ICES mar. Sei. Symp.. 192: 218-225. 1991

On the external economies of ocean ranching

Ragnar Arnason

A rnason , R. 1991. O n the external econom ies of ocean ranching. - ICES mar. Sei. Symp., 192: 218-225.

This paper examines some o f the economic implications of production externalities associated with ocean ranching. A theoretical model for investigating this situation is developed. T he analysis dem ons tra tes that , unless corrective action is under taken , an ocean ranching industry will generally not release the optimal num ber of indi­viduals into the ecosystem. M ore surprisingly perhaps, the existence of profitable ocean ranching opportunit ies implies that traditional harvesting from the ecosystem should also be modified. T he design o f economically efficient corrective mechanisms is considered. O n e m ethod is to impose the appropria te mix of taxes and subsidies. A m ore efficient m ethod involves a system of tradeable user licences or share quotas.

D ans cette é tude , les implications économ iques des externalités «d 'ocean ranching» sont examinées. Un modèle théor ique est développé pour analyser la situation en question. Il est m ontré que sans l 'action corrective, l' industrie «d 'ocean ranching» ne re lâchera pas le nom bre optimale des individus dans le système écologique. Encore plus surprenan t , l'existence des o pportun ité s profitables «d 'ocean ranching» implique que l 'exploitation traditionelle du système écologique doit être modifiée. La con­struction des mécanismes correctifs , et au m êm e temps économ iquem ent efficace, est considérée. On m ontre la possibilité d 'u n système des impôts et subventions. Une autre m éthode , plus efficace, com porte un système des permissions d 'exploitation marchands, ou des quotas proportionnels .

Ragnar Arnason: Department o f Economics, University o f Iceland, Oddi. 101 Reyk­javik, Iceland.

Introduction

Ocean resources are finite and economic expansion is making them increasingly scarce. It follows that allo­cation of ocean resources between alternat ive and often

conflicting uses is unavoidable. This paper deals with a part icular aspect of this problem, namely the uti­lization of marine resources for extensive mariculture on the one hand and tradit ional fisheries on the other. Both activities are based on the surplus production of a common ecological system. Consequently they are in terdependent . The operations of mariculture firms

alter the production possibilities of the tradit ional fish­

ing firms and vice versa. This const itutes an example of

external economies in production (see, e .g ., Layard and

Walters , 1978).N umerous potential externalities may be associated

with extensive mariculture. A degree of biological com­

petition between the cultured stock and indigenous

marine species and sometimes predatory relationships

are to be expected in most cases. This means that, generally, mariculture will influence the availability of

other valuable ocean stocks and vice versa. This obviously very broad class of externalities may be referred to as biological externalities. The competi tion

between farmed and wild salmon for limited marine sustenance and the possibility of genetic contamination of the latter by the former, discussed by Isaksson ( 1988), const itute examples of significant biological externalities in commercial mariculture. A no the r example of bio­logical externalities in extensive mariculture, considered by Anderson ( 1985), concerns the competition between farmed salmon from different ocean ranching opera ­

tions.The activities of mariculture firms may also directly

affect the harvesting opportunit ies of o ther mariculture

firms as well as those of tradit ional fisheries. This class

of production externalities may be referred to as har­

vesting externalities. Thus, cultured individuals orig­inating from an ocean ranching operation may actually

be harvested by a d ifferent ocean ranching operation or

traditional fishing activities. The latter of these exter­

nalities in the case of salmon ranching was analysed by

Anderson (1985). Not surprisingly. A nderson found that access bv tradit ional fisheries to ranched salmon

218

during part of its life cycle inhibited the development of private ocean ranching operations.

This paper restricts its at tention to the biological

externalities associated with extensive mariculture. The paper ignores harvesting externalities that are a prom i­

nent aspect of many salmon ranching operations for instance in the North Pacific. It should be noted, however, that in many o ther mariculture operations, e.g. crustacean mariculture and some ocean ranching

operations, harvesting externalities are insignificant.

