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A Note on ITQs and Optimal Investment
Journal of Environmental Economics and Management 40, 181᎐188 Ž2000. doi:10.1006rjeem.1999.1109, available online at http:rrwww.idealibrary.com on
A Note on ITQs and Optimal Investment Rognvaldur Hannesson ¨ The Norwegian School of Economics and Business Administration, Helle¨ eien 30, N-5045 Bergen, Norway E-mail: [email protected] Received May 19, 1999; revised September 27, 1999; published online August 10, 2000 This paper considers the incentives to invest under an ITQ management regime when labor is rewarded by the so-called share system. It is shown that the share system is likely to result in overinvestment under ITQs. Labor market power of crew, reflected in a high labor share of the catch, might correct for this and might even prevent excessive investment when there is competition for a total catch quota. 䊚 2000 Academic Press
1. INTRODUCTION It is frequently alleged that individual transferable quotas ŽITQs. provide incentives to invest optimally in fishing boats. In a situation where there is free access to competing for a given total catch, actual and potential boat owners have incentives to invest for the purpose of getting a larger share of the resource rent. These incentives do not disappear until all rents have been absorbed by fishing costs of one form or another, at which point the net contribution of a marginal fishing vessel may well be negative. Under an ITQ regime there is no incentive to invest for the sole purpose of getting a share of the resource rent; the catch that can be taken by each individual boat owner is given by his quota share, and he has an incentive to invest in a way that minimizes his cost for taking the catches that he is entitled to, according to his quota share. As will be shown below, this does not guarantee an optimal level of investment unless the fishermen’s wage rate is given and equal to their opportunity cost. In the so-called ‘‘share system’’ practiced in most fisheries there will be an incentive either to overinvest or to underinvest in the fishing fleet, depending on the boat owner’s share of the catch. The purpose of this paper is to examine the incentives to invest in an ITQ regime where fishermen are remunerated through a share system and to compare this to optimal management and competition for a given total catch. 2. THE MODEL We shall compare three regimes, optimal management, competition for a given total catch, and an ITQ regime where each boat owner has a catch quota equal to a given share in the total allowable catch Ž Q .. All boats will be assumed identical and so will the shares per boat, the latter being 1rN, where N is the number of boats. With competition for a given total allowable catch each boat will also be assumed to get a share 1rN, but N will of course be different from what obtains in an ITQ 181 0095-0696r00 $35.00 Copyright 䊚 2000 by Academic Press All rights of reproduction in any form reserved.
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regime. The equality of shares when there is competition for a given total catch may be thought of either as the expected outcome of a competition between identical boats and crew or as a result of a regulation where each boat gets the same share of the total allowable catch but where there is free entry to the fishery. We assume that the total allowable catch is a random variable with a known, time-independent probability distribution. In the real world, total allowable catches are set on the basis of stock assessments and recommendations by fisheries biologists. These recommendations are based on rules believed to be adequate for the fish stocks under consideration. Two such rules are the constant fishing mortality rule, which amounts to fishing a given proportion of the fishable stock, and the constant escapement rule, which amounts to fishing everything in excess of some target escapement. Two real-world examples are the catch rule applied to the Icelandic cod stock, which allows for catching 25% of the fishable stock, and the rule applied to Barents Sea capelin, where the target escapement is half a million tonnes of the spawning stock. Since the fishable stock is in part determined by random environmental fluctuations, the application of the said rules makes the total allowable catch a random variable. In this paper we abstract from the stock᎐growth relationship that in part determines the total allowable catch, as this would complicate the model without adding any new insight.1 The autonomous character of the environmental fluctuations is also assumed for simplicity. In the real world these fluctuations appear to be cyclical, with each cycle lasting a number of years. This cyclical pattern raises some interesting questions of timing of investment, but these are peripheral to the problem being considered here. A further simplification is that the catch capacity of each fishing vessel is assumed to be given and independent of the density of the stock being fished.2 This catch capacity is denoted by k. Hence, the amount caught by a fishing vessel in year t will be min Ž k, Q trNt . .
Ž 1.
Optimal Management Consider now, as a point of reference, the investment in the fishing fleet under optimal management. The condition for optimum investment can be found by maximizing the expected annual resource rent Ž EV . in the fishery with respect to the number of vessels Ž N .,
EV s Ž p y c .
kN
HQ
Qf Ž Q . dQ q kN Ž 1 y F Ž kN . . y Ž d q r . KN y wN, Ž 2 .
min
1 Models with a deterministic stock᎐growth relationship and random environmental fluctuations can be found in w2x and w3x. These models do not, however, consider the effect of the share system on optimal investment. 2 This relationship will prevail if the density of a fish stock is always the same and independent of the size of the stock. This means that the area occupied by a stock shrinks proportionally as the stock is depleted. There is some evidence that this relationship holds approximately for stocks like herring and capelin which live close to the surface and are concentrated in large shoals Žsee, e.g., Bjørndal w1x and Ulltang w4x..
