The name is absent

∑      ∑j  1 mj    Ал         2λ

(    ∑i= ι li + ∑ ι mj ) Vn aL ^τ  c²xL '

where

τ The tax rate applied to phosphorous loading.

L τ denotes the low tax rate and H τ denotes the high tax rate.

l The lobbying effort of farmers in favour of a low tax rate.

m The lobbying effort of greens in favour of a high tax rate.

To find the optimum lobbying efforts l* and m*, one finds the values of l_i
and mj for which the first derivative is equal to zero, i.e. dE {Π_F} /dli = 0 and
dE {ΠG} /dmj = 0. (These values will maximize the expected pay-offs provided
the profit functions are concave, i.e. if their second derivatives are negative.)
Therefore we begin by solving:

d_        ∑η= 1 li Λ             2 ʌ

dl ∑ηι l l ∑η _rn (ɪn ^αL^τ c¹xLτ)
dlⁱ    i=1 lⁱ + j=1 mj

∑η= 1 li      Ал            2 ∖   ,'

∑nι / -J-∑η m Vn aHτ - ^c1xH τ) ^- li
i=¹1 li +   j=² 1 mj

For simplicity, we assume that all the communities are approximately the
same size, that is, they contribute an equal amount of lobbying effort, so that
∑n= ₁ l_i = n₁l and ∑n== ₁ mj = n₂m. Equation (35) then becomes

⇔ n1n2m lnaLτ - c1x²_Lτ - ln aH τ + c1x²_Hτ = (n1l + n2m)²
which expanded is
(n1l)² + 2n2mn1l + (n2m)² - n1n2m ln aLτ - c1x²_Lτ - ln aHτ + c1x²_Hτ = 0

19

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