ere7: renewable resources fisheries growth rates in biological resources steady-state harvest...
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ERE7: Renewable Resources
• Fisheries• Growth rates in biological resources• Steady-state harvest
– Perfect market – Open access
• Dynamic harvesting• Policy intervention
Last week
• Resources and Reserves• Social optimum and a model for a
perfectly competitive market• Sensitivity analysis
– Increase in interest rate and resource stock– Change in demand and extraction costs
• Market failure– Monopoly
• Taxes and subsidies• Reality
Renewable ResourcesRenewable flow resources• Such as solar, wave, wind and geothermal energy• These energy flow resources are non-depletable
Renewable stock resources• living organisms: fish, cattle and forests, with a natural
capacity for growth• inanimate systems (such as water and atmospheric
systems): reproduced through time by physical or chemical processes
• arable and grazing lands as renewable resources: reproduction by biological processes (such as the recycling of organic nutrients) and physical processes (irrigation, exposure to wind etc.).
• They are capable of being fully exhausted.
Fish catch
Catches, 1995-97, cf 85-87
• Sea fish: 73 mln t, +7%• Freshwater fish: 6 mln t, +19%• Mollusc: 11 mln t, +38%• Aquaculture: 34 mln t, +166%
(mostly Asia)• Fish provides 16% of animal
protein, 6% of total protein
1
9
18
47
21
4
0 10 20 30 40 50
Recovering
Depleted
Overfished
Fully fished
Moderately exploited
Underexploited
Percentage, %
Source: Garcia and de Leiva Moreno (2001)
State of world stocks in 1999
Biological growth processes
• Change of population:
– g is the intrinsic growth rate (birth rate minus mortality rate) of the population
• With an upper bound it becomes:
– An example: (simple) logistic growth curve
dSS gS
dt ( )S g S Sor ?
(1 ) ( )MAX
dS SS g S G S
dt S
Logistic growth curveStock (S)
Time
SMAX
SMIN
SZERO
Smax
Steady state harvest
S0
G(S)
MSY
Stock
S G H
In steady state: and 0G H S
Rate of change: G, H
A Simple Harvesting Model
Harvest ( , )H
H H E S eES eSE
Stock growth f unction ( )S G S H
Costs C wE
Revenue
Price = ( ), 0
V PH
PP P H
H
Exploitation
eE0S
eE1S
eE2SeE3S
SS0
h3 h2
h1
h0
E3> E2 > E1> E0
H
EeS
Effort:
Harvest: H eESG, H
Exploitation (2)
E
H
E0 E1 E2 E3
E3> E2 > E1> E0
h3
h2
h1
h0
Profit Maximisation
C=wE
EE0
Total costs: C wE
V PHTotal revenue:
V=PHV-C=MAX
EProf
CProf
VProf
V, C
Open Access, Steady State
( , )H
H H E S eES eSE
( ) 0 ( )S G S H H G S
H
C wE weS
V PH
w
C H V PHeS
C wE V PH
Net growth of stock in steady state:
Harvest:
Cost:
Revenue:
For open access:
w
PeS
Equilibria: V C ( )G S Hand
CostsHProf
HOA
EEProf EOA Emax
Profit maximisation and open access equilibrium
Revenue
Open access vs Restricted access fisheries
• Consequences of open access: entry continues until all rents are dissipated (profit per boat = zero).
• Stock sizes will tend to be lower, and harvest rates will tend to be higher (but may not always be) compared with a restricted access fishery.
• Extinction is more likely, but will not necessarily happen.
Introducing time
0
max ( ) ( , ) dt
itt t t t
Ht
NPV V H C H S e t
( ) ( , ) ( )t t t t t t tL V H C H S p G S H
0 t t
tt t t
L V Cp
H H H
t t t t
t t t
L C Gp ip ip p
S S S
( )t tS G S H
Necessary conditions:
Equations of motion:
Objective function:
Hamiltonian:
t
t t t t tt
CV PH p P
H
iSocial optimum is market outcome iff:
Interpretation
t t tt t
C Gip p p
S S
the value of postponing revenue ( )tip p P c
the change in valuetp
the change in harvesting costsCS
the change in growth times the shadow
value of the stock
Gp
S
Interpretation (2)
t
ttt t
p GCi p
Sp S
Hotelling: the discount rate equals
the proportionate growth in net price plus
the proportionate reduction in harvesting costs plus
the marginal natural growth rate
Profit maximisation and stock effect (1)
0tp
t tt t
G Cip p
S S
In steady state:
Add units to the stock if:
t t
G Cip p
S S
Harvest additional units if:
Stock effects if:
t t
G Cip p
S S
1
t t t
G Ci
S p SFundamental equation:
and ( ) 0G S
Profit maximisation and stock effect (2)
• If harvesting costs do not depend on stock size:
• If harvesting costs depend on stock size:
• For a given i:– Stock size is higher– dG/dS is lower since (dC/dS)/p is negative– i> dG/dS
0
t t
C Gi
S S
1
t t t
G Ci
S p S
Slope = i - [-(C/S)/P]
Slope = i
SSPV*SPV
G(S)
Harvest Costs and Stock Effect
Sum up• Equilibrium conditions:
– Dynamic
– Static
• Static profit maximisation equilibrium only if i=0
• Open access equilibrium is independent of discount rate
t t tt t
C Gip p p
S S
C G
ip pS S
C G
pS S
Fisheries• If H>G, fish stocks fall, perhaps to (local)
extinction• Reasons
– Open access, little incentive to preserve– It may be profitable ...– Ignorance and uncertainty– Variability, shocks, disturbances
• Contributing factors– High market price, high elasticity– Low harvesting costs– Low stock growth– High discount rate
Renewable Resource Policy
• End open access• Information• Create forward or future markets• Taxes• Tradeable permits• Technical restrictions• Time restrictions
Fishery Policy in the EU
• Early 1970s first common fishery policy (CFP)
• Equal access to waters of the member states to all EU fisherman
• Principal instrument: species-specific total allowable catch (TAC)– Set annually based on scientific advise– Divided into quotas– Discarding and black fish make TAC difficult
to determine
Why did the CFP fail?
• Principle of equal access is not shared by the fisherman
• Political interference with the TAC to protect fisherman
• Centralised structures• Fishing fleet is far too large• „Flag“ ships• Tension between support for ship
building industry and economic efficiency
What could be done?• Individual tradable quotas
– A large number of fisherman will exist the industry
– Does nothing to stop cheating– Political interference– Might lead to buy out
• Vessel licensing– No pretence for monitoring– Difficult to determine total killing power– Conflicts with social objectives
• Abandoning the principle of equal access