ITQs AND OPTIMAL INVESTMENT
183
where we have made use of Ž1.. The meanings of the symbols are as follows: p is the price of fish, assumed constant and independent of the volume of landings, 䢇
c is the operating cost per unit of fish excluding wages, also assumed constant, 䢇
Qmin and Qmax are the lower and upper limit, respectively, for the total allowable catch, 䢇
f Ž Q . is the probability density function for Q and F Ž Q . s HQQmi n f Ž s . ds is the cumulative distribution function for Q, 䢇
䢇
d is the rate of depreciation of boats,
䢇
r is the rate of interest,
䢇
K is the investment cost for a boat,
䢇
w is the opportunity cost of labor used on each boat.
Note that all boats are identical, with an identical crew. This is, needless to say, a simplification but can be thought of as a long-term equilibrium with a common and constant technology and a constant opportunity cost of labor. The first-order condition for maximizing Ž2. is
Ž p y c . k Ž 1 y F Ž kN . . s Ž d q r . K q w.
Ž 3.
The interpretation of this is straightforward. On the left-hand side is the expected value of the marginal catch, i.e., the value of the catch taken by a boat which is fully used, multiplied by the probability that an additional boat will be needed. This probability is equal to the probability that the total allowable catch will exceed the total capacity of the fleet, 1 y F Ž kN .. On the right-hand side we have the annual capital cost of a boat plus the annual opportunity cost of labor used on the boat. Competition for a Gi¨ en Total Catch Then consider free competition for a given total catch. Assume that the crew gets a fixed share 1 y x of the gross value of the catch 3 and that the boat owner keeps the share x. The expected rent kept by the boat owner Ž ER. would be QU
ER s Ž px y c .
HQ
Q
N min
f Ž Q . dQ q k Ž 1 y F Ž QU . . y Ž d q r . K ,
Ž 4.
where QU s minŽ kN, Qmax .. With free competition for a total quota, new boat owners would enter the fishery or existing ones would expand until ER s 0. Hence, the number of boats in equilibrium would be given by
Ž px y c .
QU
HQ
Q
N min
f Ž Q . dQ q k Ž 1 y F Ž QU . . s Ž d q r . K .
Ž 5.
3 The assumption that the crew gets a share of the gross value is not critical for the results given below, as can be seen by simply eliminating c in the equations and letting p denote price net of all costs. The crew share systems of the real world are often complicated, allowing some operating costs to be deducted before the share is calculated. Which costs are deductible is a matter of negotiation between boat owners and crew or their respective unions.
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184
Indi¨ idual Transferable Quotas Finally, consider the ITQ regime. Consider a situation where all boat owners have equal quota shares, 1rN, and each owns one boat. Consider a boat owner whose boat needs to be replaced. He faces two alternatives: he can either invest in a new boat or sell his quota share to somebody else. The equilibrium in the ITQ regime will be characterized by equality between the rent that the boat owner would obtain if he invests in a new boat and the income he would get if he quits the industry and sells or leases his quota to somebody else. If he invests in a new boat, the annualized value of the quota share will be equal to the expected rent ŽEq. Ž4... If he leases his quota he would maximize his lease income by leasing an equal share to each of the remaining boat owners. This lease income would be obtained in a competitive leasing market, and the market price of selling the quota would be the capitalized value of the lease income over an infinite time horizon, provided that quota rights are secure. The lease fee the remaining boat owners are prepared to pay is equal to the increased rent they would be able to obtain by increasing their quota holdings, as determined by reducing the number of boats in the fleet by one unit and distributing its quota among the remaining boats. Approximating this by treating N as a continuous variable, we get yN
⭸E R ⭸N
s Ž px y c .
QU
HQ
min
Q N
f Ž Q . dQ.
Ž 6.
Note that an increase in the quota share is valuable only when the total allowable catch is less than the capacity of the fleet or the maximum total allowable catch, whichever is less. Putting Eqs. Ž4. and Ž6. equal gives 4
Ž px y c . k Ž 1 y F Ž kN . . s Ž d q r . K .
Ž 7.
