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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

Introduction

While breeding of terrestrial animals was implemented about 8 000years ago and substituted to hunting rapidly, it took us a very longtime to repeat the experience with fish. Aquaculture exists in manyparts of the world since the Middle Ages but did not replace fishinguntil now.

Population growth and increase in standards of living in developingcountries =⇒ growing demand for animal protein.

However,

increase of breeding limited by land use conflicts, andthe maximum capture fishery potential from world’s oceans has beenreached: 61% of world assessed marine fish stocks are fully exploited,30% are overexploited (FAO 2014).


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 fish production in 1980, 27% in2000, 42% in 2012 (FAO 2014).

The optimistic view is that aquaculture is going to replace at leastpartially open-sea fishing, helping to make fisheries sustainable, andproviding food security for many developing countries.


Is aquaculture really an option? NO

The technology presents limitations in terms of environmentalsustainability:

inland and coastal farms cause the destruction of natural habitats;release of untreated water and feeces damages ecosystems (pathogeninvasion);use of fertilizers =⇒ euthrophication;aquaculture depends on low value wild fish as an input.

FIFO: number of tons of wild fish necessary to produce 1 ton offarmed fish. For carnivorous species (salmon) it may reach ' 5.Huge. Very ineffi cient technology.


Motivation

Investigate the impact of aquaculture on fish consumption, welfare andwild fish stocks, taking into account:

1 its dependence on reduction fisheries;2 consumer preferences;3 biological interactions.


Sketch of the model

Stylized model including thedemand side, an edible fish fishery,a reduction fishery and aquaculture,where:

fisheries are in open access;

wild edible fish and farmed fishare strong substitutes;

aquaculture harvests feed fishto grow farmed fish; the wildedible fish feeds on the samestock.

the more carnivorous thefarmed fish species, the moreineffi cient its productiontechnology.E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 7 / 30

The demand side

Utility function of the representative consumer:

U(Y1t ,Y2t ) = [(1− α)Y1− 1

σ1t + αY

1− 1σ

2t ]1/(1− 1σ )

Y1 / Y2: consumption of wild edible fish / farmed fishσ > 1: elasticity of substitution

Partial equilibrium: consumers’total spending on fish I exogenousand stationary

Budget constraint:

P1tY1t + P2tY2t = I ∀t

Demand functions: Y d1t (P1t ,P2t , I ) and Yd2t (P1t ,P2t , I ).


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-valuepelagic species) the prey.Evolution of the 2 stocks:

X1t = F1(X1t ,X3t )

X3t = F3(X1t ,X3t )

with

F1(X1t ,X3t ) = a1X1t − b1X 21t + d1X1tX3tF3(X1t ,X3t ) = a3X3t − b3X 23t − d3X1tX3t

d1 ≥ 0, d3 ≥ 0; b1, b3 ≥ 0; a1 ≥ 0, a3 > 0.E. Regnier & K. Schubert (Paris 1 & PSE) Is Aquaculture Really an Option? A Theoretical Analysis VEAM 2015 9 / 30

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:

a1b1<a3d3

Under this condition the unique stable SS is SS 4; otherwise, it is SS3 =⇒ this condition is supposed to be satisfied.


The baseline situation: capture fishery alone

Harvest:Y1t = q1E1tX1t

q1: catchability coeffi cient; E1t : effort.In open access effort E1 adjusts to resource rent:

E1t = β (P1tY1t − cE1t )

Demand function:

Y d1t =IP1t

Equilibrium of the wild fish market at each date: Y1t = Y d1 (P1t ).Eliminating P1 and Y1 yields:

X1t = F1(X1t ,X3t )− q1E1tX1tE1t = β (I − cE1t )X3t = F3(X1t ,X3t )


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.


SS 3 irrelevant by assumption (both species coexist absent humanintervention; fishing the predator cannot worsen things for the prey).

Condition of existence of SS 4:

I < Iw (d1) =cq1

(a1 +

a3d1b3

)Iw : maximum revenue consumers can spend on fish without inducingthe extinction of the edible species. Increasing function of d1.

When I < Iw (d1), the relevant SS is the interior SS 4; it is globallystable (stable node or a stable focus, depending on the parameters).

Otherwise, species 1 collapses in the long run and the relevant SS isSS 2.