Actually, the model to be presented below can be easily extended to include harvesting as well as biological

externalities. Such a comprehensive approach, how­ever, adds substantially to the complexity of the analy­

sis and is not undertaken in this paper.The existence of biological externalities implies that

under unregulated market conditions profit maximizing behaviour by mariculture enterprises and traditional

fishing firms is socially suboptimal. The ob jective of this paper is to characterize the nature of this inefficiency and to specify a modified institutional framework that

induces private firms to take the socially appropriate account of the externalities.

The article is organized broadly as follows: A theor ­etical model to analyse the situation is presented in the next section. The economic inefficiencies of private

decisions are examined in the following section. Insti­tutional arrangements to correct for the externalities are considered in a section called “Correction mech­anisms". Finally, in the last section, the main results of the paper are summarized.

Model

In this section a simple model for examining the basic biological externalities associated with extensive mari­

culture is developed. To simplify the presentation, the model is confined to two sectors, a mariculture sector and a tradit ional fisheries sector. Extension of the model to include more sectors is straightforward.

A typical extensive mariculture operation consists of releasing individuals into the sea to be recovered at a later date when they have undergone some biological development. A t the time of release, the individuals may be assumed to have a certain unit value. The recovered individuals have another unit value. The pro ­

cess is economically attractive if the aggregate value

of recovered individuals exceeds that of the released

individuals by a sufficient margin.Consider now a specific mariculture industry. For the

sake of concreteness this may be thought of as ocean

ranching. However, as will become clear, the model is

sufficiently general to accom modate a wide range of

o ther mariculture activities including enclosed tech­niques, i.e. mariculture in sea cages and similar tech­niques.

Let there be I firms in the industry. Let r(i,t) denote the number of individuals released into the sea by firm i and h(i,t) the num ber of individuals recovered or, more aptly, harvested by firm i at both at time t. Thus, r(i.t) and h(i,t) are flow variables although both may be zero except at discrete points o f time. Moreover, let z(i,t) represent the num ber of individuals in the ocean at time t belonging to firm i. zfi.t) in o ther words represents firm i’s stock of the cultured species. The

variables r( i,t ), h(i,t) , and z(i,t) may be taken to be

non-negative for all i and t.The total stock of cultured individuals is defined by:

Z(t> = Z i Z ( i . t ) , (1)

The stocks belonging to the firms are assumed to

change according to the differential equat ion:

z(i) = flz(i)/at = K(Z,x:i) + r(i). all i, (2)

where x represents the stock size of o ther species in the ecology and, for convenience of nota tion, explicit reference to the time variable, t, has been d ropped (as

will be done frequently in what follows). As previously mentioned, r(i) denotes the num ber of individuals

released by firm i at time t. The functions K(Z.x;i) on the o ther hand describe the instantaneous change in

number of individuals already released. In mariculture this is usually composed of two factors, natural mortality and harvesting. As harvesting may be regarded as fishing mortality, the functions K(Z,x;i) may be referred to as

the mortality functions.It is assumed that K(Z.x;i) 0. K(0.x:i) = K(0,0:i) =

(1 and that K(Z,x;i) is jointly concave in x and z with KZ,K/Z s 0. This means that mortal ity increases at least proportionately with own stock size. The effect of the stock size of o ther species may on the o ther hand be either positive or negative. (An abundance of natural

prey for the cultured fish will generally reduce mortality

St o ck Si ze , z(i)

---------------------------------------------------

M o r t a l i t y

Figure 1. Mariculture morta lity function.

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while an abundance of competing species will increase it). Note finally tha t the mortality function may differ across firms, i.e. with the index i. The shape of the mortality function is il lustrated in Figure 1.