This is identical to the condition for optimum capacity ŽEq. Ž3.., with one important exception: the given opportunity cost of labor Ž w . is replaced by the crew share of the gross catch value. Equation Ž7. can be written as
Ž p y c . k Ž 1 y F Ž kN . . y p Ž 1 y x . k Ž 1 y F Ž kN . . s Ž d q r . K . Comparing this to Eq. Ž3., we find that the ITQ regime will result in an optimal investment in the fishing fleet if p Ž 1 y x . k Ž 1 y F Ž kN . . s w,
Ž 8.
that is, if the crew share when the boat is fully used multiplied by the probability that the boat will be fully used is equal to the opportunity cost of labor. But this In Eq. Ž4. we have set QU s kN, as investment in fleet capacity beyond what is necessary to take the largest possible allowable catch will never happen in an ITQ regime, while it may well happen under competition for a given total allowable catch. 4
ITQs AND OPTIMAL INVESTMENT
185
implies that the expected crew share would in fact be higher than the opportunity cost of labor, because the crew would also get something when the boat is not used to its full capacity. Equation Ž8. would not be satisfied if the crew share parameter Ž1 y x . were determined by an equilibrium in the labor market such that the expected remuneration of labor on fishing boats must be equal to their opportunity wage; Ž1 y x . would be smaller than implied by Ž8., the left-hand side would be less than the right-hand side, and the boat owners would overinvest, because their labor costs would be too low. There is another way of looking at the equilibrium condition implied by the equality of Eqs. Ž4. and Ž6.. Equation Ž4. expresses the net expected revenue of an additional boat, ignoring the fact that an additional boat would reduce the expected catch value for the rest of the fleet. Equation Ž6. expresses the reduction in the expected catch value of the rest of the fleet caused by adding another boat. Subtracting Eq. Ž6. from Eq. Ž4. would express the true net marginal revenue of adding another boat. The optimum level of investment is that which makes this net marginal revenue equal to zero. The ITQ regime would result in an optimal investment if the crew were remunerated with a fixed wage equal to the opportunity wage. Equation Ž5. would then be
Ž p y c.
QU
HQ
min
Q N
f Ž Q . dQ q k Ž 1 y F Ž QU . . s Ž d q r . K q w,
Ž 5X .
and Eq. Ž7. would be identical to Eq. Ž3.. The reason the share system distorts the incentive to invest is that the gain from obtaining an additional quota for an existing boat must be shared with the crew. This reduces the amount boat owners are willing to pay for leasing or buying an additional quota. This makes it more attractive to invest in a new boat relative to leasing or selling one’s quota to the rest of the fleet. If the wage rate were parametric the value of an additional quota would accrue unabridged to the boat owner who buys or leases the quota, and consequently he would be willing to pay a higher lease fee. This would make it relatively more attractive for a quota owner to lease or sell his quota rather than invest in a new boat. Consider the crew share Ž1 y x . that makes the crew income equal to its opportunity cost Ž w .. The investment would be optimal if the wage were parametric. This must mean that the amount existing boat owners would be willing to pay for the quota of a boat that is about to be scrapped would be equal to the rent that could be obtained by renewing the boat. Now let that same income be determined through a crew share. The value of the quota if used to operate a new boat remains the same, but the willingness to pay for an additional quota for existing boats will be less, because the crew will get a share of the benefit. This cannot be an equilibrium; the number of boats would increase, depressing the rent of each, while the quota used by each boat would become smaller, raising the lease value of the quotas until both become equal at a higher level of fleet investment. Hence, the share system itself increases investment compared to a parametric wage that provides the same income, by making the leasing or selling of quotas less attractive than investing in new boats. Raising the crew share will, needless to say, reduce overall investment by making it less profitable.
¨ ROGNVALDUR HANNESSON
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3. AN EXAMPLE Suppose the total allowable catch is evenly distributed between Qmin and Qmax . The density and cumulative distribution functions become f Ž Q. s
1
F Ž Q. s
,
Qmax y Qmin
Q y Qmin Qmax y Qmin
.
For easy numerical calculation, put Qmax s 100 and Qmin s 0. With these assumptions, the equations that determine the investment level under the three regimes will be as follows: Optimal management: kN
Ž p y c. k 1 y
ž
100
/
Ž 3X .
s Ž d q r . K q w.
Competition for a given total catch:
Ž px y c . k
Ž min Ž kN, 100. .
2
200kN
q 1 y min 1,
ž
kN 100
/
s Ž d q r. K.
Ž 5Y .
Individual transferable quotas:
Ž px y c . k 1 y
ž
kN 100
/
Ž 7X .
s Ž d q r. K.
