D AND E Suppose that a fishery with N identical fishers faces the following constraints: Total Allowable Catch Constrain

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D AND E
Suppose that a fishery with N identical fishers faces the
following constraints:
Total Allowable Catch Constraint: Q = TNh,
Season Length Constraint: T ≤1,
Participation Constraint: π = T[ph −c(h)] −w ≥0,
where c(h) = h2, Q > 0, p > 0 and w > 0. T is the season
length (measured in fraction of a year), Nis the number of fishers,
and h is the harvest per fisher per unit time. Note that fishery
rents,if any, are R = Nπ. Let p = 4, w = 1, and Q = 100.
(a) Assume that the total allowable catch (TAC) constraint always
binds. On a graph with N on
the vertical axis and h on the horizontal axis, draw the
season-length and participation constraint
boundaries and identify the feasible combinations of N and h.
(b) Derive the open access equilibrium {hOA,NOA,TOA}, and identify
the open access equilibrium as
OA on your graph. What are the rents ROA under open access?
Explain.
(c) Consider a limited entry restriction of the form N ≤NOA/2.
Derive the limited entry equilibrium
{hLE ,NLE ,TLE ,vLE }, where vLE is the equilibrium limited entry
permit price. Identify the
limited entry equilibrium on your graph as LE, and explain whether
rents RLE are positive.
Compare this equilibrium with the open access equilibrium.
(d) Consider a harvest restriction of the form h ≤hOA/2. Derive the
harvest constrained equilibrium
{hHC ,NHC ,THC }, and identify it as HC on your graph. Solve for
the rents, RHC . Compare this
equilibrium with the open access equilibrium.
(e) Suppose that quotas are allocated so that each fisher under
open access receives q = Q/NOA quo-
tas. Let the market price for quotas be m. Solve for the ITQ
equilibrium {hIT Q,NIT Q,TIT Q,mIT Q}.
Identify the ITQ equilibrium on your graph as ITQ and solve for the
ITQ rents, RIT Q. Com-
pare this to the open access eqiulibrium. Explain whether or not
fishers who received quotas but
do not actively fish under the ITQ equilibrium are made better off
relative to the open access
equilibrium