The notion that a fishing vessel's costs are a function of its "effort" is a useful paradigm in fishery analysis. This paper elaborates on this micro theoretic approach, and proposes a way to view the cost of effort relation as the interaction of capital intensity decisions and the length of the fishing season. The model indicates that capital intensity decisions are affected by season closures, and that season closures can be used to redistribute wealth among different classes of fishermen.Production Economics, Resource /Energy Economics and Policy,

Karpoff, Jonathan M.

English

Research Papers in Economics

Time,  Capital Intensity, and the
Cost  of  Fishing  Effort
Jonathan M.  Karpoff
The notion  that a fishing  vessel's costs  are a function of its "effort"  is  a useful paradigm  in
fishery  analysis.  This  paper elaborates  on  this micro theoretic  approach,  and proposes  a way to
view  the  cost  of effort  relation  as the  interaction  of capital  intensity  decisions  and the  length
of the fishing season.  The model indicates  that capital intensity decisions are affected  by season
closures,  and that season  closures  can be  used to redistribute  wealth among  different classes  of
fishermen.
In microanalysis of the fishery it is often
useful to view the relation between a com-
mercial  fishing  vessel  and  the  fishery  in
the  same  light  as  the  neoclassical  firm-
industry  relation.  This  approach  was  for-
mally proposed by Anderson,  who used  it
to contrast the open access  and maximum
economic  yield  solutions  and  to examine
the effects of regulations  at both the firm
and  industry  levels.  The  basis  for  this
analysis  is  to  view  a  vessel's  effort  as  its
decision  variable.  The  vessel's  catch  rate
depends on its total fishing effort  and  the
average productivity of the fishery, which
in turn is affected  by the effort of  all fish-
ing  vessels.  Since  effort  effectively  be-
comes  the  vessel's  (intermediate)  output,
the cost of producing  effort  is assumed to
have  "neoclassical"  characteristics,  i.e.,
eventually  decreasing  returns  to  scale
cause  marginal  costs  to increase.  As  a  re-
sult,  the  long-run  marginal  and  average
costs  are  displayed  as  in  Figure  1. The
vessel  is  considered  a  small  enough  por-
tion of the fishery  to be  not only  a price-
taker,  but  an  "average-returns-to-effort-
taker."  The  vessel  owner  then  optimizes
Jonathan M.  Karpoff  is Assistant Professor of Finance
at the University of Washington.
The  author  gratefully  acknowledges  the  helpful
comments of Dick Johnston  and the anonymous  ref-
erees.  Financial support was provided by NOAA grant
no.  NA84AA-D-00011,  Washington  Sea  Grant  Pro-
gram budget  no.  62-8553.
Western Journal  of Agricultural Economics, 10(2):  254-258
© 1985  by the Western  Agricultural  Economics  Association
where  marginal cost of effort  equals  fish-
ery-wide  average  returns  to effort.
This  paper  explores  in  more  detail  a
special  case  of the  cost  of  effort  relation
depicted  in  Figure  1.  This  relation  has
been presumed by several  researchers [see
Visigilio;  Clark,  1980],  who,  like  Ander-
son,  have  used  it  in  comparative  static
analysis of the fishery. But the assumption
of increasing marginal cost has been called
an "ad  hoc  formulation"  by Clark  [1985,
p. 90].  And it is not immediately clear that
actual  costs  of  producing  effort  in  many
fisheries  are  so  well  behaved.  Casual  ob-
servation  and  some  limited  data  suggest
that short-run marginal  costs of effort are
roughly constant. The incremental  cost of
fishing an extra day, setting and retrieving
a  net one  more  time,  or setting  an  extra
pot  or trap  is  not an  increasing  function,
at least over the  relevant range.'  If  short-
run  marginal  costs  are  roughly  constant,
what  is  implied  about fishery  models?  At
first glance, it would appear that the equi-
librium  number  of  vessels  is  indetermi-
nate.  Anderson's  prediction  that  entry
Data  from an  extensive  survey  of fishermen's  costs
and revenues  in the Alaska salmon fisheries  support
the notion that short-run  marginal costs are roughly
constant [see Larson for  a description  of the survey
and summary  of results].  Operating expenses  which
vary  with  the  time  spent  fishing-fuel,  food,  ice,
supplies-are  a relatively small portion of total costs,
and  do  not  increase  at  an  increasing  rate  as  time
spent  fishing  increases.Cost of Fishing Effort
limitations preserve  a portion  of the  fish-
ery's  value  could  be invalid,  and  Clark's
analysis  of  fishery  regulations  would  be
significantly altered.