The expected remuneration of the crew Ž EM ., to be compared with the opportunity wage cost Ž w ., will be as follows: Competition for a given total catch: EM s p Ž 1 y x . k
Ž min Ž kN, 100. . 200kN
2
q 1 y min 1,
ž
kN 100
/
.
Individual transferable quotas: EM s p Ž 1 y x .
k2N 200
qk 1y
ž
kN 100
/
.
Figures 1 and 2 show optimal investment, i.e., number of boats Ž N ., and the expected remuneration of the crew Ž EM . as functions of the boat owner’s share of the catch value, for given values of the remaining parameters.5 For comparison, the 5
These values are as follows: k s 1, d s 0.1, r s 0.05, p s 1, c s 0.2, K s 1, w s 0.25.
ITQs AND OPTIMAL INVESTMENT
187
FIG. 1. Number of boats in alternative regimes.
FIG. 2. Expected remuneration of crew in alternative regimes.
optimal level of investment for a given opportunity cost of labor employed on each boat is also shown. As already stated, the number of vessels will always be greater when there is competition for a given total catch than when the fishery is managed by ITQs. Investment under the ITQ regime could be either higher or lower than the optimal level, depending on how large a share of the catch value the boat owner retains. There is reason to expect that ITQs would result in excessive investment. The crew’s expected remuneration must be at least as high as the opportunity wage of the crew; otherwise the boat owners would not succeed in hiring crew. Suppose, as is not unreasonable, that the opportunity wage is equal to the opportunity cost of labor Ž w .. In that case we know from Eq. Ž8. that the crew share which gives the boat owners incentives to invest optimally is higher than the opportunity cost of the crew. Therefore, the crew share could be reduced without making it impossible to recruit labor to the fishery. But then the boat owner’s share of the catch value would rise, providing an incentive to invest in more vessels. Hence, overinvestment in fishing vessels would be compatible with an equilibrium in the labor market. To achieve optimal investment it would be necessary that the labor hired on the fishing fleet be powerful enough to negotiate contracts that give them a greater remuneration than needed to cover their opportunity wage. But labor power is no panacea; it could be too large in the sense of giving incentives to underinvest rather than overinvest in an ITQ regime. A high enough degree of labor power could even provide so strong a deterrent against investment that the equilibrium
188
¨ ROGNVALDUR HANNESSON
investment with competition for a given total catch would be less than optimal. Risk aversion on labor’s behalf, combined with a higher variability of incomes in fishing than in alternative industries, would achieve similar results by making it necessary to pay a risk premium to labor working in the fishing industry. These points are illustrated by Figs. 1 and 2. The expected remuneration of labor under an ITQ regime becomes equal to the opportunity wage when the boat owner’s share of the catch value is 63%. So high a share gives the boat owners incentives to overinvest. The boat owner share which is compatible with optimal investment in an ITQ regime is 50%, which would give the crew some income over and above their opportunity wage. If the boat owner’s share were to fall below 40% there would not be any overinvestment even with competition for a given total catch. 4. CONCLUSION In this article it has been shown that ITQs do not necessarily provide incentives for optimal investment in fishing boats when the remuneration of the crew is determined as a share of the catch value. This does not necessarily make ITQs less desirable than other management regimes; the share system would probably distort the investment incentives under alternative regimes to a similar or even greater extent. Competition for a total allowable catch is particularly likely to result in overinvestment, and as shown by the numerical example in the preceding section, it might even result in a greater number of boats than needed to take the largest total allowable catches on record. The most likely investment distortion under ITQs with a share system is toward overinvestment. In the event that crew labor has market power and is able to negotiate a remuneration exceeding its opportunity wage, the investment incentives for boat owners will be weakened, possibly to the point that there will be underinvestment with competition for a given total catch. For such market power to prevail, however, it would be necessary for labor on fishing vessels to put up entry barriers for this segment of the labor market, an event which is perhaps none too likely. REFERENCES 1. T. Bjørndal, Production economics and optimal stock size in a North Atlantic fishery, Scand. J. Econom. 89, 145᎐164 Ž1987.. 2. R. Hannesson, ‘‘Bioeconomic Analysis of Fisheries,’’ Fishing News Books, Oxford Ž1993.. 3. R. Hannesson, Optimal catch capacity and fishing effort in deterministic and stochastic fishery models, Fish. Res. 5, 1᎐21 Ž1987.. 4. Ø. Ulltang, Factors affecting the reaction of pelagic fish stocks to exploitation and requiring a new approach to assessment and management, in ‘‘The Assessment and Management of Pelagic Fish Stocks’’ ŽA. Saville, Ed.., Vol. 177, pp. 489᎐504, Conseil International pour l’Exploration de Ž1980.. la Mer, Rapports et Proces ˆ Verbaux des Reunions ´
