Aaron Hatcher
CEMARE, Department of Economics,
University of Portsmouth, United Kingdom aaron.hatcher@port.ac.uk
PRELIMINARY VERSION 1
Abstract
In the literature on Individual Transferable Quotas (ITQs) as a …shery management tool, relatively little attention has been paid to the implications of market power for the behaviour of quota markets. Using a simple dominant …rm/competitive fringe model, this paper examines the quota demands of dominant …rms with market power in the quota market only and in both quota and output markets and considers the implications for the e¢ ciency of
ITQ markets. The model allows for both non-compliance with quotas and the possibility that the dominant …rm may choose to hold excess quota, so e¤ectively becoming voluntarily compliant.
JEL Classi…cation: D21, D45, Q22
Keywords: ITQs, tradeable quotas, market power, non-compliance
This paper examines the impact of a dominant …rm in an ITQ …shery, considering …rstly a …rm with market dominance only in the quota market and then secondly a …rm with market power in both quota and output markets. Both compliant and non-compliant behaviours are considered.
Despite often expressed concerns, and in contrast to the quite extensive literature on
1
Paper prepared for the 42nd Annual Meeting of the Canadian Economics Association, University of British
Columbia, Vancouver, 6-8 June 2008.
1

market imperfections in markets for pollution permits, relatively few published studies have examined the implications of market power and non-compliance for ITQ markets in …sheries. Anderson (1991) examines the pro…t-maximising behaviour of a (compliant) dominant …shing …rm which has market power in both the quota market and the corresponding output market. He …nds that if the dominant …rm is initially allocated all the quota, in exercising monopoly power it will …nd it pro…table to hold quota in excess of its level of production, so increasing the output price. In the case where the dominant
…rm initially owns no quota, however, there is no incentive for the …rm to hold excess quota, a result which Anderson generalises to any dominant …rm with monopsony power in the quota market. In a recently published paper, Anderson (2008) revises this earlier conclusion, but neglects then to explore fully the conditions for the exercise of market power in both quota and output markets. In addition, the possibility of non-compliance is not considered. In the only other paper speci…cally addressing market power in an
ITQ …shery, Armstrong (2008) explores e¢ ciency conditions in a dynamic quota allocation model, along the lines of a dynamic pollution permit model in Hagem and Westskog
(1998) but focuses only on market power in the quota market, not the output market.
2
There are only two published studies which analyse the impacts of non-compliance upon
ITQ markets. Chavez and Salgado (2005) examine the properties of an ITQ market when
…rms cheat, although their analysis follows closely that of the pollution permit literature in assuming that …rms’expected penalties for non-compliance depend upon level violations of quota demands (e.g., Malik 1990, 2002), so that they derive very similar results. Hatcher
2
In the pollution permit literature, a paper by Misiolek and Elder (1989) examine the simultaneous exercise of market power in permit and output markets, but here permits and output are not directly related, as they are in an ITQ market. These authors also do not consider either cheating or the holding of excess permits.
2

(2005) also examines the e¤ect of non-compliance on a quota market, but with a more general speci…cation of the violation argument in the …rm’s expected penalty function.
Here the impact of non-compliance on the quota market is found to be less straightforward, with the “level violations” model arguably being a special case.
In the next section of the paper we outline the basic model. A following section then looks at the behaviour of a dominant …rm with market power only in the quota market, which essentially mirrors the literature on pollution permits (e.g., Malik, 2002). We then consider market power in both quota and output markets. Provided the dominant
…rm’s initial quota endowment is positive, the …rm may choose to hold excess quota in relation to its output level, or it may cheat, depending upon the relative capacities of the dominant …rm and competitive fringe and the slopes of the demand curves for quota and output. If the initial quota allocation to the dominant …rm is zero, on the other hand, it will unambiguously cheat. After brie‡y considering the impact of non-compliance in the competitive fringe, a …nal section contains some concluding remarks.
We consider a single species, single product, …shery and assume that the …sh stock size is
…xed. There are N independent pro…t-maximising …rms in the …shery. There is a single dominant …rm, indexed i = 1 , and a competitive fringe of i = 2 ; ::N …rms, which we represent by a single price taking …rm denoted with the subscript F .
For the price taking …rm, short run gross pro…ts, i.e., pro…ts before any payments for
3