Harvesting by mariculture firm i is taken to be a

function only of its ins tantaneous stock of fish in the ocean, z(i,t):

h(i,t) = H(z(i , t) ; i) , all i. (3)

This simplification ignores the time-lag between the release and recovery tha t characterizes most mariculture

processes. Modelling this time-lag explicitly, however, substantially complicates the mathematics without add ­ing significantly to the understanding of the basic p rob ­

lems addressed in this paper.The harvesting funct ions, H(z;i) are assumed to have

the property tha t H(0;i) = 0, all i, and to be twice

continuously differentiable and concave, i.e. H z > 0 and H zz « 0. This last assumption ensures that harvesting

at best increases proportionately with the stock size. Assuming that recovered individuals have a given aver­age weight, H(z;i) may be taken to be measured in

weight units. The shape of the harvesting functions is

il lustrated in Figure 2.The costs associated with release of individuals is

described by the function:

c = C(r( t) ; i) , C(();i) = 0, C r > Ü and C rr > 0. (4)

This cost function reflects the unit price of individuals ready to be released as well as o ther costs associated

with the release process.Finally, the unit value of recovered individuals net of

harvesting costs is denoted by s. (Note that for modelling purposes this price may be chosen to reflect the time-lag between the release of individuals and the subsequent

H a r v e s t i n g , H(z(i))

S to c k Size , z(i)

Figure 2. M ariculture harvesting function.

2 2 0

harvesting, i.e. s = s ° e x p ( - ô t ) , w here s° represents the

current value of recovered individuals, b the rate of discount, and x the time-lag between release and ha r ­vesting).

According to these specifications, the instantaneous

profit funct ions for the firms are:

jt(i) = s x H(z(i)) - C(r( i)) , all i, (5)

where the t index has been suppressed. The present value of profits from operating a mariculture firm is given by the integral:

PV(i) = I [s x H(z(i)) - C ( r ( i ) ) ] e x p ( -ô x t) dt, all i,■o

(6)

where ö > 0 denotes the rate of discount.The representation of the tradit ional fisheries sector

is even more simplistic. First, as this paper is not con­cerned with the m anagem ent of the fisheries as such, the fishing sector will be modelled in an aggregate form.

This means that individual firms are disregarded and

different species represen ted by one biomass. O th e r ­wise, the modelling of the fisheries sector follows the standard bio-economic practice of for example Clark and M unro (1982) and A rnason (1989).

The aggregate harvesting funct ion is represen ted by:

Y(e(t) ,x ( t)) , Y(0,x(t)) = Y(e(t) .0) = 0. (7)

where e(t) refers to fishing effort and x(t) to the biomass of the fish stock at time t. The funct ion Y(e,x) is taken to

be increasing and concave jointly in both its arguments .

The aggregate harvesting cost function is:

W (e(t)) , W(0) = 0. (8)

This cost function is assumed to be increasing and weakly convex in fishing effort , e(t).

The fish stock is assumed to grow according to the equation

x(t) = dx(t) /a t = G(x(t) ,Z(t)> - Y (e(t) ,x(t)) . (9)

The natural growth function, G (x ,Z ) , is assumed to

be twice continuously differentiable with the following properties:

G(x ,) = G (x 2) = 0,

where x 2 > x, 3= 0 and G" (x .Z) = d: G (x ,Z ) /ô x 2 < 0.

The function G (x ,Z ) is in o the r words unimodal and concave and there exists a biomass level for which growth is positive.

Finally, p denotes the m arke t price of catch. Naturally p, e, and x are taken to be non-negative.

Given these specifications, the instantaneous profit function in the fishery is given by:

4) = p x Y(e,x) - W(e). (10)

The present value of future profits in the fisheries sector

is given by the expression:

f [p x Y(e,x) - W(e)] x e x p ( - ô . t ) dt. (11)4)

Assuming tha t all economic prices in the model, in part icular p,s, and ô, accurately reflect the cor­responding social values, it follows (see, e.g., Debreu.

1959) that the profit functions (5) and (10) and their integral counterparts (6) and (11) measure social b en ­efits. In this case, the present value of social benefits

from running both activities, i.e. the mariculture and

the fishery, is:

f p j i t + 4>] x e x p ( - ö t ) dt = f [ I :(s x H(z) - C(r))o

+ p x Y(e,x) - W(e)] x e x p ( - ô t ) dt. (12)

The model that has now been described involves three

different types of biological externalities. First, the mariculture firms impose a certain externality on each other. This is due to the total stock of cultured fish entering the mortality function of each firm, i.e. the