A Note on ITQs and Optimal Investment Rognvaldur Hannesson ¨ The Norwegian School of Economics and Business Administration, Helle¨ eien 30, N-5045 Bergen, Norway E-mail: [email protected] Received May 19, 1999; revised September 27, 1999; published online August 10, 2000 This paper considers the incentives to invest under an ITQ management regime when labor is rewarded by the so-called share system. It is shown that the share system is likely to result in overinvestment under ITQs. Labor market power of crew, reflected in a high labor share of the catch, might correct for this and might even prevent excessive investment when there is competition for a total catch quota. 䊚 2000 Academic Press
1. INTRODUCTION It is frequently alleged that individual transferable quotas ŽITQs. provide incentives to invest optimally in fishing boats. In a situation where there is free access to competing for a given total catch, actual and potential boat owners have incentives to invest for the purpose of getting a larger share of the resource rent. These incentives do not disappear until all rents have been absorbed by fishing costs of one form or another, at which point the net contribution of a marginal fishing vessel may well be negative. Under an ITQ regime there is no incentive to invest for the sole purpose of getting a share of the resource rent; the catch that can be taken by each individual boat owner is given by his quota share, and he has an incentive to invest in a way that minimizes his cost for taking the catches that he is entitled to, according to his quota share. As will be shown below, this does not guarantee an optimal level of investment unless the fishermen’s wage rate is given and equal to their opportunity cost. In the so-called ‘‘share system’’ practiced in most fisheries there will be an incentive either to overinvest or to underinvest in the fishing fleet, depending on the boat owner’s share of the catch. The purpose of this paper is to examine the incentives to invest in an ITQ regime where fishermen are remunerated through a share system and to compare this to optimal management and competition for a given total catch. 2. THE MODEL We shall compare three regimes, optimal management, competition for a given total catch, and an ITQ regime where each boat owner has a catch quota equal to a given share in the total allowable catch Ž Q .. All boats will be assumed identical and so will the shares per boat, the latter being 1rN, where N is the number of boats. With competition for a given total allowable catch each boat will also be assumed to get a share 1rN, but N will of course be different from what obtains in an ITQ 181 0095-0696r00 $35.00 Copyright 䊚 2000 by Academic Press All rights of reproduction in any form reserved.
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182
regime. The equality of shares when there is competition for a given total catch may be thought of either as the expected outcome of a competition between identical boats and crew or as a result of a regulation where each boat gets the same share of the total allowable catch but where there is free entry to the fishery. We assume that the total allowable catch is a random variable with a known, time-independent probability distribution. In the real world, total allowable catches are set on the basis of stock assessments and recommendations by fisheries biologists. These recommendations are based on rules believed to be adequate for the fish stocks under consideration. Two such rules are the constant fishing mortality rule, which amounts to fishing a given proportion of the fishable stock, and the constant escapement rule, which amounts to fishing everything in excess of some target escapement. Two real-world examples are the catch rule applied to the Icelandic cod stock, which allows for catching 25% of the fishable stock, and the rule applied to Barents Sea capelin, where the target escapement is half a million tonnes of the spawning stock. Since the fishable stock is in part determined by random environmental fluctuations, the application of the said rules makes the total allowable catch a random variable. In this paper we abstract from the stock᎐growth relationship that in part determines the total allowable catch, as this would complicate the model without adding any new insight.1 The autonomous character of the environmental fluctuations is also assumed for simplicity. In the real world these fluctuations appear to be cyclical, with each cycle lasting a number of years. This cyclical pattern raises some interesting questions of timing of investment, but these are peripheral to the problem being considered here. A further simplification is that the catch capacity of each fishing vessel is assumed to be given and independent of the density of the stock being fished.2 This catch capacity is denoted by k. Hence, the amount caught by a fishing vessel in year t will be min Ž k, Q trNt . .
Ž 1.
Optimal Management Consider now, as a point of reference, the investment in the fishing fleet under optimal management. The condition for optimum investment can be found by maximizing the expected annual resource rent Ž EV . in the fishery with respect to the number of vessels Ž N .,
EV s Ž p y c .
kN
HQ
Qf Ž Q . dQ q kN Ž 1 y F Ž kN . . y Ž d q r . KN y wN, Ž 2 .
min
1 Models with a deterministic stock᎐growth relationship and random environmental fluctuations can be found in w2x and w3x. These models do not, however, consider the effect of the share system on optimal investment. 2 This relationship will prevail if the density of a fish stock is always the same and independent of the size of the stock. This means that the area occupied by a stock shrinks proportionally as the stock is depleted. There is some evidence that this relationship holds approximately for stocks like herring and capelin which live close to the surface and are concentrated in large shoals Žsee, e.g., Bjørndal w1x and Ulltang w4x..