quota (or …nes for non-compliance), are given by the (social) bene…t function
B
F
( q
F
) pq
F c
F
( q
F
) ; (1) where q
F is the catch, p is the output price and c
F
( q
F
) are variable costs. With c
0
F
( q
F
) > 0 and c 00
F
( q
F
) > 0 we have B
F
( q
F
) strictly concave in q
F
. The necessary condition for
(unconstrained) pro…t maximisation is then the usual
B
0
F
( q
F
) p c
0
F
( q
F
) = 0 : (2)
In a given period, a …shery manager sets a total quota, or Total Allowable Catch (TAC), for the …shery, denoted by . Quota is freely (costlessly) traded between …rms and each
0 at market equilibrium, where we assume the …rm demands an amount of quota Q i market clearing condition i =1
Q i
Q
1
+ Q
F
= (3) always holds.
A quota compliant competitive …rm, i.e., a …rm which chooses Q
F
= q
F irrespective of any …nancial incentive to do otherwise, faces the short run pro…t maximisation problem max q
F
;Q
F
F
B
F
( q
F
) rQ
F s : t : q
F
0 ; Q
F
0 ; Q
F q
F
; (4) where r is the short run (rental) price of quota.
3 The corresponding Lagrangian function is
L = B
F
( q
F
) rQ
F F
( q
F
Q
F
) (5)
3
Note that the …rm’s initial allocation of quota is assumed to be zero where the quota price is parametric to the
…rm. In this case a non-zero initial quota allocation makes no di¤erence to the pro…t-maximising behaviour of the …rm.
4

and the Kuhn-Tucker conditions for an optimum are
L q
= B
0
F
( q
F
)
F
0 ; q
F
0 ; L q q
F
= 0 ;
L
Q
= r +
F
0 ; Q
F
L = q
F
+ Q
F
0 ;
F
0 ; L
Q
Q
F
= 0 ;
0 ; L
F
= 0 :
For q
F
= Q
F
> 0 , we have the necessary …rst-order conditions
B
0
F
( q
F
) =
F and r =
F and hence the usual decision rule for a compliant price taking …rm
B
0
F
( q
F
) = r > 0 :
(6a)
(6b)
(6c)
(7)
(8)
(9)
The quota demand Q
F
( r ) of the …rm at a quota price r is then given by the inverse of the marginal bene…t function B 0
F
( q
F
) evaluated at r , thus
Q
F
( r ) = q
F
( r ) B
0 1
F
( r ) : (10)
While the quota price is parametric to an individual competitive …rm, it is endogenous to the fringe as a whole. Let the fringe demand for quota at a price r be Q
F
( r ) , then if Q
F
( r ) = Q
1
(the residual quota supply to the fringe), r is the market-clearing
(equilibrium) quota price. Given the concavity of B
F
( q
F
) , the fringe inverse quota demand r ( Q
1
) is decreasing in [ Q
1
] and is zero, we assume, if [
(or greater than) the unconstrained fringe output B
0 1
F
(0) .
Q
1
] is just equal to
5