K(2|Z(i),x:i) functions. Because of this relationship a decision by one firm to increase its rate of release will

affect the fish mortal ity suffered by the o ther firms. Second, the activity of the tradit ional fishing firms affects the economics of the mariculture firms. Again

this occurs via the mortality function of the mariculture firms. The stock size of the wild fish, x, is an argument in this function. Thus, by its decisions on fishing effort the tradit ional fishery alters the stock of wild fish and consequently the mortality of cultured fish. The third externality is imposed on the tradit ional fishery by the mariculture industry. The natural growth function of the wild species, i.e. G (Z .x ) . depends on the stock size of the cultured species. Flence the decisions of the mariculture firms affect the fishing opportunit ies of the

traditional fishing firms.

The economic inefficiency of private behaviour

This section examines the effects of the production

externalities outl ined in the previous section on the

economics of the mariculture and fishing industries. The strategy is to com pare socially optimal operations

of these two industries with private behaviour. For

this purpose it will be assumed the firms are profit maximizers and the relevant market prices correctly

reflect the respective economic values.

O ptim al o pera t ions

The social objective is to maximize the collective econ­

omic benefits of the mariculture and fishing industries. On the assumptions discussed above, this amounts to maximizing the present value of aggregate profits in these industries subject to the constraints imposed by nature. More precisely, the problem is:

Max J = I [Zi(s x H(z) - C(r))

all r(i),e

+ p x Y(e,x) - W(e)] x e x p ( - ô t ) dt. (13)

Subject to: (i) z(i) = K(Z,x;i) + r( i) , i = 1,2.........1.(ii) x(t) = G (x ,Z) - Y(e,x),

(iii) r(i) S 0, all i,

(iv) e & 0.

The solution to this problem consists of a time path

for the control variables r(i) and e. This path is usually referred to as the optimal path or optimal programme. According to Pontrvagin 's (1962) Maximum Principle,

the necessary conditions for an interior, i.e. non-zero,

solution to the problem include:

Cr(il = u(i), i = 1.2.......... 1, (13.1)

( p - o ) x Y e = W c, (13.2)

where the u(i)’s and o represent the shadow values of

additional stock units of the cultured and wild species respectively along the optimal path. The message of

condition (13.1) thus is that in mariculture the marginal cost of release should equal the value of an additional stock unit in the ocean. Correspondingly condition (13.2) states tha t the marginal revenue of fishing effort evaluated at m arket prices less the shadow of biomass

left in the sea should equal marginal cost of effort.The development of the shadow values of cultured

and wild fish stocks along the optimal path is given by the following set of differential equations:

|l(i) - 6n(i) = - s x H z(i) - o x G z(i) - I ,n ( i) x Kz(i),

i = 1,2......... 1. (13.3)

à — ä x o = - p x Y , - ö X G , + ö X Y I + 2| |i ( i) x K x.

(13.4)

Notice tha t all the externalities contained in the basic model appear as functional determinants o f the shadow

values of the fish stocks. The externalities imposed by

mariculture firm i on o ther mariculture firms and the

traditional fishing industry are represented by the te rms

2 j * i n ( j ) x Kz(i) and a X G z(i) respectively in Equation

( 13.3). The externality imposed by the traditional fishing industry on the mariculture firms on the o ther hand is

represented by the term 2,u(i) x Kx in equation (13.4).

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Condit ions (13.3) and (13.4) define a dynamic system that is not particularly transparent. The picture becomes considerably clearer in equilibrium where stock sizes are constant and consequently à = |i(i) = 0 for all i.