The aquaculture sector and feed fishery

Feed fishery (species 3):

X3t = F3(X1t ,X3t )− Y3tE3t = β [P3tY3t − cE3t ]Y3t = q3E3tX3t

Aquaculture: farmers are in competition on the farmed fish (species2) market.

Production function:

Y2t = k(Y3t )γ, γ ∈]0, 1[

k ∈]0, kmax]: effi ciency of aquaculture in converting feed fish intofarmed fish. The lower k the less effi cient aquaculture is (the higherthe FIFO).


The coupling

Prices adjust so that the 3 fish markets are in equilibrium.

Final dynamic system: X1t = F1(X1t ,X3t )− q1E1tX1tE1t = β [(1− At )I − cE1t ]X3t = F3(X1t ,X3t )− q3E3tX3tE3t = β [γAt I − cE3t ]

withAt

1− At=

(α

1− α

) 1σ(k (q3E3tX3t )

γ

q1E1tX1t

) σ−1σ

where At ∈ ]0, 1[ characterizes market interactions (it is a function ofthe price ratio).


Interior steady state

Capture fishery + aquaculture Capture fishery alone

X1 = b3Λ

(x1 + y1A

)X ∗1 =

b3Λ x1

E1 = Ic (1− A) E ∗1 =

Ic

X3 = − d3Λ(x3 + y3A

)X ∗3 = − d3Λ x3

E3 = γ Ic A

A = α1−α

(k(q3E3X3)

γ

q1E1X1

) σ−1σ

Λ = b1b3 + d1d3,x1 = a1 + a3d1

b3− q1 I

c , y1 =(q1 − d1

b3γq3

)Ic ,

x3 = a1 − a3b1d3− q1 I

c , y3 =(q1 + b1

d3γq3

)Ic


Proposition

A suffi cient condition of existence of an interior steady state where wildfishing in open access and aquaculture coexist is:

I < I := c(a1q1+a3

γq3

)Under this condition the interior steady state is unique.(ii) Absent biological interactions (d1 = d3 = 0), the unique interiorsteady state, when it exists, is globally stable; this remains true whenbiological interactions are moderate (suffi cient conditions for stability are:d1 ≤ b3 q1q3 , d3 ≤

b1γ ). Besides, whatever the level of biological interactions,

if consumer spending I is suffi ciently small, the unique steady state isglobally stable.(iii) If I ≥ I , when d1 ≤ d1 := b3 q1γq3

, there is no interior steady state; but

when d1 > d1 there may exist up to 2 interior steady states.


To go further on stability, numerical simulations (assumption: d3/d1remains the one of the reference calibration when d1 varies). Showthat:

in the region where there exist 2 SS, either both are unstable or one isunstable and the other stable, the stable one corresponding to thesmaller A.the interior SS may become unstable before or after I is reached; thensimultaneous collapse of the 2 wild fish stocks.


Comparison with the baseline

Proposition

From an initial situation where the wild edible fishery is in open access,introducing aquaculture, with a wild feed fishery also in open access, leadsin the long run to:(i) a smaller total effort devoted to fishing;(ii) a higher stock of edible wild fish and a lower price iff d1 < d1, and viceversa, and a lower feed fish stock in all events;(iii) an ambiguous effect on wild fish consumption when d1 < d1, adecrease of wild fish consumption when d1 > d1, and an ambiguous effecton total fish consumption in all events;(iv) a higher utility when d1 ≤ d1, but a possibly negative effect on utilitywhen d1 > d1.


Moderate biological interactions: Strong biological interactions:d1 < d1 d1 > d1

E1 + E3 < E ∗1 E1 + E3 < E ∗1

X1 > X ∗1 X1 < X ∗1

P1 < P∗1 P1 > P∗1

Y1

{> Y ∗1 = 0 when Iw (d1) < I < IT Y ∗1 otherwise

Y1 < Y ∗1

U > U∗ U T U∗


Depending on the strength of biological interactions results change deeply.

Moderate b.i.: the effects of market interactions dominate the effectsof biological interactions. Consequences of the introduction ofaquaculture conform to intuition: it is GOOD.

Strong b.i.: the effects of biological interactions dominate those ofmarket interactions. The introduction of aquaculture may be BAD. Inparticular, when I < I < Iw (d1) introducing aquaculture may lead toa decrease in welfare, and even to the instability of the system andthe collapse of both fish stocks, which would have survived absentaquaculture.