Consider, …rst, a situation in which the dominant …rm can exert market power in the quota market, but is a price taker in the output market (this might be the case, for example, if other, separately-managed, …sheries produced an identical product for the same market).
The dominant …rm’s short run pro…t maximisation problem is max q
1
;Q
1
B
1
( q
1
) r ( s : t : q
1
0 ; Q
1
Q
1
) Q
1
0 ; Q
1 q
1
;
Q
1
(11) where Q
1 is
0 is the initial allocation of quota to the …rm. The corresponding Lagrangian
L = B
1
( q
1
) r ( ) Q
1
Q
1 1
[ q
1 and the Kuhn-Tucker conditions for an optimal solution are
Q
1
] (12)
L q
= B
0
1
( q
1
)
1
L
Q
= r ( ) + r
0
( ) Q
1
Q
1
+
1
0 ; q
1
0 ; Q
0
1
; L
0 ; q q
1
= 0 ;
L
Q
Q
1
= 0 ;
L = q
1
+ Q
1
0 ;
1
0 ; L
1
= 0 :
(13a)
(13b)
(13c)
For Q
1
= q
1
> 0 ; we then have, solving for
1
,
B
0
1
( q
1
) = R
1
( Q
1
) 0 ; (14) where R
1
( Q
1
) r ( ) r
0
( ) Q
1
Q
1 is the dominant …rm’s marginal revenue from selling quota if Q
1
> Q
1
, or its marginal cost of purchasing quota if Q
1
< Q
1
.
Given r ( ) > 0 and r 0 ( ) < 0 , we can see that where Q
1
< Q
1
(the dominant …rm is behaving as a monopolist in the quota market) we have R
1
( Q
1
) < r ( ) and hence
6

B 0
1
( q
1
) < r ( ) , whereas if Q
1
> Q
1
, we have R
1
( Q
1
) > r ( ) and hence B 0
1
( q
1
) > r ( ) .
Only in the case where Q
1
= Q
1 is the market equilibrium quota price the e¢ cient price, where the marginal costs of production are equated across all …rms. Otherwise, the quota price faced by the competitive fringe is either too low, so that the competitive …rms overproduce relative to the dominant …rm, or it is too high, so that the competitive …rms under-produce relative to the dominant …rm. In summary,
Q
1
> Q
1
) R
1
( Q
1
) > r; B
0
1
( q
1
) > r;
) R
1
( Q
1
) = r; B
0
1
( q
1
) = r; Q
1
= Q
1
Q
1
< Q
1
) R
1
( Q
1
) < r; B
0
1
( q
1
) < r:
This is the basic e¢ ciency result found by Hahn (1984) for a market in pollution permits
(see also van Egteren and Weber, 1996, and Malik, 2002).
If the dominant …rm …nds it pro…table to hold quota in excess of its requirement for production ( Q
1
> q
1
> 0 ), from the complementary slackness condition in (13c) we must have
1
= 0 , so that
B
0
1
( q
1
) = R
1
( Q
1
) r ( ) r
0
( ) Q
1
Q
1
= 0 ; (16) which, given r ( ) > 0 and r 0 ( ) < 0 , requires Q
1
< Q
1
. Thus, the dominant …rm will only hold excess quota if it is initially over-endowed with quota to the extent that its marginal revenue from selling quota is zero when Q
1
> q
1
. Here, the dominant …rm’s output is unconstrained by quota, so that B 0
1
( q
1
) = 0 . This is (in slightly di¤erent form) the result found by Malik (2002) for a dominant …rm in an emissions permit market. Note that, even if the TAC were to exceed the total unconstrained industry output, if the initial allocation of quota to the dominant …rm were large enough it could restrict the supply of
7

quota to the competitive fringe and hence restrict the total level of output.
For a non-compliant …rm with quota market power, we can replace the constraint term in the Lagrangian with an expected penalty term
1
( v
1
) , where v
1 v
1
( q
1
; Q
1
) is the …rm’s quota violation. For q
1
; Q
1
> 0 ; we then have the …rst order conditions
B
0
1
( q
1
) =
@
1
( v
1
)
@q
1
0 and
R
1
( Q
1
) =
@
1
( v
1
)
@Q
1
0 :
Subtracting (18) from (17) and rearranging, we obtain the joint decision rule
Where Q
1
B
0
1
( q
1
) = R
1
( Q
1
) +
@
1
( v
1
)
@q
1
+
@
1
( v
1
)
@Q
1
0 : q
1
, by assumption @
1
( v
1
) =@q
1
= @
1
( v
1
) =@Q
1
= 0 and hence
(17)
(18)
(19)
B
0
1
( q
1
) = R
1
( Q
1
) = 0 ; which, again, requires Q
1
< Q
1
. We could have, uniquely, B 0
1
( q
1
) = R
1
( Q
1
) = 0 as an unconstrained solution where Q
1
= q
1
. Otherwise, if we allow the …rm to be noncompliant, it will seek to cheat wherever it has no incentive to hold excess quota. This has the obvious (and not entirely trivial) corollary, as noted by Malik (2002) in the context of pollution permits, that it is possible for a dominant …rm to be “over-endowed” with quota such that it will not violate.
When the …rm is cheating, notice that if the expected penalty depends only upon the level violation size ( v
1 q
1
Q
1
), as is universally assumed in the pollution permit literature, then @
1
( v
1
) =@q
1
= @
1
( v
1
) =@Q
1 and hence we have
B
0
1
( q
1
) = R
1
( Q
1
)
8