Thus, in equilibrium these shadow values are given by:

M-(i) = (s x H z(i) + a x G m

t l ( i u ( j ) x y / ( i ) - K/:j|), (14)

a = (p x Y x + 2jjx(i) x Kx)/(6 - G x + Y x). (15)

Equations (14) and (15) provide guidance concerning the optimal response of the control variables to the externalities in equilibrium. If for instance the t ra ­

ditional fishery has a positive shadow value, i.e. o > 0,

and the stock size of the cultured species has a negative

effect on the growth of the wild fish, i.e. G z(i)< 0 . Equation (14) states that ^t(i) should be less than would otherwise be the case. Recalling condition (13.1) and

the assumption that C rr > 0 this implies that the rate of release should be reduced. Thus, maximization of the aggregate economic benefits of the mariculture and

fishing industry implies tha t if the mariculture activity

adversely affects a valuable tradit ional fishery mari­culture operations should be correspondingly reduced. Equation ( 14) and condition (13.1) also show that if the

activity of each mariculture firm adversely affects the operations of the o the r mariculture firms, i.e. Kz(i) < 0,

then the operat ions of every mariculture firm, assuming they are profitable, should normally be correspondingly

reduced and vice versa.If, on the o ther hand, there are no externalities cre­

ated by the mariculture industry Equation (14) reduces

to:

H(i) = s X H z(i)/ö .

In o ther words, |i(i) simply equals the present value of the contribution of one additional unit of firm i's stock of cultured fish in the ocean to its revenue. Not sur­prisingly. this should, according to condition (13.1),

equal the marginal cost of release.Similarly. E qua tion (15) and condition (13.2) show

that if the stock of uncultured fish. x. increases the mortality of cultured species, i.e. Kx < 0. then tra ­ditional fishing activity should be correspondingly

increased and vice versa.

T he m aricu l tu re industry: p rivate profit maximizing b eh a v io u r

Private mariculture firms will a t tempt to arrange their

operations so as to maximize the present value of profits:

Max [ [ ( s x H ( z ( i ) ) - C ( r ( i ) ) ] x e x p ( - ô t ) d t, all i.

r(i)(16)

Subject to: (i) z(i) = K(Z,x;i) + r(i),

(ii) r(i) 3= 0.

The individual firm, in o ther words, takes the stock

sizes of o ther mariculture firms as well as that in the traditional fishery as exogenous in its own profit maxi­mization process. Notice that this is perfectly rational. These variables are by assumption not under the control of the firm.

For firm i. an interior solution to this problem includes the necessary conditions:

C r(i) = a( i) . (16.1)

à(i) - b x a( i ) = - s x H z(l| - a(i ) x Kz(i), (16.2)

where a(i) represents firm i’s evaluation of the shadow value of its fish stock.

O n som ewhat simplified assumptions concerning the functions H(z(i)), C ( r ( i ) ) and K(Z,x;i) the nature of the solution to the firm’s profit maximizat ion problem can

be il lustrated with the help of the phase diagram in

Figure 3.Figure 3 illustrates the nature of optimal paths for

r(i) and z(i ) over time given that the exogenous variables

remain constant. Each path in the diagram is optimal

for some initial and terminal conditions. For an infinite time horizon, however, the only paths that can be optimal are those resulting in an equilibrium position.

In this case there are two equilibria, the origin, (0.0) and the point labelled A in the diagram. The optimal path to this latter equilibrium is indicated by the broad

arrow's in the diagram. Accordingly, if the initial state is one of little or no stock of fish in the ocean, the

optimal program m e is to begin with a relatively high rate of release which is gradually reduced until an equi­librium is attained. Alternatively , if the initial position is characterized by a relatively high stock size, the optimal path towards equilibrium consists of an initially low rate of release which gradually increases until an

Figure 3. O ptim al mariculture: phase diagram.

2 2 2

equilibrium is reached. If, on the o ther hand, the firm

has a finite time horizon, optimal paths must hit the z(i) axis and ultimately reach the origin.

Comparing the private profit maximizing conditions (16.1) and (16.2) with the correspondingly socially opti­mal ones in (13.1) and (13.3), it becomes clear that

private mariculture firms ignore the externalities they impose on other mariculture firms and tradit ional fish­eries. More precisely, their evaluation of the shadow value of their stock of fish in the ocean differs from the social evaluation. In equilibrium the private shadow of

stock size is given by:

a(i) = s x H , (i)/ ( ô + K z(i>). (17)

which ignores the terms o x G z(i) and n (j ) x Kz(i) found in the corresponding social equation, i.e. (14).

