Common Pool Politics and Inecient Fishery
Management
Julia Homann and Martin Quaas
July 8 2014
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
1/24
Outline
1
Motivation
2
Model Set-up
3
The Common Pool Politics
4
Conclusion
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
2/24
Motivation
• 30% of sh stocks worldwide overshed in 2009 (FAO 2012)
• most important tool in sheries management: total allowable
catch (TAC)
• in some countries the TAC system is quite successful (e.g. New
Zealand, Iceland)
• in others it is not (e.g. EU, Chile)
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
3/24
Motivation
• our approach: dierent institutional set-up may lead to
dierent levels of eciency of TAC management
• successful - single person decision
• not successful - council decision
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
4/24
Motivation
• our approach: dierent institutional set-up may lead to
dierent levels of eciency of TAC management
• successful - single person decision
• not successful - council decision
Does group decision-making result in ineciently high TACs?
And if so, under which conditions?
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
4/24
The Model
Assumptions I
• TACs are set by a group of decision-makers (in a council)
• decisions are made with majority voting
• decisions on TACs are based on a dynamic game in discrete
time
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
5/24
The Model
Assumption II
• two types of decision-makers: patient (p ) and impatient (i )
with discount factors ρ > ρ
p
i
• objective: nd optimal escapement that maximises discounted
prots considering the choice of escapement of the other group
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
6/24
The Model
Assumptions III
• escapement = stock − harvest:
s
t
= x − h where h = TAC
t
t
(1)
t
• current prots:
xt
π(h ) =
Z
t
(p − c (x ))dx ≡ π(x ) − π(s )
t
t
(2)
st
• stock dynamics:
x +1 = z g (s )
t
with
t
t
(3)
E (z ) = 1; [z , z ] ⊂ [0, ∞)
t
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
7/24
The Model
Assumptions IV
• majority
m=
•
•
m can change over time due to elections
(
i
p
if majority of impatient decision-makers
if majority of patient decision-makers
(4)
q is the probability of an impatient majority
(1 − q ) is the probability of a patient majority
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
8/24
Optimal Fisheries Management (Clark 1990)
• assume: majority is not changing
• maximisation problem:
∞
X
δ
max E (
sj
t
=1
t
−1
(π(x ) − π(s )))
t
t
subject to
x +1 = z g (s )
t
t
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
t
(5)
9/24
Optimal Fisheries Management (Clark 1990)
• assume: majority is not changing
• maximisation problem:
∞
X
δ
max E (
sj
t
=1
t
−1
(π(x ) − π(s )))
t
t
subject to
x +1 = z g (s )
t
t
t
(5)
• optimal feedback strategy: constant escapement
s ? (x ) = min{x ; s ? }
j
j
with
j = {i ; p }
and
s?
p
>
s?
i
> 0 (6)
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
9/24
The Common Pool Politics
• assume: change in majority is possible
• implication: choice of escapement of the other group has to be
considered in own optimal management decision
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
10/24
The Common Pool Politics
• Bellman equation v (x , m) to nd optimal escapement (with
j = {i ; p}):
v (x , m) = π(x ) − π(ŝ (x )) + ρ (q v (zg (ŝ (x )), i )
+(1 − q ) v (zg (ŝ (x )), p ))
j
j
j
j
•
ŝ
j
(7)
= optimal feedback strategy of majority
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
11/24
The Common Pool Politics
• Bellman equation v (x , m) to nd optimal escapement (with
j = {i ; p}):
v (x , m) = π(x ) − π(ŝ (x )) + ρ (q v (zg (ŝ (x )), i )
+(1 − q ) v (zg (ŝ (x )), p ))
j
j
j
j
•
ŝ
j
(7)
= optimal feedback strategy of majority
• optimal feedback strategy: constant escapement
ŝ (x ) = min{x ; ŝ }
j
j
with
j = {i ; p}
and
ŝ
p
>
ŝ
i
> 0
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
(8)
11/24
The Common Pool Politics
Proposition 1.
Patient decision-makers do not deviate from their
optimal escapement strategy, i.e. their dominant strategy is
ŝ (x ) = s ? (x ).
p
p
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
12/24
The Common Pool Politics
Proposition 2.
Impatient decision-makers deviate from their
optimal escapement policy if and only if s ∗ > zg (s ∗ ).
p
i
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
13/24
The Common Pool Politics
Proposition 2.
Impatient decision-makers deviate from their
optimal escapement policy if and only if s ∗ > zg (s ∗ ).
p
i
This is given if ρ − ρ > ρ̄.
p
i
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
13/24
The Common Pool Politics
Proposition 2.