In this paper I argue that models which
assume  increasing  costs  are,  in  general,
valid.  Short-run  marginal  costs  in  many
fisheries  do  eventually  increase,  and  the
application  of  neoclassical  cost  curves  in
the production of effort poses no problem.
Other  fisheries  which  appear  to  best  be
characterized  by  constant short-run  mar-
ginal  costs  still  have  increasing  long-run
marginal  costs.  The  reason  is  because  of
the unique  role of "time"  in the  produc-
tion activities of many fisheries.  Access  to
the  fishery  is  constrained  by  regulating
authorities. This affects  the capital invest-
ment decision, since larger vessels become
less economical  as the length of the fishing
season is reduced. A related concern  is that
season  closures  impose  higher  costs  on
highly  capitalized  fishermen  than on  less
capitalized  fishermen.  This  has  implica-
tions for the  political  economy  of  fishing
regulation, since season  closures become  a
tool for redistributing  wealth among  fish-
ermen  who differ in capital intensity.
The  argument  is  presented  in  the  fol-
lowing section. I start with two simple ob-
servations  which  characterize  many  fish-
eries and proceed with a simple graphical
(and static)  exposition.  Two  implications
are  discussed  in the third  and concluding
section.
A Model  of the Cost  of Effort
The  first  observation,  discussed  above,
is that short-run marginal costs  (defined as
those  within  a  given  fishing  season)  ap-
pear  to  be  constant.2 The  second  obser-
vation  is that, unlike  most productive  ac-
tivities,  a  vessel's  access  to a  key input-
the  fishery-is often  limited with  respect
to  time.  Season  limitations  are sometimes
2 More  accurately,  marginal  cost  is roughly  constant
only up to some point of "saturation"  of the capital
stock.
$
MC
C
Effort per unit  time
Figure  1.  Long-Run  Marginal  and Average
Costs  of  Fishing  Effort.
dictated  by  biological  factors,  for  exam-
ple,  in the  case  of  near-shore  capture  of
an anadromous species such as salmon. But
in  many  more  fisheries  it  is  a  regulatory
agency  that  forces  a  season  closure,  as  a
means  of  preventing  biological  overex-
ploitation  of  the  fish  stock. 3 Season  clo-
sures impose a unique type of cost on par-
ticipating  fishermen.  Fishermen  make
expenditures on capital equipment which
cannot be used for a good part of the year.
During  a  fishing  season,  they  are  often
forced  to  sit idle  or  find  alternative  em-
ployment,  perhaps  in  another  fishery,
while awaiting  the re-opening  of the fish-
ery.  These  costs  depend  in large  part  on
the characteristics of the fisherman's  cap-
ital  stock.  We  should  therefore  expect
fishermen  to  consider  the  length  of  the
fishing  season  and the prospect  of  season
closures in making capital expenditure de-
cisions.
Consider the following model. In a giv-
en  fishing season,  average  cost  of effort  is
a declining function of the time employed
in the harvest.  However, the biological or
regulatory constraint on the length of time
one  can  fish limits each  vessel's  ability to
fully  exploit  these  economies,  and  the
right-hand  portion  of the short-run  aver-
s The regulatory constraint  is typically binding,  even
in seasonal  fisheries which  face biological  time con-
straints.
255
KarpoffWestern Journal of Agricultural Economics
age cost curve  is truncated.  Vessel owners
can  substitute  capital  intensity  for  time
spent fishing  to increase effort, but at some
point  this  substitution  becomes  uneco-
nomical,  as  the  harvesting  capacity  of  a
more capitalized  vessel becomes more se-
verely constrained  by the time limitation.
Over a  given  fishing  season  a  vessel  with
fixed  capital  has  average  cost  of  effort
which declines  with  effort  (i.e.,  the time
engaged  in  the  fishery).  But  prior  to  a
choice  of  "plant size"  (i.e.,  capital  inten-
sity),  the  vessel  operator  considering  the
tradeoff  of capital  and  available  time to
fish faces decreasing returns to capital in-
vestment and hence, to effort. In the long-
run, marginal cost increases  with effort.
To illustrate,  express  each  vessel's  total
costs  c as  an increasing  function  of vessel
effort e.  Fishing effort is divided into two
components,  a vessel's capital  intensity or
"catching  power"  k,  and  the  amount  of
time spent  fishing  during  the fishing  sea-
son t.4 "Catching  power" is a standardized
measure  of  all  relevant  vessel  and  gear
characteristics,  similar  to  the  "standard-
ized fishing  unit" commonly found  in the
literature [e.g.,  Clark,  1985,  p. 38],  except
that  it  is  a  stock  measure  and  does  not
have  a time dimension  associated with  it.