as before (though here violation implies B 0
1
( q
1
) ; R
1
( Q
1
) > 0 ), so that B 0
1
( q
1
) = r when
Q
1
= Q
1
, as in the case of a compliant …rm. If, however, the expected penalty depends upon the relative size of the violation ( v
1 q
1
=Q
1
), then in the …rst order conditions we have
@
1
( v
1
)
@q
1
=
0
1
( v
1
)
1
Q
1 and
@
1
( v
1
)
@Q
1
=
0
1
( v
1
) q
1
Q
1
2
; so that (18) becomes
B
0
1
( q
1
) = R
1
( Q
1
) +
0
1
( v
1
)
1
Q
1
Here q
1
> Q
1 implies that q
1
Q
1
2
> 0 :
0 < B
0
1
( q
1
) < R
1
( Q
1
) ; or, substituting for 0
1
( v
1
) and then rearranging, q
1
Q
1
=
R
1
B 0
1
( Q
1
)
( q
1
)
> 1 :
Now, we have
(20)
(21)
(22)
Q
1
> Q
1
) R
1
( Q
1
) > r; B
0
1
( q
1
)
R r;
Q
Q
1
1
= Q
< Q
1
1
) R
1
( Q
1
) = r; B
0
1
( q
1
) < r;
) R
1
( Q
1
) < r; B
0
1
( q
1
) < r:
In this case, where the non-compliant dominant …rm is a net purchaser of quota it is possible that it will produce where B 0
1
( q
1
) = r . Here, total industry production would be e¢ ciently allocated, although, since the dominant …rm is cheating, it will exceed the TAC.
Otherwise, Q
1
Q
1 unambiguously implies B
0
1
( q
1
) < r . Note that where Q
1
= Q
1
, we have R
1
( Q
1
) = r and hence q
1
=Q
1
= r=B 0
1
( q
1
) , as would be the case for a non-compliant
9

competitive …rm.
4
Now consider a compliant …rm with market dominance in both the quota and output markets (this might arise in a situation where the entire output market is supplied by one
…shery under ITQ management). The …rm’s short run pro…t maximisation problem can now be written max q
1
;Q
1
B
1
( q
1
; p ( q )) r ( s : t : q
1
0 ; Q
1
Q
1
; p ( q )) Q
0 ; Q
1 q
1
;
1
Q
1
(24) where q q
1
+ q
F is the combined output of the dominant …rm and the competitive fringe and p ( q ) is the inverse consumer demand for that output, with, we assume, p
0
( q ) < 0 .
Note that changes in p ( q ) impact upon both the dominant …rm’s own gross pro…t B
1
( ) and, indirectly through the e¤ect on gross pro…ts in the competitive fringe, the equilibrium quota price r ( ) (we continue to assume a compliant fringe, so that q
F
= Q
F
= Q
1
).
The corresponding Lagrangian and the Kuhn-Tucker conditions for an optimum are
L = B
1
( q
1
; p ( q )) r ( Q
1
; p ( q )) Q
1
Q
1 1
[ q
1
Q
1
] ; (25)
4 This is the ratio result obtained in Hatcher (2005) where expected penalties are a function of relative violations.
10

