The name is absent

We recognise this as a second-order polynomial of the form dX² + eX + f = 0,
where

X = n1l

d= 1,

e = 2n2m and

f = (n2m)² - n1n2m lnaL τ - c1x²_{L τ} - lnaH τ + c1x²_{H τ} ,
which has two roots X of the form

Substituting for d, e and f , and keeping only the positive root of the polynomial,
we obtain the farmers’ optimal lobbying effort:

We note that l andm are dependent on each other. By noticing, from equations
(36) and (38), that

and by substituting back into equations (37) and (39), we can express the
respective optmimal lobbying effort of farmers and ‘greens’, l* and m* as

l* =   nɪn ⁽lnaLτ - cιx²L_τ - lnaHτ + cιx∏_τ)^{2 (}lnahτ - C2X²H_τ - lnaLτ + C2X²L_τ⁾

[nɪ (ln aLτ - cιX²L_τ - ln aHτ + cιX²H_τ) + n (lnaHτ - C₂X²H _τ - ln aLτ + c2xL_τ)]2

(40)

and

_m* =  nɪn (ln aLτ - C1X²L_τ - ln aHτ + C1X2_lτ) (ln aHτ - C2X2_{1 τ} - ln aLτ + C2X²L_τ)²

[nɪ (ln aLτ - CiX²L_τ - lnaHτ + cιx∏_τ) + n2 (ln ahτ - c2x²H_τ - lnaLτ + c2xL_τ)]2

(41)

In the following section, we use these results to study the impact of the
lobbying efforts on the optimal tax policy derived in section 3.6 and depicted
in section 3.8.

20

<<   19   20   21   22   23   24   25   >>

More intriguing information