1.
Is Aquaculture Really an Option? A Theoretical Analysis
Esther Regnier & Katheline Schubert
Paris School of Economics, University Paris 1 Panthéon-Sorbonne
VEAM 2015
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 1 / 30

2.
Introduction
While breeding of terrestrial animals was implemented about 8 000
years ago and substituted to hunting rapidly, it took us a very long
time to repeat the experience with …sh. Aquaculture exists in many
parts of the world since the Middle Ages but did not replace …shing
until now.
Population growth and increase in standards of living in developing
countries =) growing demand for animal protein.
However,
increase of breeding limited by land use con‡icts, and
the maximum capture …shery potential from world’s oceans has been
reached: 61% of world assessed marine …sh stocks are fully exploited,
30% are overexploited (FAO 2014).
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 2 / 30

3.
Is aquaculture really an option? YES
Annual average growth rate of aquaculture from 1970 to 2012: 8.6%
(FAO 2014). Fastest growing food industry.
Aquaculture provided 9% of world …sh production in 1980, 27% in
2000, 42% in 2012 (FAO 2014).
The optimistic view is that aquaculture is going to replace at least
partially open-sea …shing, helping to make …sheries sustainable, and
providing food security for many developing countries.
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 3 / 30

4.
Is aquaculture really an option? NO
The technology presents limitations in terms of environmental
sustainability:
inland and coastal farms cause the destruction of natural habitats;
release of untreated water and feeces damages ecosystems (pathogen
invasion);
use of fertilizers =) euthrophication;
aquaculture depends on low value wild …sh as an input.
FIFO: number of tons of wild …sh necessary to produce 1 ton of
farmed …sh. For carnivorous species (salmon) it may reach ' 5.
Huge. Very ine¢ cient technology.
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5.
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 5 / 30

6.
Motivation
Investigate the impact of aquaculture on …sh consumption, welfare and
wild …sh stocks, taking into account:
1 its dependence on reduction …sheries;
2 consumer preferences;
3 biological interactions.
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 6 / 30

7.
Sketch of the model
Stylized model including the
demand side, an edible …sh …shery,
a reduction …shery and aquaculture,
where:
…sheries are in open access;
wild edible …sh and farmed …sh
are strong substitutes;
aquaculture harvests feed …sh
to grow farmed …sh; the wild
edible …sh feeds on the same
stock.
the more carnivorous the
farmed …sh species, the more
ine¢ cient its production
technology.E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 7 / 30

8.
The demand side
Utility function of the representative consumer:
U(Y1t , Y2t ) = [(1 α)Y
1 1
σ
1t + αY
1 1
σ
2t ]1/(1 1
σ )
Y1 / Y2: consumption of wild edible …sh / farmed …sh
σ > 1: elasticity of substitution
Partial equilibrium: consumers’total spending on …sh I exogenous
and stationary
Budget constraint:
P1t Y1t + P2t Y2t = I 8t
Demand functions: Y d
1t (P1t , P2t , I) and Y d
2t (P1t , P2t , I).
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 8 / 30

9.
Biological interactions
Biological interactions between the two wild species may exist or not
(Peruvian anchovy and Norwegian farmed salmon).
When they exist, they are of the predator-prey type. Species 1
(high-value edible species) is the predator, species 3 (a low-value
pelagic species) the prey.
Evolution of the 2 stocks:
˙X1t = F1(X1t , X3t )
˙X3t = F3(X1t , X3t )
with
F1(X1t , X3t ) = a1X1t b1X2
1t + d1X1t X3t
F3(X1t , X3t ) = a3X3t b3X2
3t d3X1t X3t
d1 0, d3 0; b1, b3 0; a1 0, a3 > 0.
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10.
4 possible long run steady states absent human intervention:
1 collapse of both populations;
2 collapse of population 1 only;
3 collapse of population 3 only;
4 coexistence of both populations.
Condition of existence of SS 4:
a1
b1
<
a3
d3
Under this condition the unique stable SS is SS 4; otherwise, it is SS
3 =) this condition is supposed to be satis…ed.
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 10 / 30

11.
The baseline situation: capture …shery alone
Harvest:
Y1t = q1E1t X1t
q1: catchability coe¢ cient; E1t : e¤ort.
In open access e¤ort E1 adjusts to resource rent:
˙E1t = β (P1t Y1t cE1t )
Demand function:
Y d
1t =
I
P1t
Equilibrium of the wild …sh market at each date: Y1t = Y d
1 (P1t ).
Eliminating P1 and Y1 yields:
8
<
:
˙X1t = F1(X1t , X3t ) q1E1t X1t
˙E1t = β (I cE1t )
˙X3t = F3(X1t , X3t )
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 11 / 30

12.
Again, 4 possible steady states:
1 collapse of both populations;
2 collapse of population 1 only;
3 collapse of population 3 only;
4 coexistence of both populations.
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 12 / 30

