A Model of Regulated Open Access Resource Use

20
HOMANS AND WILEN
The comparative statics properties summarized in Table I assume an ‘‘interior’’
equilibrium in the sense that the fishery is characterized by a joint equilibrium
where regulations are binding. Circumstances where active regulation is necessary
exist where there is an equilibrium intersection of the two equations representing
the industry and regulator behavior. The circumstances which will lead to a
regulated open access equilibrium can be described as follows. Begin with the
relationship which describes the level of cumulative effort ET defined as
max
1 PqX 0
ETmax
ln Ž B1.
q
for some arbitrary level of biomass X 0. Note that this defines a rectangular
hyperbola in E, T space and hence can be compared with the regulatory agency’s
choice which is also defined by a rectangular hyperbola, namely
1 X 0
ETreg
ln . Ž B2.
q Ž 1 d. X0c
A joint or binding temporary regulatory equlibrium occurs whenever the maximum
level of effort which dissipates unregulated rents or ETmax
is greater than the
amount of total fishing effort desired by the regulatory agency ET reg. Thus the
condition for existence of a temporary regulatory equilibrium is
PqX0 X0
ETmax
ETreg
. Ž B3.
Ž 1 d. X0c
Thus a regulated equilibrium is likely to occur when P, q, or X0
are large, or when
is small, or whenever d or c are small. Note that d small implies that regulators
are particularly concerned about high exploitation rates.
The above refers to the Ž temporary equilibrium.
case where X0
is some arbitrary
value which could of course be its long run open access steady state value. In
general, however, a full long run equilibrium must not only have the industry
earning zero rents, but the biomass must also be in equilibrium at that state. The
long run steady state biomass level that would evolve in an unregulated Ž Gordon.
system is
'
2
Ž . Ž .
a 1 1 a 4bPq
XG , Ž B4.
2b
while the biomass level that would emerge in a regulated open access system is
given by Eq. Ž 11.
in the text. The complete characterization of necessary conditions
for a binding long run regulated open access equilibrium is given when these are
inserted into Eq. Ž B3.
above, or
PqXG
Xsafe
. Ž B5.
Ž 1d. Xsafe
c