Impatient decision-makers deviate from their
optimal escapement policy if and only if s ∗ > zg (s ∗ ).
p
i
This is given if ρ − ρ > ρ̄.
p
i
The impatient decision-makers will then choose a strictly lower
escapement level than their individually optimal one, i.e.
ŝ (x ) < s ? (x ).
i
i
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
13/24
The Common Pool Politics
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
14/24
The Common Pool Politics
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
15/24
Conclusion
• annual TAC update procedure induces uncertainty regarding
next period's majority and its choice of escapement
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
16/24
Conclusion
• annual TAC update procedure induces uncertainty regarding
next period's majority and its choice of escapement
• given that
(a) the current majority is impatient
(b)
ρ − ρ > ρ̄
p
i
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
16/24
Conclusion
• annual TAC update procedure induces uncertainty regarding
next period's majority and its choice of escapement
• given that
(a) the current majority is impatient
(b)
ρ − ρ > ρ̄
p
i
uncertainty motivates the reduction of the impatients'
escapement level
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
16/24
Conclusion
• annual TAC update procedure induces uncertainty regarding
next period's majority and its choice of escapement
• given that
(a) the current majority is impatient
(b)
ρ − ρ > ρ̄
p
i
uncertainty motivates the reduction of the impatients'
escapement level
• problem could be solved by a binding agreement including a
harvest-control-rule between both groups of decision-makers
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
16/24
Alternative Management
Agreement including transfer payments
"∞
#
"∞
X
X
E
δ −1 (π(x ) − π(s ∗ (x ))) > E
δ
t
t
p
t
p
t
=1
t
=1
t
i
−1
#
(π(x ) − π(s ∗ (x )))
t
i
t
(9)
• optimal harvest-control-rule
s ∗ (x )
=
s∗
p
• patient decision-makers will compensate the impatient
decision-makers in form of direct transfer payment, log-rolling,
etc.
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
17/24
Thank you for your attention!
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
18/24
Optimal Fisheries Management (Clark 1990)
• current prots
xt
R
(p − c (x ))dx ≡ π(x ) − π(s )
t
t
st
• maximisation problem:
max
∞
X
si
t
• gives
=1
δ
t
−1
(π(x ) − π(s )) subject to
t
t
x +1 = z g (s )
t
t
t
(10)
s ? = min{x ; s ? } as solution of
j
j
π 0 (s ) = ρ
j
• (4) implies that
g 0 (s )π0 (g (s ))
s ? is increasing in ρ
j
j
(11)
(Clark 1990)
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
19/24
Bellman equations I
• Bellman equations v (x , m) of the impatient decision-makers
v (x , i ) = π(x ) − π(ŝ (x )) + ρ (q v (zg (ŝ (x )), i )
+(1 − q ) v (zg (ŝ (x )), p ))
(12)
v (x , p) = π(x ) − π(ŝ (x )) + ρ (q v (zg (ŝ (x )), i )
+(1 − q ) v (zg (ŝ (x )), p ))
(13)
i
i
i
i
p
i
p
p
• with
ŝ (x ) as feedback strategy of the patient decision-makers
p
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
20/24
Bellman equations II
• Bellman equations
V (x , m) of the patient decision-makers
V (x , i ) = π(x ) − π(ŝ (x )) + ρ (q V (zg (ŝ (x )), i )
+(1 − q ) V (zg (ŝ (x )), p ))
(14)
V (x , p) = π(x ) − π(ŝ (x )) + ρ (q V (zg (ŝ (x )), i )
+(1 − q ) V (zg (ŝ (x )), p ))
(15)
p
i
i
i
p
p
p
p
• with ŝ (x ) as feedback strategy of the impatient
decision-makers
i
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
21/24
Alternative Management
Agreement without transfer payments (Breton and Keoula 2014)
• maximize the weighted sum of the present values for both
groups
(16)
max E [αV (x ) + (1 − α)v (x )]
( )
s x
• α reects the majority in the council
• optimal harvest-control rule
s (x )
= max {s ∗ ; x } with
s∗
i
≤
s∗
≤
s∗
p
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
22/24
Optimal Fisheries Management
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
23/24
Literature
Breton, M., Keoula, M. Y., 2014. A great sh war model with
asymmetric players. Ecological Economics 97 (0), 209 223.
Clark, C. W., 1990. Mathematical Bioeconomics, 2nd Edition.
Wiley, New York.
Julia Homann
Christian-Albrechts-University International Institute of Fishery Economics and Trade
July 7 - July 11 2014 - Brisbane
Kiel
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