The name is absent

Figure 3: Nash Equilibrium Loading with Two Welfare Functions and Tax

4 Lobbying, Political Ambition and their Impact on
the Optimal Tax

Consider the case where the lake is in a eutrophic state in spite of a current
tax on phosphorous loading. The green communities have a preference for an
oligotrophic lake and consider that the current tax rate is too low. The n com-
munities face an election to elect a single politician. The politician favoured by
the green communities promises to implement a higher tax on phosphorous that
will bring phosphorous loading down so as to reverse the lake to an oligotrophic
state. The farming communities favour a politician who promises to maintain
the tax at its current low level.

Figure 4 shows the Nash equilibrium loading with a low tax, τ = 1, together
with the curve of the Nash equilibrium loading with the optimal tax τ* = 29.78,
as given by equation (27). Note that in the context of a low tax, the high eu-
trophic Nash equilibrium could prevail, whereas in the case of the optimal tax,
only one Nash equilibrium is possible.

4.1 Lobbying to Influence Policy Outcomes

Each group applies lobbying effort to influence the policy outcome. The green
communities lobby in favour of a high tax and the farmers lobby for a low tax
on phosphorous loading. The lobbying effort of each agricultural community i
is denoted by li and the lobbying effort of each green community j is denoted
by mj .

We apply the Tullock model of rent-seeking (Tullock, 1980) to obtain the
probability of each groups’ lobbying efforts being successful at having their de-

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