with
L
Q
=
L q
=
@B
1
( )
@q
1
+
@B
1
( ) p
0
@p ( q )
@ q
( q )
@q
1
@B
1
( ) p
0
@p ( )
( q )
@ q
@Q
1 r ( )
@r ( )
@p ( q ) p
0
@ q
( q )
@q
1
Q
1
Q
1 q
1
0 ; L q q
1
= 0 ;
@r ( )
@Q
1
Q
1
Q
1
@r ( )
@p ( q ) p
0
( q )
@ q
@Q
1
Q
1
Q
1
0 ; L
Q
Q
1
= 0 ;
1
0 ;
(26a)
Q
1
+
1
(26b)
0 ;
L = q
1
+ Q
1
0 ;
1
0 ; L
1
= 0 : (26c)
For Q
1
= q
1
> 0 , we then have
@B
1
( )
@q
1
+ p
0
( q )
@ q
@q
1 q
1
Q
1
Q
1
=
1
0 (27) and r ( ) +
@r ( )
@Q
1
Q
1
Q
1 p
0
( q )
@ q
@Q
1 q
1
Q
1
Q
1
=
1
0 ; (28) where we have used @B
1
( ) =@p ( ) = q
1 and @r ( ) =@p ( q ) = 1 .
5 Note that here @B
1
( ) =@q
1 and @r ( ) =@Q
1 are equivalent to B 0
1
( q
1
) and r 0 ( ) in the previous section.
Solving (27) and (28) for
1
, we obtain the joint optimal decision rule
@B
1
( )
+ p
0
( q )
@q
1
@ q
@q
1
@ q
+
@Q
1 q
1
Q
1
Q
1
= R
1
( Q
1
) ; where, as before, R
1
( Q
1
) r ( ) + @r ( ) =@Q Q
1
(29)
Q
1
. The additional term on the LHS of (29) captures the …rm’s net marginal impact upon its own gross pro…ts B
1
( ) , as well as its revenues from, or costs of, quota trade, through the e¤ect of its own output and quota demand upon the total industry output q and hence the market price p ( q ) .
5
Since the competitive fringe is assumed to be compliant, we have r ( ) = B
0
F
@r ( ) =@p ( q ) = 1 .
( q
F
) p ( q ) c
0
F
( q
F
) , and hence
11

In order to examine the dominant …rm’s impact upon total output, we can …rstly write
@ q
@q
1
= dq
1 dq
1
+
@q
F
@q
1
= 1 +
@q
F
;
@q
1 where @q
F
=@q
1 is the …rm’s conjectural derivative for the output of the competitive fringe in relation to its own output. We can give some substance to @q
F
=@q
1 in terms of the fringe supply function as
@q
@q
F
1
@q
F
@p ( q ) p
0
( q )
@ q
@q
1
:
With a compliant fringe under ITQs, we know that, all else equal, @q
F
=@p ( q ) = 0 , i.e., the output supply of the fringe is constrained by its residual quota supply, i.e., q
F
= Q
F
= Q
1
.
6
Hence, @q
F
=@q
1
= 0 (Cournot) and therefore @ q =@q
1
= 1 . Similarly, we can write
@ q
@Q
1
@q
1
=
@Q
1
@q
F
+
@Q
1
= 0 +
@q
F
@Q
1
:
Here, given market clearing in the quota market, a compliant fringe implies @q
F
=@Q
1
=
@Q
F
=@Q
1
= 1 , so that @ q =@Q
1
= 1 .
If @ q =@q
1
= 1 and @ q =@Q
1
= 1 , then @ q =@q
1
+ @ q =@Q
1
= 0 and (29) collapses to
@B
1
( )
@q
1
= R
1
( Q
1
) ; as in the case of a …rm with dominance only in the quota market. Although (given a compliant fringe) Q
1
= q
1 implies that the …rm has no net e¤ect upon total industry output (which always remains at the level of the TAC), only where q
1
= Q
1
Q
1
> 0 are the …rst order conditions equivalent to those for a …rm with dominance only in the quota market. In that case, however, note that we cannot have @B
1
( ) =@q
1
= R
1
( Q
1
) = 0 , since R
1
( Q
1
) = 0 requires Q
1
Q
1
< 0 . In other words, if buying quota, the …rm will
6 This assumes, of course, that the fringe quota supply [ Q
1
] remains binding.
12

