Operational tools and adaptive management

L
w
L
S
0
0
L
w
0
and
(
L
S
0
if
where L denotes the Lagrange equation. Solving for the Lagrangian multiplier, γ S , and
equating gives
S
U
w
U
w
MS
0
F
0
U
w
U
w
MS
F
S
Rearranging, we obtain the equality of the marginal rates of substitution between w and w0 of
the national authorities and the fishers.
w
w
0
U1
U1
U
w
U
w
MS
MS
0
U
w
U
w
F
F
0
w
w
0
U2
U2
Solving for w provides the following solution to the optimal tax/subsidy rate;
MS
1
MS
1
F
1
F
MS
( ) ( )
w *
(17)
F
1
Solving for the Lagrangian multiplier gives
S
0
The inequality holds if we assume that the incentive scheme influences the pay-off to both the
principal and the agent.
This implies that the participation constraint is binding, and thus
F
U ( w , w,
E )
F0
U
(19)
0
j
Inserting for w* in (13), we can solve for the lump sum transfer:
F
1
F
1
M
j
F
F F0
* 2
* E C U
w 0*
w1
w1
(20)
4a
2a
F
1
where C F is given above.
0;
L
S
0
if
S
0)
(14)
(15)
(16)
(18)
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