From the Hamiltonian first order conditions for this problem,
and
λ i(t) = 2cιx(t) + λi(t)
2x(t)
(x2(t) + 1)2
λ j (t) = 2c2x(t) + λj (t)
b+ρ-
2x(t)
(x2(t) + 1)2
(24)
(25)
The optimal steady-state tax rate is found by setting each of λ(t), λi(t) and
λj (t) equal to zero and solving to find λ*, λ* and λ*. From optimal management
equation (14):
(nι + П2)
a(t)
λ(t) =
This holds for all t, therefore this is also true for steady-state λ* and a*, i.e.
λ*
(nι + n2)
a*
To find λ*, one solves
λ i(t)
⇒ λ*
2cιx(t) + λi(t)
—2c1x(t)
b+ρ-
b+ρ-
2x(t)
(x2(t) + 1)2
2x(t)
(x2(t) + 1)2
Similarly, one finds that
λj =
— 2C2X(t)
2x(t)
(x2(t) + 1)2
(26)
Substituting back into (22), gives the optimal constant tax:
(nι + П2) + П1
a* (nι + n2)
/
—2c1x(t)
П2
(П1 + П2 )
/ ∖
— 2C2X(t)
2x(t)
(x2(t) + 1)2
∖
b + ρ —
2x(t)
(x2(t) + 1)2
)
|
/ (n1 + n2) 1 |
∖ 2x(t)(n1c1 + n2c2) |
|
a* (n1 + n2) ∖ |
b+ρ— ]) |
(nɪ + n2) _ ɪ
a* a*
14
More intriguing information
1. LAND-USE EVALUATION OF KOCAELI UNIVERSITY MAIN CAMPUS AREA2. THE CO-EVOLUTION OF MATTER AND CONSCIOUSNESS1
3. Spectral density bandwith choice and prewightening in the estimation of heteroskadasticity and autocorrelation consistent covariance matrices in panel data models
4. Needing to be ‘in the know’: strategies of subordination used by 10-11 year old school boys
5. Housing Market in Malaga: An Application of the Hedonic Methodology
6. The resources and strategies that 10-11 year old boys use to construct masculinities in the school setting
7. IMPROVING THE UNIVERSITY'S PERFORMANCE IN PUBLIC POLICY EDUCATION
8. The name is absent
9. Innovation in commercialization of pelagic fish: the example of "Srdela Snack" Franchise
10. The name is absent