Thus, it emerges tha t private behaviour in the mari­culture industry will in general not be socially optimal. Only if there are no externalities, i.e. G z(l) = 0 and

K z(j) = 0, o r the externali ties cancel out, i.e.

a x G z(i) + I j # , [x(j) x Kz(i) = 0, for all i, will private mariculture firms act in a socially optimal manner.

T h e fishing industry

A well-managed fishing industry will a t tempt to solve

the profit maximization problem:

Max f p x Y(e,x) - W(e)] x e x p ( - ô t ) d t . (18)e

Subject to: (i) x(t) = G (x .Z ) - Y(e,x).(ii) e 5= 0.

The necessary conditions for a solution include:

( p - ß) x Y c = W e, (18.1)

ß - ô x ß = - p x Y , - ß X G , + ß x Y ,. (18.2)

In equilibrium the shadow value of biomass is given by:

ß = p x Y x/ ( 0 - G x + Y x). (19)

Comparing this equat ion with the corresponding one for social optimum, i.e. (15), it emerges that profit maximizat ion in the fishery ignores the externality it

imposes on the mariculture industry represented by the

terms 2 ^ 0 ) x Kx in (15). Thus maximization of profits

in the fishing industry violates social optimality con­

ditions unless either the mariculture industry is socially

unprofitable, i.e. |i(i) = Ofor all i, o r the fishing industry

creates no externali ty, i.e. Kx = 0.

S hadow values in equi l ibrium

It may be helpful to obta in explicit expressions for the

relationship between the private and the socially optimal evaluations of the shadow values of the fish stocks in

equilibrium. First comparison of Equation ( 14) and ( 17)

yields:

H(i) = a(i) + (o x G z(i) + u ( j ) x Kz(i))/ (0 - Kz(i)).

(20)

This means that if both industries are socially profitable

and, as seems likely, G Z(,) and Kz(i) are negative, a(i), the private evaluation of the shadow value of stocks

exceeds the true social value. It follows, as we have seen, tha t the rate of release of cultured individuals into the ocean will be too high and the stock of cultured fish

in the ocean excessive from a social point of view.Comparison of Equations (15) and (19) on the o ther

hand yields:

a = ß + ( I , H ( i ) x K x) / ( ö - G x + Yx). (21)

This means that if the mariculture industry is socially profitable, i.e. |x(i) > 0, and the stock size of wild fish increases the mortality of cultured fish, i.e. Kx < 0, then

private evaluation of the shadow value of wild fish stocks exceeds their true social value. It follows, as explained earlier, that the biomass of wild fish will exceed socially

optimal levels or, alternat ively, catch rates will be too

low. If the mortal ity of cultured fish is reduced with the size of wild fish stocks, i.e. Kx > 0, these results are

reversed.

Correction mechanisms

The analysis in the previous section makes it clear

that private profit maximization in the mariculture and fishing industries generally yields suboptimal results. The problem is that both industries ignore the exter­

nalities they impose on the o ther via the ecological interaction of their fish stocks. In addition, private firms

in the mariculture industry ignore the externalities they impose on each other. This, as has been demonstrated , leads to an erroneous evaluation of the shadow values of marginal stock sizes. The mariculture firms therefore generally release the wrong numbers of cultured indi­viduals into the ocean and the fishing firms employ the wrong level of fishing effort. The loss of economic benefits due to these errors depends on the empirical situation but may easily be substantial. It is therefore of considerable importance to devise mechanisms that

induce private firms to act in a socially optimal manner.

Taxes and subsidies

Since the work of Pigou (1912), it has been recognized

that many externalities can be corrected by imposing

corrective taxes and subsidies. Comparing the social optimality conditions for the mariculture firms, i.e.

223

Equation (13.1), with the corresponding private ones, i.e. Equation (16.1), we find that the private firms use the shadow value a(i) instead of the optimal one |j,(i).

