Unilateral Actions the Case of International Environmental Problems

mation about costs. The insight gained in the first part of the paper is used in
section 5 to model a situation, where unilateral actions are possible, which is
formally shown in section 6. In section 7, we relax the assumptions and this
shows the robustness of our results. Finally, an alternative specification of the
way environmental policy is determined is given in section 8, while section 9
concludes the paper.

2. Model

First, a model of an international environmental problem that resembles the
original specification of Hoel (1991) will be presented. This will enable us to
use Hoel’s model as a benchmark and his results as a point of departure for fur-
ther analysis. The set of countries is I = {1,2,..., N} . Each country emits ei, the
polluting substance, which cause environmental degradation both domestically
and abroad. For simplicity, assume auniformly mixed pollutant giving rise to a
global emission problem. Hence, each country is affected by the total emission
level e = ∑ei . Let the emission level in the case of no environmental concern
i

be e_i^o , and assume that e_i ∈ [0,e_i^o].² Compared to e_i^o , a country might undertake
certain reduction effort. Let q_i = e_i^o - e_i be the actual reduction level of country
i, hence the level of reductions is measured by how much emissions are reduced
compared to e_i^o . We have that q_i ∈ Q_i = [0, e_i^o] . Due to the global pollutant as-
sumption, it is the total reduction level, q = ∑qi , that is relevant for a country’s
i

reduced level of environmental degradation.

2 Although the possibility of emissions above e_i^o cannot simply be excluded, we dismiss this
possibility here. See Brandt (2002) for a model where, for strategic reasons, emissions are
increased above the short run optimal levels (and possibly above e_i^o ).

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