ITQs AND OPTIMAL INVESTMENT
183
where we have made use of Ž1.. The meanings of the symbols are as follows: p is the price of fish, assumed constant and independent of the volume of landings, 䢇
c is the operating cost per unit of fish excluding wages, also assumed constant, 䢇
Qmin and Qmax are the lower and upper limit, respectively, for the total allowable catch, 䢇
f Ž Q . is the probability density function for Q and F Ž Q . s HQQmi n f Ž s . ds is the cumulative distribution function for Q, 䢇
䢇
d is the rate of depreciation of boats,
䢇
r is the rate of interest,
䢇
K is the investment cost for a boat,
䢇
w is the opportunity cost of labor used on each boat.
Note that all boats are identical, with an identical crew. This is, needless to say, a simplification but can be thought of as a long-term equilibrium with a common and constant technology and a constant opportunity cost of labor. The first-order condition for maximizing Ž2. is
Ž p y c . k Ž 1 y F Ž kN . . s Ž d q r . K q w.
Ž 3.
The interpretation of this is straightforward. On the left-hand side is the expected value of the marginal catch, i.e., the value of the catch taken by a boat which is fully used, multiplied by the probability that an additional boat will be needed. This probability is equal to the probability that the total allowable catch will exceed the total capacity of the fleet, 1 y F Ž kN .. On the right-hand side we have the annual capital cost of a boat plus the annual opportunity cost of labor used on the boat. Competition for a Gi¨ en Total Catch Then consider free competition for a given total catch. Assume that the crew gets a fixed share 1 y x of the gross value of the catch 3 and that the boat owner keeps the share x. The expected rent kept by the boat owner Ž ER. would be QU
ER s Ž px y c .
HQ
Q
N min
f Ž Q . dQ q k Ž 1 y F Ž QU . . y Ž d q r . K ,
Ž 4.
where QU s minŽ kN, Qmax .. With free competition for a total quota, new boat owners would enter the fishery or existing ones would expand until ER s 0. Hence, the number of boats in equilibrium would be given by
Ž px y c .
QU
HQ
Q
N min
f Ž Q . dQ q k Ž 1 y F Ž QU . . s Ž d q r . K .
Ž 5.
3 The assumption that the crew gets a share of the gross value is not critical for the results given below, as can be seen by simply eliminating c in the equations and letting p denote price net of all costs. The crew share systems of the real world are often complicated, allowing some operating costs to be deducted before the share is calculated. Which costs are deductible is a matter of negotiation between boat owners and crew or their respective unions.
¨ ROGNVALDUR HANNESSON
184
Indi¨ idual Transferable Quotas Finally, consider the ITQ regime. Consider a situation where all boat owners have equal quota shares, 1rN, and each owns one boat. Consider a boat owner whose boat needs to be replaced. He faces two alternatives: he can either invest in a new boat or sell his quota share to somebody else. The equilibrium in the ITQ regime will be characterized by equality between the rent that the boat owner would obtain if he invests in a new boat and the income he would get if he quits the industry and sells or leases his quota to somebody else. If he invests in a new boat, the annualized value of the quota share will be equal to the expected rent ŽEq. Ž4... If he leases his quota he would maximize his lease income by leasing an equal share to each of the remaining boat owners. This lease income would be obtained in a competitive leasing market, and the market price of selling the quota would be the capitalized value of the lease income over an infinite time horizon, provided that quota rights are secure. The lease fee the remaining boat owners are prepared to pay is equal to the increased rent they would be able to obtain by increasing their quota holdings, as determined by reducing the number of boats in the fleet by one unit and distributing its quota among the remaining boats. Approximating this by treating N as a continuous variable, we get yN
⭸E R ⭸N
s Ž px y c .
QU
HQ
min
Q N
f Ž Q . dQ.
Ž 6.
Note that an increase in the quota share is valuable only when the total allowable catch is less than the capacity of the fleet or the maximum total allowable catch, whichever is less. Putting Eqs. Ž4. and Ž6. equal gives 4
Ž px y c . k Ž 1 y F Ž kN . . s Ž d q r . K .
Ž 7.