It follows immediately tha t the appropriate corrective

tax (or subsidy) is:

<t>(i) = M-(i) - “ (0- (22)

Imposing this tax on the releases by firm i modifies the

private profit maximizing condition (16.1) to

Cr(i) = a<i) + <t> = a(i) + n(i) - a(i) = n(i),

which is identical to the socially optimal rule.Similarly, the appropriate corrective tax for the fish­

ing industry is:

Q = o - ß. (23)

Imposing this tax on landings modifies the private profit

maximizing condition (18.1) to

( p - p - f i ) x Y c = ( p - p - o + P ) x Y t

= ( p - o ) x Ye = W e.

which is identical to the socially optimal rule.This m e thod of correcting for the externalities is

analytically elegant and appears intuitive. If for instance tradit ional fisheries reduce the mortality of cultured

individuals because for example the indigenous species preys on the cultured one, it seems reasonable that fishing should be encouraged. This is exactly what hap ­

pens. As E quation (21) makes clear, private evaluations of the shadow value of fish stock, namely ß, exceeds the social value o in this case. Therefore the tax f i is negative, which am ounts to a subsidy on landings.

There are. however, severe difficulties in the practical em ployment o f the corrective tax. First, the optimal tax generally changes over time in response to changed exogenous conditions and along the path towards equi­librium. It must therefore be continuously recalculated. Second, the optimal tax is general ly not uniform across firms. Only if the firms are identical will there be a single optimal tax for each industry. Different tax rates

for different firms is on the o ther hand somewhat dis­

turbing from a sociopolitical point of view. Third, the

informational requirem ents for calculating the optimal

tax even at a single point of time are immense. Not only

does the tax authority have to solve the social optimality problem, (13), to calculate the optimal shadow values

of stocks, bu t it has also to solve the private problems,

i.e. (16) and (18), to be able to calculate the optimal tax. These tasks require the tax authority to have at its com mand all the operat ing and biological data of the

system. Clearly, in most cases, this is unrealistic.

Individual t ransfe rab le sha re quo ta s

A more promising approach to the problem is to impose

a transferable share quota system (ITSQ ) on both sectors. This means that fishing can only take place or cultured fish re leased into the ocean if quotas for the

corresponding quantities are held. The ITSQ system has been described by A rnason (1989). The individual share quotas give the holder a right to a certain fraction or share of the total al lowable quantity each period. The quotas are pe rm anen t and transferable . The total

quantity, however, is set by the managing authority.Provided the industry is profitable and there is a

reasonably well-developed market for the share quotas, it was shown by A rnason (1989) tha t the ITSQ system induces profit maximizing firms to take the appropriate

account of the externali ties in their decisions. The social managem ent problem is thus reduced to choosing the

optimal level o f the total al lowable quantity. Moreover, as shown by A rnason (1989), the optimal total allowable

quantity coincides, under reasonably unrestrictive con­ditions, with the maximal market value of the share

quotas. The social m anagem ent problem thus becomes the particularly simple one of altering total allowable

quantit ies until the market value of the share quotas is maximized. This approach to the m anagem ent problem has been referred to as the Minim um Information M an ­agement System (MIMS).

Discussion

Extensive mariculture will generally al ter production possibilities in tradit ional marine industries. A lte rna ­tively. tradit ional harvesting activities will generally affect production possibilities in the mariculture indus­try. As shown in the paper , under these circumstances private profit maximization is unlikely to generate maxi­mal economic benefits.

The inefficiency of private decisions, however, d e ­pends crucially on the actual ecological relationship between cultured and wild species. If this relationship is strong, private decisions will diverge significantly from the socially optimal ones and special m anagem ent meas­

ures are called for. If the ecological relationship is weak, on the o ther hand, private decisions will be approxi­

mately correct and m anagem ent is unnecessary. This

indicates the importance of ecological research in con­nection with extensive mariculture.

However, if the mariculture as well as traditional

marine activities are organized under the individual transferable share quo ta system (ITSQ) from the outset ,

the need for centralized research is very much reduced. The basic reason is that under this m anagem ent system the firms will tend to take the appropriate account of the production externali ties in question irrespective of

w hether they are large or small. U nder the ITSQ system, m oreover, profit maximizing firms will find it to their

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advantage to learn about the ecological relationship of the situation. Thus, information of this nature will

become a valuable commodity and the appropriate am ount of research may be commissioned by private firms.

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