13.
SS 3 irrelevant by assumption (both species coexist absent human
intervention; …shing the predator cannot worsen things for the prey).
Condition of existence of SS 4:
I < Iw (d1) =
c
q1
a1 +
a3d1
b3
Iw : maximum revenue consumers can spend on …sh without inducing
the extinction of the edible species. Increasing function of d1.
When I < Iw (d1), the relevant SS is the interior SS 4; it is globally
stable (stable node or a stable focus, depending on the parameters).
Otherwise, species 1 collapses in the long run and the relevant SS is
SS 2.
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14.
The aquaculture sector and feed …shery
Feed …shery (species 3):
˙X3t = F3(X1t , X3t ) Y3t
˙E3t = β [P3t Y3t cE3t ]
Y3t = q3E3t X3t
Aquaculture: farmers are in competition on the farmed …sh (species
2) market.
Production function:
Y2t = k(Y3t )γ
, γ 2]0, 1[
k 2]0, kmax]: e¢ ciency of aquaculture in converting feed …sh into
farmed …sh. The lower k the less e¢ cient aquaculture is (the higher
the FIFO).
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15.
The coupling
Prices adjust so that the 3 …sh markets are in equilibrium.
Final dynamic system:
8
>><
>>:
˙X1t = F1(X1t , X3t ) q1E1t X1t
˙E1t = β [(1 At )I cE1t ]
˙X3t = F3(X1t , X3t ) q3E3t X3t
˙E3t = β [γAt I cE3t ]
with
At
1 At
=
α
1 α
1
σ k (q3E3t X3t )γ
q1E1t X1t
σ 1
σ
where At 2 ]0, 1[ characterizes market interactions (it is a function of
the price ratio).
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 15 / 30

16.
Interior steady state
Capture …shery + aquaculture Capture …shery alone
bX1 = b3
Λ x1 + y1
bA X1 = b3
Λ x1
bE1 = I
c (1 bA) E1 = I
c
bX3 = d3
Λ x3 + y3
bA X3 = d3
Λ x3
bE3 = γ I
c
bA
bA = α
1 α
k(q3
bE3
bX3)
γ
q1
bE1
bX1
σ 1
σ
Λ = b1b3 + d1d3,
x1 = a1 + a3d1
b3
q1I
c , y1 = q1
d1
b3
γq3
I
c ,
x3 = a1
a3b1
d3
q1I
c , y3 = q1 + b1
d3
γq3
I
c
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 16 / 30

17.
Proposition
A su¢ cient condition of existence of an interior steady state where wild
…shing in open access and aquaculture coexist is:
I < I := c
a1
q1
+
a3
γq3
Under this condition the interior steady state is unique.
(ii) Absent biological interactions (d1 = d3 = 0), the unique interior
steady state, when it exists, is globally stable; this remains true when
biological interactions are moderate (su¢ cient conditions for stability are:
d1 b3
q1
q3
, d3
b1
γ ). Besides, whatever the level of biological interactions,
if consumer spending I is su¢ ciently small, the unique steady state is
globally stable.
(iii) If I I, when d1 d1 := b3
q1
γq3
, there is no interior steady state; but
when d1 > d1 there may exist up to 2 interior steady states.
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 17 / 30

18.
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 18 / 30

19.
To go further on stability, numerical simulations (assumption: d3/d1
remains the one of the reference calibration when d1 varies). Show
that:
in the region where there exist 2 SS, either both are unstable or one is
unstable and the other stable, the stable one corresponding to the
smaller bA.
the interior SS may become unstable before or after I is reached; then
simultaneous collapse of the 2 wild …sh stocks.
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20.
Comparison with the baseline
Proposition
From an initial situation where the wild edible …shery is in open access,
introducing aquaculture, with a wild feed …shery also in open access, leads
in the long run to:
(i) a smaller total e¤ort devoted to …shing;
(ii) a higher stock of edible wild …sh and a lower price i¤ d1 < d1, and vice
versa, and a lower feed …sh stock in all events;
(iii) an ambiguous e¤ect on wild …sh consumption when d1 < d1, a
decrease of wild …sh consumption when d1 > d1, and an ambiguous e¤ect
on total …sh consumption in all events;
(iv) a higher utility when d1 d1, but a possibly negative e¤ect on utility
when d1 > d1.
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 20 / 30

21.
Moderate biological interactions: Strong biological interactions:
d1 < d1 d1 > d1
bE1 + bE3 < E1
bE1 + bE3 < E1
bX1 > X1
bX1 < X1
bP1 < P1
bP1 > P1
bY1
(
> Y1 = 0 when Iw (d1) < I < I
T Y1 otherwise
bY1 < Y1
bU > U bU T U
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 21 / 30

22.
Depending on the strength of biological interactions results change deeply.
Moderate b.i.: the e¤ects of market interactions dominate the e¤ects
of biological interactions. Consequences of the introduction of
aquaculture conform to intuition: it is GOOD.
Strong b.i.: the e¤ects of biological interactions dominate those of
market interactions. The introduction of aquaculture may be BAD. In
particular, when I < I < Iw (d1) introducing aquaculture may lead to
a decrease in welfare, and even to the instability of the system and
the collapse of both …sh stocks, which would have survived absent
aquaculture.
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 22 / 30

