The name is absent

equilibrium at (0.7402, 0.0902). Note that both of these points are above the
point at which the lake flips to a eutrophic state. This means that when the
green communities and agricultural communities do not cooperate, the lake will
be in a eutrophic state.

Figure 2: Nash Equilibrium Loading with Two Welfare Functions

3.5 Optimal Taxation with Two Interest Groups

Our benevolent politician therefore wants to find the tax rate that will achieve
the optimal social welfare outcome derived in section 3.1 without the need for
management. The effect of the tax will be to modify each community’s welfare
function and induce each one to modify its phosphorous loading accordingly.
With the tax, the agricultural and green communities will each

x²(t)

x(t) = a(t) - bx(t) +           = 0,

x²(t) + 1

n1           n2

^a(t) = £ ai(^t) ⁺ £ aj^(t)

i=1         j=1

x² (t)

x(t) = a(t) - bx(t) + -₁        = 0,

x²(t) + 1

n1           n2

^a(t) = £ ai(^t) + £ aj^(t)

i=1         j=1

12

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