not freely set q
1
= Q
1
Q
1
, or, in the case where Q
1
= 0 , it will not freely set q
1
= Q
1
.
For the dominant …rm to hold excess quota ( Q
1
> q
1
), we require
1
= 0 in the Kuhn-
Tucker conditions and hence from (27) and (28) we will have
@B
1
( )
@q
1
+ p
0
( q ) q
1
= p
0
( q ) Q
1
Q
1
R
0 (30) and r ( ) +
@r ( )
@Q
1 p
0
( q ) Q
1
Q
1
= p
0
( q ) q
1
> 0 ; (31) where we have rearranged terms in order to distinguish the marginal impacts on revenues from the catch and on revenues from (costs of) quota sales (purchases). Whereas, from
(31), marginal quota costs/revenues are always positive, from (30) the marginal revenue from the catch may be negative where it is pro…table to further increase output in order to reduce the output price and hence reduce the cost of buying quota. In the case where
Q
1
= Q
1
, notice, the dominant …rm produces where
@B
1
( )
@q
1
+ p
0
( q ) q
1
= 0 ; which is simply the usual rule for a monopoly producer. At the same time, we have r ( ) = p 0 ( q ) q
1 and hence @B
1
( ) =@q
1
= r ( ) , so that total output, although it may be below than the TAC, is e¢ ciently produced. Here, the dominant …rm’s initial allocation is such that it does not exercise market power in the quota market, although it does in the output market.
Combining (30) and (31) we can observe that
@B
1
( )
@q
1
= R
1
( Q
1
) = p
0
( q ) Q
1
Q
1 q
1
> 0 : (32)
Here, we must again have @B
1
( ) =@q
1
= R
1
( Q
1
) > 0 , since, given r ( ) > 0 , R
1
( Q
1
) 0
13

implies Q
1
Q
1
< 0 and hence p 0 we therefore require Q
1
Q
1 q
1
( q ) Q
1
Q
1 q
1
< 0 and hence Q
1
> 0 . Given p 0 ( q ) < 0 , in (32)
Q
1
< q
1
. This immediately excludes the possibility that a dominant …rm will withdraw quota from the market when its initial allocation Q
1 is zero, but otherwise Q
1
> q
1 does not now require Q
1
> Q
1
. Thus it appears that, given market power in the output market as well as in the quota market, a dominant …rm will purchase quota in order to withhold it from the market, provided that
Q
1 is strictly positive. Notice that Q
1
= q
1 is also feasible as an unconstrained solution to
(24) given the same condition, but not otherwise. In either case, Q
1
> 0 ensures that, if the dominant …rm is a net purchaser of quota, the amount of quota purchased is strictly less than its output. Rearranging the RHS of (32), we can also observe that, if the …rm is holding excess quota, we will always have
[ Q
1 q
1
] < Q
1
; i.e., the amount of excess quota held (if any) is strictly less than the …rm’s initial allocation
(this could provide a general “rule of thumb” for the avoidance of monopoly output restriction under ITQs).
The result implied by (32) contrasts with the …nding of Anderson (1991) that, if the dominant …rm were a net purchaser of quota, it would never be pro…table for it to restrict its output “because any increase in the price of the marketable output will be transferred into an increase in the purchase price of ITQs” (p.296). Anderson’s (1991) conclusion appears to derive from his assumption that, in the quota monopsony case, Q
1
= 0 , so that, as we have seen, the …rm will indeed not hold excess quota. In a very recent paper,
Anderson (2008) revises this earlier conclusion, although without a full formal analysis of
14