It can also be viewed as including the har-
vest potential which accrues from the hu-
man capital embodied  in  the skipper and
crew. The  time component  t is consistent
with a comparative static framework.  It is
treated  here  as  an  input  available  to the
vessel  during  the  fishing  season,  and  can
be thought of  as the  number  of days  the
vessel is employed  during the fishing  sea-
son.  Thus,  t is  combined  with k, up to  its
maximum  allowable  level  T,  to  produce
effort,  which  is  measured  in  "standard-
ized fishing  unit days."  T is set  either by
4 Effort  is  often  treated  as  an  input  in  the  fishery
production  function.  This model  is  consistent  with
this practice, only the process is taken  back one step
to examine  how effort  is produced.  See Karpoff  for
a more complete model of fishery revenues and costs.
256
f(k
2)
f(k
i)
f(k
0)
Figure  2.  Total  Cost-of-Effort  Curves  for
ko  < k  <  k2.
Effort  per
Fishing  Season
Figure 3.  Marginal and Average  Cost-of-Ef-
fort Curves.
biological  factors  or, more frequently,  by
a regulating  agency.  It is assumed that ac-
cess  to any t  >  T has infinite cost. 5
These assumptions imply
5 More  generally,  fishing  beyond  T  has  a finite  ex-
pected  cost,  e.g.,  the  expected  fee  from  violating
the  season  closure.  Notice  that,  as  described,  the
production function  for effort  can be expressed  e =
kt.  This  is a Cobb-Douglas  function that  is homo-
geneous  of degree two,  which  represents very sub-
stantial  scale  economies.  However,  this  is  not  con-
sidered  a  problem,  for  several  reasons.  First,  the
expansion  of  effort  is  constrained  by  t  <  T.  The
substantial economies  up to the point t =  T suggest
that fishermen  will  use  the  input  "time"  up  to  its
maximum allowable  amount T. Second, while there
may  be  substantial  economies  in producing  effort,
the fisherman faces  diminishing marginal returns to
effort in the production  of fish.  Third, the expansion
of effort  is constrained by its cost,  as described  be-
low. And fourth, this formulation is very descriptive
of many fisheries.
December 1985Cost of Fishing Effort
e = e(k,  t),  Oe/dk >  0,  Oe/Ot  > 0,  t <  T  (1)
c  = c(e(k,  t)), dc/de  >  0.  (2)
For a  given  k,  the maximum  possible  ef-
fort level  is e*(k)  =  e(k, T).  It is  useful  to
further  specify  the cost function  to incor-
porate  the  notion  of  constant  short-run
marginal  cost.  Subdivide  total  costs  into
"fixed"  and "variable"  components:
c  =  f(k) + v(k,  t),  (2')
where
df/dk  >  0, a(v/e)/dk  <  0, dv/8t  >  0.
Fixed  cost f represents  the  investment  in
vessel and gear  which does  not vary with
the  number  of  days  they  are  employed
during the  season.  Variable  cost  v repre-
sents the cost of operating  a vessel  during
the  fishing  season.  While  fixed  costs  in-
crease  with  the  vessel's  catching  power,
average  variable  and  marginal  costs  of
producing  effort  decline  with  increased
capital  intensity.  Intuitively,  larger  ves-
sels, or vessels equipped with gear that in-
creases  their  ability  to  harvest  fish,  incur
greater  fixed  cost but lower marginal  cost
per  unit  of  effort.6  Increasing  the  time
spent fishing,  on the other  hand, does not
affect fixed costs but does increase expen-
ditures  on variable  cost  components  such
as fuel, ice, and  crew.
These  cost  relations  are  illustrated  in
Figures  2  and  3.  Figure  2  displays  total
cost  of  effort  curves  for  three  levels  of
capital intensity,  ko  < k,  < k2. Fixed costs
which  increase  in  k  are  represented  by
higher vertical  axis intercepts.  Decreasing
marginal costs of effort are represented by
lower  slope  terms.  Notice  that  the  time
6 It  is  important  to  again  point  out that  "effort"  is
the (intermediate)  output  of the k and t inputs,  and
is  measured  in  standardized  units.  Thus,  it  is  pos-
sible that investment in k can increase  total variable
costs,  but  to avoid  a  degenerate  case  in  which  all
vessels  employ  the minimum  possible  level  of k,  it
must be assumed that average  variable cost per unit
effort  decreases  over  some range of k.  As drawn  in
Figures  2  and  3,  marginal  cost  is  constant  for  a
given  k,  so  dv
2/d2t = 0.
constraint  t  <  T  imposes  a  limit  on  the
amount of effort  a  vessel  can  expend  for
a  given  k.  Thus,  each  cost curve  is  trun-
cated at its maximum level of effort, e*(k).