Improving the effi ciency of aquaculture

Assumption: no biological interactions.Comparative statics exercise on k in the neighborhood of the interiorsteady state. An increase in k corresponds either to technical progress(technique effect) or to a shift in the composition of the farmedproduct (composition effect).

Proposition

(i) Long term stocks, efforts and prices in the edible fishery and the feedfishery evolve in opposite directions according to k. The evolution ofcatches depends on the initial state of the fisheries (heavily exploited ornot).(ii) When the wild fish stocks are heavily exploited in the initial steadystate, the edible fish stock and catch rise with k at the expense of the feedfish stock and catch, while the effort and the price decrease in the firstsector and increase in the latest. The production of farmed fish increases,and its price decreases. Consumer utility increases.


Extension 1: Endogenous consumer tastes

When consumer preferences depend on k (through α or σ), increasing kmeans not only having a more effi cient aquaculture technology(productivity effect) but also breeding a composite product that consumerslike less, or that is less substitutable to wild fish (preference effect).

Proposition

The effects of an improvement in aquaculture effi ciency are completelyreversed, if the weight affected to farmed fish or the elasticity ofsubstitution between wild and farmed fish becomes suffi ciently low as thecomposite farmed product becomes less carnivorous.

As k increases, the preference effect may progressively dominate theproductivity effect. Our conjecture is that there exists a utility-maximizingfarmed product composition.


Extension 2: Regulation

1 We compare the reference case (wild edible fishery in open access, noaquaculture) to a situation where the wild edible fishery is optimallyregulated.

2 We study the effects of the introduction of aquaculture when:

the edible fishery is regulated by a price-taker agency maximizing thepresent value of the infinite stream of rents from this fishery;the feed fishery is either in open access or regulated by another agency;the two agency may either operate separately (they do not take intoaccount biological interactions), or cooperatively (ecosystemmanagement, optimum).


Wild edible fishery regulated, no aquaculture

Proposition

Absent aquaculture, at the interior steady state:(i) The stock of species 1 is higher when the wild edible fishery isregulated than when it is in open access. As a consequence, the stock ofspecies 3 is lower.(ii) There exists a threshold level of consumer spending Ir (d1, r) < Iw (d1)under which the price of wild fish is higher when the wild edible fishery isregulated than when it is in open access, and the catch lower, and abovewhich it is the contrary. As a consequence, when I < Ir (d1, r), regulatingthe wild edible fishery makes consumers less well-off.


Part (i): the purpose of regulation —the recovery of the fish stock— isactually achieved, whatever the circumstances.

Part (ii): regulation may not benefit consumers, compared to openaccess. This is the consequence of the interaction of two effects:

1 when the fishery is regulated, stock recovery =⇒ increase of the catch=⇒ decrease of the price;

2 the regulator has an incentive to increase the price and restrict thecatch in order to increase the rent.When consumer spending is high, the fishery in open access is on theverge of collapsing. The fish price spike is accompanied by a very lowcatch, which harms consumers. In this case, the first effect ofregulation dominates, and regulation is beneficial to consumers. Whenconsumer spending is low, the second effect dominates, and regulationis harmful for consumers.


Introducing aquaculture

Proposition

Absent biological interactions, from an initial situation where the capturefishery is optimally regulated: (i) the stock of species 1 (resp. species 3) islarger (resp. smaller) in the long run when aquaculture is introduced, and(ii) the profit of the edible fishery is smaller, whatever the managementscheme adopted for the feed fishery.


When biological interactions exist,

introducing aquaculture leads to a decline in both the feed and theedible wild fish stocks, and may lead to a decreased utility, in spite ofthe fact that more consumption options are offered to consumers;

except in the case of an ecosystem management of both fisheries.


Conclusion

Many hopes are placed in aquaculture.

But we have shown that when biological interactions between the wildedible fish population and the feed fish population are strong,introducing aquaculture harms the wild edible fish stock and mayharm consumer utility as well.

In the good case where the introduction of aquaculture is beneficial,potential options in order to improve its sustainability:

Improving FIFO ratios through technological progress (?).Finding a relevant substitute to feed fish.Modifying consumer preferences (?) Further investigations needed toshed light on consumers’behavior towards farmed products.

Anyway, from a food security point of view, aquaculture appears as awaste of animal protein since it removes quantities of fish from thesea to produce lower quantities of fish flesh. Feed fish could directlybe used as food.


"is aquaculture really an option? a theoretical analysis" - “phân thích lí thuyết:...

Economy & Finance