the problem.
7 But, notice, the dominant …rm will not freely even match its quota holdings to its output if the initial quota allocation is zero, which implies that, in this case, the
…rm will cheat.
If we relax the assumption of compliance, we can see that while Q
1
< q
1 is the only possible unconstrained solution to (24) if Q
1
= 0 , it is also an unconstrained solution if
Q
1
> 0 . Note that if, in (30), Q
1
= 0 , then we have
@B
1
( )
@q
1
+ p
0
( q ) q
1
= p
0
( q ) Q
1
0 ; (33) i.e., marginal revenues may be negative due to the exercise of market power in the quota market. Since here we also have r ( ) +
@r ( )
@Q
1
Q
1
= p
0
( q ) [ Q
1 q
1
] > 0 ; we can see that the …rm’s quota demand may be positive even where r ( ) > 0 , i.e., the
…rm may purchase quota even though it is not subject to any enforcement.
If the …rm is non-compliant, however, we assume as before that it expects to incur a penalty
1
( v
1
) for a violation v
1 v
1
( q
1
; Q
1
) . Then, again letting @ q =@q
1
= 1 and
@ q =@Q
1
= 1 , for Q
1
< q
1 we would have the …rst order conditions
@B
1
( )
@q
1
+ p
0
( q ) q
1
Q
1
Q
1
=
@
1
( v
1
)
@q
1
> 0 and
R
1
( Q
1
) + p
0
( q ) q
1
Q
1
Q
1
=
@
1
( v
1
)
@Q
1
> 0 ;
(34)
(35)
7 The setting of Anderson’s (2008) paper is rather di¤erent to this one. He distinguishes between “traditional”or
“capacity-based”market power and “permit-based”market power, which he treats separately. The primary focus of his analysis is then the possibility that one quota-holding …rm might …nd it pro…table to lease the productive capacity of other …rms in order to control the market supply of …sh.
15

and hence
@B
1
( )
@q
1
= R
1
( Q
1
) +
@
1
( v
1
)
+
@q
1
@
1
( v
1
)
@Q
1
0 ; as we had previously. Here, though, Q
1
< q
1 implies that total output exceeds the TAC and hence the output price is lower than if the …rm is compliant. Increasing output beyond the quota limit, i.e., cheating, will clearly reduce unit revenues from the catch but will also reduce the costs of quota if the …rm is a net purchaser of quota.
In summary, if the initial endowment of quota to the dominant …rm is greater than zero, the …rm may choose to withhold quota from the market or to cheat, or indeed to match quota and output. The results in general appear to be ambiguous and hence (presumably) parameter-speci…c, depending upon the relative production capacities of the dominant
…rm and the competitive fringe as well as the relative slopes of the consumer inverse demand curve for the industry output and the (fringe) inverse quota demand curve for quota. If, on the other hand, the dominant …rm’s initial quota allocation is zero, it will unambiguously be non-compliant, although even in the absence of enforcement the …rm’s quota demand may then be non-zero.
The foregoing assumes not only market-clearing in the quota market but also compliance on the part of the competitive fringe. The exercise of market power by the dominant
…rm is a little less straightforward if the fringe is non-compliant. Assume, to begin with, that expected penalties in the fringe depend upon the level violation size (as is generally assumed in the literature). In this case, B 0
F
( q
F
) = r ( ) in the fringe and
16