The  associated  short-run  average  and
marginal cost curves are illustrated in Fig-
ure 3.  Notice that, in each  case, short-run
average  costs  would  continue  to  decline,
except  that  the  time  limitation  prohibits
the fisherman from more fully "spreading
out"  her  fixed  cost over  a larger  amount
of effort.  Over  some range  (e.g.,  from  k0
to  k1),  higher  levels  of  k  can  be  used  to
expand  effort  at  lower  average  cost.  But
the time constraint  becomes more binding
for more capitalized  vessels  until,  as with
k2, short-run  average  cost  is  never  lower
than it is  for some other k.
"Long  run"  is  typically  used to denote
the  time  horizon  over  which  fixed  costs
can be adjusted. Adopt this convention and
permit fishermen to adjust k between fish-
ing seasons.  Then, prior to a season, a fish-
erman  faces  a  set  of  short-run  cost  rela-
tions  as in  Figure  3.  The  lower envelope
of  all  short-run  average  cost  curves  rep-
resents the menu of long-run cost options.
It is the-long-run  average  cost curve  illus-
trated  by  the  dashed  line  in  Figure  3.
Thus, one  obtains a long-run  average  cost
curve  with  the  familiar  U-shape.  Unlike
Anderson,  Visigilio,  and  Clark  [1980],
however,  it  is  derived  from  a  series  of
short-run  curves,  each  of which  is  down-
ward sloping.
Two  Implications
The  intent  of this  paper  is to  reconcile
assumptions  of  "normal"  looking  cost  of
fishing  effort  curves  with  observations
about  real-world  short-run  fishing  costs
and the presence of regulatory control over
the  length  of the  fishing  season  in many
fisheries.  Its  major  implication  is  that  a
vessel's  optimum  capital  intensity  de-
pends on the length  of the fishing  season.
The  model  predicts  that,  ceteris paribus,
optimum  "plant  size"  is  an  increasing
257
KarpoffWestern Journal of Agricultural  Economics
function  of  the length  of the  fishing  sea-
son.  This can be seen by reference  to Fig-
ure  3.  Reducing  the length  of the  fishing
season T causes each short-run curve to be
truncated  at  lower  effort  levels.  Since
higher levels of k can now be utilized over
a shorter  fishing season,  they  lose some of
their cost advantages.  The  effect  is to  de-
crease the  effort  level  at  which  LRAC  is
minimized.  In  an  open-access  fishery
comprised  of homogeneous  vessels,  com-
petition  among  vessels  would  force  each
one  to  operate  at  its  minimum  LRAC.
Even  if  vessels  are heterogeneous,  the ef-
fects  are  the  same:  less  capital  intensive
vessels become more cost effective.  This is
consistent  with evidence  that larger, cap-
ital intensive vessels do not earn the high-
est  profits in some  fisheries  subject  to fre-
quent  season  closures.7
This  leads to  an implication  about  the
political  economy  of  fishing  regulation.
Stricter  time  constraints  penalize  more
capital intensive vessels  relatively heavily.
If political sentiment  lies with smaller op-
erators,  regulation  through the control  of
the  fishing  season  can  be  used  to  favor
smaller  vessels  at  the  expense  of  larger
vessels.  This  is  consistent  with  the  argu-
ment  made  in  Karpoff,  that  many  "tra-
7 For example,  the Alaska Commercial  Fisheries En-
try Commission has conducted extensive fiscal mod-
eling of many Alaska fisheries at the individual ves-
sel  level,  and  reports  that  the  largest  and  highest
grossing  vessels  often  do not  have the  highest  net
incomes.  It appears  that these vessels  are overcapi-
talized.  [Source:  Kurt Schelle,  Director of Research,
Alaska  Commercial  Fisheries Entry Commission.]
ditional" forms of fishery regulation create
wealth  transfers  among  classes  of  fisher-
men.  It  is  also  consistent  with  the  argu-
ment  made  by  Morehouse  and  Rogers,
who  point  to  the  fact  that  many  of  the
regulatory  controls  used  in  the  Alaska
salmon fisheries  have been designed to fa-
vor indigenous fishermen over "outsiders"
who are typically more capitalized.
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TIME, CAPITAL INTENSITY, AND THE COST OF FISHING EFFORT

TIME, CAPITAL INTENSITY, AND THE COST OF FISHING EFFORT

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