23.
Improving the e¢ ciency of aquaculture
Assumption: no biological interactions.
Comparative statics exercise on k in the neighborhood of the interior
steady state. An increase in k corresponds either to technical progress
(technique e¤ect) or to a shift in the composition of the farmed
product (composition e¤ect).
Proposition
(i) Long term stocks, e¤orts and prices in the edible …shery and the feed
…shery evolve in opposite directions according to k. The evolution of
catches depends on the initial state of the …sheries (heavily exploited or
not).
(ii) When the wild …sh stocks are heavily exploited in the initial steady
state, the edible …sh stock and catch rise with k at the expense of the feed
…sh stock and catch, while the e¤ort and the price decrease in the …rst
sector and increase in the latest. The production of farmed …sh increases,
and its price decreases. Consumer utility increases.
E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 23 / 30

24.
Extension 1: Endogenous consumer tastes
When consumer preferences depend on k (through α or σ), increasing k
means not only having a more e¢ cient aquaculture technology
(productivity e¤ect) but also breeding a composite product that consumers
like less, or that is less substitutable to wild …sh (preference e¤ect).
Proposition
The e¤ects of an improvement in aquaculture e¢ ciency are completely
reversed, if the weight a¤ected to farmed …sh or the elasticity of
substitution between wild and farmed …sh becomes su¢ ciently low as the
composite farmed product becomes less carnivorous.
As k increases, the preference e¤ect may progressively dominate the
productivity e¤ect. Our conjecture is that there exists a utility-maximizing
farmed product composition.
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25.
Extension 2: Regulation
1 We compare the reference case (wild edible …shery in open access, no
aquaculture) to a situation where the wild edible …shery is optimally
regulated.
2 We study the e¤ects of the introduction of aquaculture when:
the edible …shery is regulated by a price-taker agency maximizing the
present value of the in…nite stream of rents from this …shery;
the feed …shery is either in open access or regulated by another agency;
the two agency may either operate separately (they do not take into
account biological interactions), or cooperatively (ecosystem
management, optimum).
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26.
Wild edible …shery regulated, no aquaculture
Proposition
Absent aquaculture, at the interior steady state:
(i) The stock of species 1 is higher when the wild edible …shery is
regulated than when it is in open access. As a consequence, the stock of
species 3 is lower.
(ii) There exists a threshold level of consumer spending Ir (d1, r) < Iw (d1)
under which the price of wild …sh is higher when the wild edible …shery is
regulated than when it is in open access, and the catch lower, and above
which it is the contrary. As a consequence, when I < Ir (d1, r), regulating
the wild edible …shery makes consumers less well-o¤.
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27.
Part (i): the purpose of regulation –the recovery of the …sh stock–is
actually achieved, whatever the circumstances.
Part (ii): regulation may not bene…t consumers, compared to open
access. This is the consequence of the interaction of two e¤ects:
1 when the …shery is regulated, stock recovery =) increase of the catch
=) decrease of the price;
2 the regulator has an incentive to increase the price and restrict the
catch in order to increase the rent.
When consumer spending is high, the …shery in open access is on the
verge of collapsing. The …sh price spike is accompanied by a very low
catch, which harms consumers. In this case, the …rst e¤ect of
regulation dominates, and regulation is bene…cial to consumers. When
consumer spending is low, the second e¤ect dominates, and regulation
is harmful for consumers.
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28.
Introducing aquaculture
Proposition
Absent biological interactions, from an initial situation where the capture
…shery is optimally regulated: (i) the stock of species 1 (resp. species 3) is
larger (resp. smaller) in the long run when aquaculture is introduced, and
(ii) the pro…t of the edible …shery is smaller, whatever the management
scheme adopted for the feed …shery.
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29.
When biological interactions exist,
introducing aquaculture leads to a decline in both the feed and the
edible wild …sh stocks, and may lead to a decreased utility, in spite of
the fact that more consumption options are o¤ered to consumers;
except in the case of an ecosystem management of both …sheries.
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30.
Conclusion
Many hopes are placed in aquaculture.
But we have shown that when biological interactions between the wild
edible …sh population and the feed …sh population are strong,
introducing aquaculture harms the wild edible …sh stock and may
harm consumer utility as well.
In the good case where the introduction of aquaculture is bene…cial,
potential options in order to improve its sustainability:
Improving FIFO ratios through technological progress (?).
Finding a relevant substitute to feed …sh.
Modifying consumer preferences (?) Further investigations needed to
shed light on consumers’behavior towards farmed products.
Anyway, from a food security point of view, aquaculture appears as a
waste of animal protein since it removes quantities of …sh from the
sea to produce lower quantities of …sh ‡esh. Feed …sh could directly
be used as food.
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