This is identical to the condition for optimum capacity ŽEq. Ž3.., with one important exception: the given opportunity cost of labor Ž w . is replaced by the crew share of the gross catch value. Equation Ž7. can be written as
Ž p y c . k Ž 1 y F Ž kN . . y p Ž 1 y x . k Ž 1 y F Ž kN . . s Ž d q r . K . Comparing this to Eq. Ž3., we find that the ITQ regime will result in an optimal investment in the fishing fleet if p Ž 1 y x . k Ž 1 y F Ž kN . . s w,
Ž 8.
that is, if the crew share when the boat is fully used multiplied by the probability that the boat will be fully used is equal to the opportunity cost of labor. But this In Eq. Ž4. we have set QU s kN, as investment in fleet capacity beyond what is necessary to take the largest possible allowable catch will never happen in an ITQ regime, while it may well happen under competition for a given total allowable catch. 4
ITQs AND OPTIMAL INVESTMENT
185
implies that the expected crew share would in fact be higher than the opportunity cost of labor, because the crew would also get something when the boat is not used to its full capacity. Equation Ž8. would not be satisfied if the crew share parameter Ž1 y x . were determined by an equilibrium in the labor market such that the expected remuneration of labor on fishing boats must be equal to their opportunity wage; Ž1 y x . would be smaller than implied by Ž8., the left-hand side would be less than the right-hand side, and the boat owners would overinvest, because their labor costs would be too low. There is another way of looking at the equilibrium condition implied by the equality of Eqs. Ž4. and Ž6.. Equation Ž4. expresses the net expected revenue of an additional boat, ignoring the fact that an additional boat would reduce the expected catch value for the rest of the fleet. Equation Ž6. expresses the reduction in the expected catch value of the rest of the fleet caused by adding another boat. Subtracting Eq. Ž6. from Eq. Ž4. would express the true net marginal revenue of adding another boat. The optimum level of investment is that which makes this net marginal revenue equal to zero. The ITQ regime would result in an optimal investment if the crew were remunerated with a fixed wage equal to the opportunity wage. Equation Ž5. would then be
Ž p y c.
QU
HQ
min
Q N
f Ž Q . dQ q k Ž 1 y F Ž QU . . s Ž d q r . K q w,
Ž 5X .
and Eq. Ž7. would be identical to Eq. Ž3.. The reason the share system distorts the incentive to invest is that the gain from obtaining an additional quota for an existing boat must be shared with the crew. This reduces the amount boat owners are willing to pay for leasing or buying an additional quota. This makes it more attractive to invest in a new boat relative to leasing or selling one’s quota to the rest of the fleet. If the wage rate were parametric the value of an additional quota would accrue unabridged to the boat owner who buys or leases the quota, and consequently he would be willing to pay a higher lease fee. This would make it relatively more attractive for a quota owner to lease or sell his quota rather than invest in a new boat. Consider the crew share Ž1 y x . that makes the crew income equal to its opportunity cost Ž w .. The investment would be optimal if the wage were parametric. This must mean that the amount existing boat owners would be willing to pay for the quota of a boat that is about to be scrapped would be equal to the rent that could be obtained by renewing the boat. Now let that same income be determined through a crew share. The value of the quota if used to operate a new boat remains the same, but the willingness to pay for an additional quota for existing boats will be less, because the crew will get a share of the benefit. This cannot be an equilibrium; the number of boats would increase, depressing the rent of each, while the quota used by each boat would become smaller, raising the lease value of the quotas until both become equal at a higher level of fleet investment. Hence, the share system itself increases investment compared to a parametric wage that provides the same income, by making the leasing or selling of quotas less attractive than investing in new boats. Raising the crew share will, needless to say, reduce overall investment by making it less profitable.
¨ ROGNVALDUR HANNESSON
186
3. AN EXAMPLE Suppose the total allowable catch is evenly distributed between Qmin and Qmax . The density and cumulative distribution functions become f Ž Q. s
1
F Ž Q. s
,
Qmax y Qmin
Q y Qmin Qmax y Qmin
.
For easy numerical calculation, put Qmax s 100 and Qmin s 0. With these assumptions, the equations that determine the investment level under the three regimes will be as follows: Optimal management: kN
Ž p y c. k 1 y
ž
100
/
Ž 3X .
s Ž d q r . K q w.
Competition for a given total catch:
Ž px y c . k
Ž min Ž kN, 100. .
2
200kN
q 1 y min 1,
ž
kN 100
/
s Ž d q r. K.
Ž 5Y .
Individual transferable quotas:
Ž px y c . k 1 y
ž
kN 100
/
Ž 7X .
s Ž d q r. K.
The expected remuneration of the crew Ž EM ., to be compared with the opportunity wage cost Ž w ., will be as follows: Competition for a given total catch: EM s p Ž 1 y x . k
Ž min Ž kN, 100. . 200kN
2
q 1 y min 1,
ž
kN 100
/
.
