
utility (welfare or happiness may substitute as rough
equivalents) than giving 1 Euro to a poor person. So,Low
utility increases with consumption, but at a decreasing Utility
rate. A common way to represent this is when utility,
u, of consumption, c, is represented by an isoelastic
utility function: u(c) = c(1- )/(1-), where a denotes the
elasticity of marginal utility.High
In this function, the higher F, the more rapidly
marginal utility falls with additional wealth. In other
words, a high a implies that there is little additional
utility gained from additional consumption by people
who are already rich. A higher a therefore implies a
higher aversion to inequality. Consumption
The impact of different choices for a can be shown by considering two countries, one rich (R) and one poor (P).
Suppose country R has an income ten times that of country P. The table below, adapted from Pearce (2003),
shows the value of a marginal Euro to R relative to a marginal Euro to P. For e = 0 (no equity weighting), a Euro
to R is worth the same as a Euro to P. For a= 1.0 (commonly employed in the literature), giving 10 cents to P
achieves the same utility increase as giving 1 Euro to R: marginal income to P is valued ten times more highly
than to R.
Impact of equity weighting when YR = 1OYP
0.0 0.5 0.8 1.0 1.2 1..5 2.0 4.0
Loss to R as a fraction of gain to P 1.0 0.31 0.16 0.10 0.06 0.03 0.01 ~0
Hence even though a pure utilitarian would not weight utility, a utilitarian would weight consumption flows
because of the diminishing marginal utility of consumption. These weights on consumption flows are termed
equity weights and the appropriate equity weight for consumption going to country R is (YN YR), where YN is a
benchmark (or numeraire) income level. The equity weight for consumption going to P is equivalently (YN/Yp) .
The numeraire level is important and is discussed further below.
Evidence on the correct value of a could come from: (a) lab experiments on individual behaviour; (b) revealed
preferences of individuals; (c) revealed social preferences by government spending on programs designed to
reduce inequality in the member states; (d) Member state or European government spending on programs
designed to assist other countries.
Based on evidence of individual behaviour in categories (a) and (b), Cowell and Gardiner (1999) suggest that
values between 0.5 and 4 are plausible. After examining social programs in category (c), Pearce (2003) argues
that values above e 2 are unreasonable because they imply an unrealistically high level of aversion to
inequality. Pearce (1999) concludes that values between 0.5 and 1.2 seem reasonable. Finally, cursory
inspection of foreign aid spending in category (d) would suggest that even = 1 is extremely high- for example
member state governments spend more on its relatively rich citizens than on aid to relatively poor people in other
countries. However, this finding simply reflects the inapplicability of the global utilitarian ethic to the interests
of individual nation-states.
There is another aspect to equity weighting which should also be considered. In standard economic models, the
elasticity a used in equity weighting is the same parameter as appears in the Social Rate of Time Preference:
SRTP = PRTP + * g
where PRTP is the Pure Rate of Time Preference, F is the negative of the marginal elasticity of utility with
respect to consumption, and g is the per capita GDP growth rate. From this perspective, a more consistent
approach is to specify the PRTP and elasticity that we wish to use, and derive consistent equity weights and
AEA Technology Environment, August 2005
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Watkiss, Paul; Downing, Tom; Handley, Claire & Butterfield, Ruth. The Impacts and Costs of Climate Change, text, September 2005; Oxford, England. (digital.library.unt.edu/ark:/67531/metadc29337/m1/49/: accessed January 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .