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