Individual transferable quotas: EM s p Ž 1 y x .
k2N 200
qk 1y
ž
kN 100
/
.
Figures 1 and 2 show optimal investment, i.e., number of boats Ž N ., and the expected remuneration of the crew Ž EM . as functions of the boat owner’s share of the catch value, for given values of the remaining parameters.5 For comparison, the 5
These values are as follows: k s 1, d s 0.1, r s 0.05, p s 1, c s 0.2, K s 1, w s 0.25.
ITQs AND OPTIMAL INVESTMENT
187
FIG. 1. Number of boats in alternative regimes.
FIG. 2. Expected remuneration of crew in alternative regimes.
optimal level of investment for a given opportunity cost of labor employed on each boat is also shown. As already stated, the number of vessels will always be greater when there is competition for a given total catch than when the fishery is managed by ITQs. Investment under the ITQ regime could be either higher or lower than the optimal level, depending on how large a share of the catch value the boat owner retains. There is reason to expect that ITQs would result in excessive investment. The crew’s expected remuneration must be at least as high as the opportunity wage of the crew; otherwise the boat owners would not succeed in hiring crew. Suppose, as is not unreasonable, that the opportunity wage is equal to the opportunity cost of labor Ž w .. In that case we know from Eq. Ž8. that the crew share which gives the boat owners incentives to invest optimally is higher than the opportunity cost of the crew. Therefore, the crew share could be reduced without making it impossible to recruit labor to the fishery. But then the boat owner’s share of the catch value would rise, providing an incentive to invest in more vessels. Hence, overinvestment in fishing vessels would be compatible with an equilibrium in the labor market. To achieve optimal investment it would be necessary that the labor hired on the fishing fleet be powerful enough to negotiate contracts that give them a greater remuneration than needed to cover their opportunity wage. But labor power is no panacea; it could be too large in the sense of giving incentives to underinvest rather than overinvest in an ITQ regime. A high enough degree of labor power could even provide so strong a deterrent against investment that the equilibrium
188
¨ ROGNVALDUR HANNESSON
investment with competition for a given total catch would be less than optimal. Risk aversion on labor’s behalf, combined with a higher variability of incomes in fishing than in alternative industries, would achieve similar results by making it necessary to pay a risk premium to labor working in the fishing industry. These points are illustrated by Figs. 1 and 2. The expected remuneration of labor under an ITQ regime becomes equal to the opportunity wage when the boat owner’s share of the catch value is 63%. So high a share gives the boat owners incentives to overinvest. The boat owner share which is compatible with optimal investment in an ITQ regime is 50%, which would give the crew some income over and above their opportunity wage. If the boat owner’s share were to fall below 40% there would not be any overinvestment even with competition for a given total catch. 4. CONCLUSION In this article it has been shown that ITQs do not necessarily provide incentives for optimal investment in fishing boats when the remuneration of the crew is determined as a share of the catch value. This does not necessarily make ITQs less desirable than other management regimes; the share system would probably distort the investment incentives under alternative regimes to a similar or even greater extent. Competition for a total allowable catch is particularly likely to result in overinvestment, and as shown by the numerical example in the preceding section, it might even result in a greater number of boats than needed to take the largest total allowable catches on record. The most likely investment distortion under ITQs with a share system is toward overinvestment. In the event that crew labor has market power and is able to negotiate a remuneration exceeding its opportunity wage, the investment incentives for boat owners will be weakened, possibly to the point that there will be underinvestment with competition for a given total catch. For such market power to prevail, however, it would be necessary for labor on fishing vessels to put up entry barriers for this segment of the labor market, an event which is perhaps none too likely. REFERENCES 1. T. Bjørndal, Production economics and optimal stock size in a North Atlantic fishery, Scand. J. Econom. 89, 145᎐164 Ž1987.. 2. R. Hannesson, ‘‘Bioeconomic Analysis of Fisheries,’’ Fishing News Books, Oxford Ž1993.. 3. R. Hannesson, Optimal catch capacity and fishing effort in deterministic and stochastic fishery models, Fish. Res. 5, 1᎐21 Ž1987.. 4. Ø. Ulltang, Factors affecting the reaction of pelagic fish stocks to exploitation and requiring a new approach to assessment and management, in ‘‘The Assessment and Management of Pelagic Fish Stocks’’ ŽA. Saville, Ed.., Vol. 177, pp. 489᎐504, Conseil International pour l’Exploration de Ž1980.. la Mer, Rapports et Proces ˆ Verbaux des Reunions ´