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parameters: the threshold temperature, the damages at that tempera-
ture, and the convexity of the curve.
However, we do not know any of these parameters even to a fi rst
approximation. The fi rst parameter is the tipping point, here assumed to
be 3
1
⁄
2
°C. We saw in the earlier chapters that the exact point at which
the tipping elements enter is poorly understood. Second, we need esti-
mates of damages at the threshold. I assume that the total damages are
about 0.5 percent of income at the threshold, but that is just an assump-
tion and has no empirical basis. A fi nal uncertainty involves the curva-
ture of the damage function. I assumed that it is extremely convex as
represented by a function of temperature to the twentieth power, but
this is just an illustration. There is no empirical evidence on the curva-
ture and that the function should be raised to the twentieth rather
than the fourth or the fi ftieth power.
So at this point, the focal temperature target shown in Figure 32 is
just an illustration. Different assumptions would lead to very different
results—some to higher targets, some to lower targets.
COST-BENEFIT ANALYSIS IN THE CASINO
We can use the cost-benefi t approach of the previous section to illus-
trate how uncertainties of the Climate Casino can affect climate policy.
There are many possibilities, but we can easily illustrate two polar cases.
In the fi rst example, policy follows an
expected value
principle. For
this case, we take the nontipping scenarios shown in Figures 29 through
31 but assume that we do not know the magnitude of the damages.
More precisely, assume that there is uncertainty about the size of the
damages at each temperature increase. Suppose that at a 2°C increase,
the damage is either 1 percent of income or 3 percent of income with
even odds, which gives an expected value damage of 2 percent of in-
come. (Expected value here means the statistical average; for example,
the expected value of a roll of a die is 3.5 dots.) A similar uncertainty
arises at each temperature level, and it might hold for costs as well. For
this case, a little analysis will show that we only need to consider the
average damage and cost, and the uncertainty does not affect the best
decision.
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