hence we still have @r ( ) =@p ( q ) = 1 in the …rst order conditions (26a) and (26b). Also,
@B
0
F
( q
F
) =@p ( q ) = @r ( ) =@p ( q ) = 1 implies that
@q
F
@p ( q )
= dB
0 1
F
( r ( ) ; p ( q )) dp ( q )
=
@B
0 1
F
( )
@p ( q )
+
@B
0 1
F
( )
@r ( )
= 0 ; so that
@ q
@q
1
= 1 +
@q
F
@q
1
= 1 ; as before. All else equal, if in the fringe we maintain B 0
F
( q
F
) = r ( ) , then a change in the output price does not change the fringe output. Although, given market clearing, we still have now q
F
@ q
@Q
1
@q
F
=
@Q
1
=
@B
0 1
F
@r ( )
( ) @r ( )
=
@Q
1
@q
@Q
> Q
F and hence we cannot assume that @q
F
=@Q
F
F
F
< 0 ;
= 1 since the slope of the fringe (inverse) quota demand now di¤ers from that of the marginal bene…t curve, i.e., r 0 ( ) = B 0
F
( ) : The assumption that expected penalties in the fringe depend upon level violations means that the fringe inverse quota demand becomes less elastic, 8 which implies that @q
F
=@Q
F
< 1 and hence @ q =@Q
1
> 1 .
If @ q =@q
1
= 1 but @ q =@Q
1
> 1 , then @ q =@q
1
+ @ q =@Q
1
> 0 and hence from (29) we have
@B
1
( )
@q
1
> R
1
( Q
1
) ; where now
0 < R
1
( Q
1
) < p
0
( q ) Q
1
Q
1 q
1
:
If expected penalties in the fringe depend upon the relative violation size, on the other hand (see Hatcher, 2005) then B
0
F
( q
F
) = r ( ) which implies that, in addition, in general
8 See Malik (2002), Chavez and Salgado (2005), Hatcher (2005).
17

@r ( ) =@p ( q ) = 1 and @ q =@q
1
= 1 . While fringe non-compliance complicates the analysis somewhat, since the principal e¤ect of non-compliance in the fringe is to alter the slope of the inverse quota demand curve, it does not fundamentally alter the general conclusions.
If a dominant …shing …rm has market power in the market for ITQs, but not in the output market, then it will only hold excess quota if its initial quota endowment is su¢ ciently large that its output remains unconstrained while maximising its revenues from selling quota to the competitive fringe. Otherwise, the …rm will cheat. If the dominant …rm also has market power in the output market, then depending upon the structure of both quota and output markets, as well as the dominant …rm’s own capacity in relation to total industry capacity and the TAC, the dominant …rm may be voluntarily compliant whatever its initial quota allocation, even to the extent of holding excess quota, provided its initial quota endowment is non-zero. As a corollary, we can conclude that a dominant
…rm may hold excess quota whether it exercises monopoly or monopsony power in the quota market, or even if it does not enter the quota market. If the initial quota endowment is zero, on the other hand, the …rm will, unambiguously, cheat. In this case, however, the …rm may still not hold zero quota, even in the absence of enforcement. Restricting a dominant …rm’s initial quota allocation will reduce the extent to which it may hold quota o¤ the market, but will also increase the likelihood that it will be non-compliant.
18

Anderson, L. G., 1991. A note on market power in ITQ …sheries.
Journal of Environmental Economics and Management , 21: 291-296.
Anderson, L. G., 2008. The control of market power in ITQ …sheries.
Marine Resource
Economics , 23: 25-35.
Armstrong, C. W., 2008. Using history dependence to design a dynamic tradeable quota system under market imperfections.
Environmental and Resource Economics , 39: 447-
457.
Chavez, C., and H. Salgado, 2005. Individual transferable quota markets under illegal
…shing.
Environmental and Resource Economics , 31: 303-324.
van Egteren, H., and M. Weber, 1996. Marketable permits, market power and cheating.
Journal of Environmental Economics and Management , 30: 161-173.
Hagem, C., and H. Westskog, 1998. The design of a dynamic tradeable quota system under market imperfections.
Journal of Environmental Economics and Management , 36:
89-107.
Hahn, R. W., 1984. Market power and transferable property rights.
Quarterly Journal of
Economics , 99: 753-765.
19

Hatcher, A., 2005. Non-compliance and the quota price in an ITQ …shery.
Journal of
Environmental Economics and Management , 49: 427-436.
Malik, A., 1990. Markets for pollution control when …rms are noncompliant.
Journal of
Environmental Economics and Management , 18: 97-106.
Malik, A., 2002. Further results on permit markets with market power and cheating.
Journal of Environmental Economics and Management , 44: 371-390.
Misiolek, W. S., and H. W. Elder, 1989. Exclusionary manipulation of markets for pollution rights.
Journal of Environmental Economics and Management , 16: 156-166.
20