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. PROPOSED IMMIGRATION POLICY REFORM & FARM LABOR MARKET OUTCOMES2. EMU: some unanswered questions
3. The name is absent
4. Public-private sector pay differentials in a devolved Scotland
5. The name is absent
6. Imputing Dairy Producers' Quota Discount Rate Using the Individual Export Milk Program in Quebec
7. The name is absent
8. Beyond Networks? A brief response to ‘Which networks matter in education governance?’
9. Effects of red light and loud noise on the rate at which monkeys sample the sensory environment
10. Regional dynamics in mountain areas and the need for integrated policies