The name is absent

Similarly to Maler et al. (2003), by analysing this equation, we find that
for q = 2 and 1 ≤ b ≤ 3 √^z3, the lake displays a reversible hysteresis in its
response to phosphorous loading ² . These are the parameters that will be used
to model the shallow lake that can be reversed from a eutrophic back to an
oligotrophic state. Note that in this case, eutrophication is reversible by simple
control of external phosphorous input. In this case, we can assume that all that
is needed to keep the lake in an oligotrophic state is to manage levels of external
phosphorous loading without any requirement for policy that alters the rates
of phosphorous sedimentation or recycling.

3 Optimal Tax with Two Types of Communities

In their article, Maler et al. (2003) consider the case where all communities
are able to agree on a common welfare function. They note, however, that it
is possible that different interest groups may in fact not be able to agree on
a common welfare function. In the following, the case where the communities
that share the lake are divided into two interest groups with different welfare
function is considered.

The results from this section will be used in the subsequent section to ex-
tend the dynamic shallow lake-communities’ model and consider the impact of
lobbying by the interest groups on the optimal tax, that is, on the tax that
would induce a Pareto-optimal state of the lake.

Consider that society is made up of two groups with conflicting interests:
agricultural communitites and green communities. The agricultural communi-
ties are predominantly made up of farmers who privately benefit from applying
fertilizer and, by proxy, from phosphorous loading into the lake. The green
communities are predominantly made up of people who, although they benefit
from the application of fertilizer to crops because they consume agricultural
products, have a high preference for an oligotrophic lake.

We adopt the welfare function used by Maler et al. (2003) and modify it
to create two welfare functions that each represents the preferences of the two
groups. In this scenario, the farmers attach very low importance c1 to the
ecosystem services provided by the lake, and the green communities attach
a relatively high importance c2 to ecosystem services and so c1 < c2 . The
total n communities previously considered can be divided into n1 agricultural
communities and n2 green communities.

Each agricultural community i’s welfare function is thus given by

Wi = ln ai - c1x², i = 1, . . . , n1

while each green community j ’s welfare function is given by

Wj = ln aj - c2x² j = 1, . . . , n2

where

c1 < c2    i.e., the agricultural communities have a lower relative preference

² Refer to Appendix B for the derivation os these parameters.

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