Topic 8: Forestry and Fisheries

1
Topic 8 Forestry and Fisheries

• Efficient management of commercially valuable
  biological resources

2
Fisheries some definitions

• Fishery a number of different activities and
  characteristics associated with fishing,
  including the types of fish to be harvested and
  the types of vessels and gear used.
• Demersal fish feed on ocean or lake bottoms and
  do not range over a large area (shellfish,
  lobster, cod, flounder).
• Pelagic fish free-swimming fish that migrate
  over a wide range of the ocean or rivers (tuna,
  herring, salmon).
• Property rights may vary by type of fish.

3
Current problems in marine fisheries

• Overfishing, resulting in substantially
  diminished stocks of many commercial species.
• Overcapitalization, i.e. excessive investments in
  national fishing fleets.
• Conflicts over fishing rights, both within a
  country (e.g. Native American claims) and between
  countries (Canada/Mexico vs. US).
• Coastal and water pollution/habitat loss
  threatening spawning and breeding grounds,
  affecting water quality.

4
Fish as a renewable resource

• The stock, S, or population, of fish is usually
  measured in terms of the total number of fish or
  the total biomass, the aggregate weight of the
  fish population measured at a point in time.
• The stock will grow in number or weight or both
  as new fish are born and existing fish increase
  in size.
• The stock will diminish as fish die naturally,
  are removed by predators (including humans) or
  are killed by pollution.
• Key difference compared to a nonrenewable
  resource the stock of fish will be changing over
  time, even if no harvesting occurs.

5
Growth and fisheries discrete periods

• Most biological resources are accumulating (i.e.
  resource growth adds to the resource stock

• Total net change in stock over time is equal to
  the natural growth of the population less harvest

• Natural growth of the population is assumed to
  be a function of the existing population, S0

6
Properties of the growth function, G(S0)

• The usual assumption is that G(S0) is
  bell-shaped, i.e. growth first increases,
  stabilizes then declines with the size of the
  current population.
• The biological equilibrium is the fish stock
  size where there is no growth in the fish
  population, i.e.
• S1 S0 G(S0) 0
• There are two stock sizes where this occurs
• S 0
• S K, where K is the carrying capacity of the
  marine habitat, i.e. the maximum population that
  the habitat can support.
• In absence of harvesting, or natural
  disruptions/disasters, fish populations will tend
  toward the biological equilibrium at K.

7
A simple fish harvesting model
Biological Growth G(S0)
Q0
dG(S0)/dS0 0
G(S0) Q0
dG(S0)/dS0 gt 0
dG(S0)/dS0 lt 0
Q0
0
S0
Biomass (S0)
K
S0
S0
8
Harvest depending on stock (S) and effort (E)

• Assume that the fishing industry is perfectly
  competitive with constant prices over time.
• If Q0 is the current level of harvest, assume
  that it depends on the available stock of fish,
  S0, and on the current level of fishing effort,
  E0.
• Harvesting effort refers to the economic
  resources devoted to catching fish capital goods
  (boats and gear), labor (crew) and materials and
  energy.
• Effort usually represented as a standardized
  fishing boat, of a certain size, crew number, and
  set of fishing gear.
• Effort is then measured in terms of number of
  days spent fishing by boat of the standard type.

9
Stock-yield curve with constant effort, E0

• Steady state equilibrium when harvest, Q0, varies
  with stock size, S0, holding effort, E0, fixed

Biological growth, G(S0)
Q0 Q(S0, E0)
Q0 Q(S0, E0)
G(S0) G(S0) Q0
0
S0
S0
S0
Biomass (S0)
K
10
Fishing effort, revenues and cost

• Increases in fishing effort lead to more revenues
  for the fishery but also higher costs.
• Total revenues, TR, for the fishery is total
  harvest, Q0, multiplied by the unit price, P, of
  the harvested fish, or
• TR PQ0
• Assuming that the fish stock is held constant,
  higher levels of effort will at first lead to
  rising harvest, but eventually Q will start to
  fall as effort increases.
• It follows that TR PQ(E0), and the total
  revenue curve is bell-shaped, i.e. revenues
  first increase, stabilize then decline with the
  amount of effort, E0.

11

• However, suppose that any additional unit of
  fishing effort has a constant cost, c. The total
  cost, TC, of effort spent fishing is therefore
• TC cE0
• The total profits, or total rents, ?, of the
  fishery are
• ? TR TC PQ(E0) cE0
• If the fishery is efficiently or optimally
  managed, and is able to exclude potential
  entrants, then the fishing fleet will be able to
  choose the level of effort that maximizes total
  rent, ?.
• However, under open access, the fishing fleet is
  unable to prevent new entrants, who join the
  fishery in response to any rents. Thus effort in
  the fishery increases, until total rent is
  dissipated, i.e. ? 0.

12
Open access vs efficient equilibrium for a fishery

• Rents are maximized at the effort level where
  TR-TC is greatest. Steady-state effort under open
  access occurs where TC TR

Total Revenue and Cost ()
TC cE0
Maximum Rent
TR PQ(E0)
E0
E0
Biological Growth G(S0)
Effort (E0)
Q Q(S0, E0)
Q Q(S0, E0)
Q0 G(S0) G(S0)
Biomass (S0)
K
S0
S0
13
Fishery collapse under open access

• Lower costs of effort, c, can lead to collapse
  under open access

Total Revenue and Cost ()
TR PQ(E0)
TC cE0
E0
Effort (E0)
Biological Growth G(S0)
Q Q(S0, E0 )
Q0 G(S0)
Biomass (S0)
K
S0
14
Policies to control open access fisheries

• Regulating or restricting fishing practices
• Raises the costs of fishing and thus reduces
  effort
• E.g., closing fishing areas, limiting the number
  of days fishing, limiting the number or length of
  boats, net-size restrictions, restricting engine
  horsepower, etc.
• Catch limits (Total allowable catches, TACs)
• Authorities establish a TAC, monitor catches and
  close the fishery if the TAC is reached.
• Tax on catch or fishing effort
• Tax on catch reduces total revenue of the
  fishery.
• Tax on effort raises the cost of fishing.
• Individual transferable quotas (ITQs)
• Establishes a TAC but allows fishers to trade
  their individual shares.

15
Individual transferable quotas (ITQs)

• A TAC divided into quotas for individual fishers
  which are then tradeable.
• Requires 5 components to be successful
• The TAC must be economically and biologically
  meaningful.
• The TAC must be divisible into into individual
  catch limits for each fisher in the industry.
• The individual quotas must be allowed to be
  freely bought and sold, and an authority must
  monitor who owns how many.
• The catch quotas must be enforced to ensure that
  no fisher harvests in excess of quota holdings.
• Monitor the quota market to identify problems of
  biological uncertainties, concentrated quota
  ownership and community impacts.

16
Global forestry issues

• Increasing supplies of traditional wood forest
  outputs fuelwood, logs and paper pulp to meet
  demands of expanding world populations and
  economies.
• Replacing the mining of old growth forests with
  secondary forests and plantations as sources of
  wood products.
• In developed countries, reconciling the growing
  demand for recreation uses of forests with timber
  harvesting.
• In developing countries, the growing pressure to
  convert forest land to subsistence and commercial
  agriculture.
• Accommodating new (and non-extractive) values of
  forests, such as biodiversity, carbon
  sequestration and ecosystem services (e.g.
  watershed protection).

17
Forestry for timber some definitions

• A forest is a capital good and a renewable
  resource.
• However, in forestry, the value of a timber stand
  is related to its age i.e. how old it is.
• Value of a stand also depends on whether
  harvesting is based on a single-period or
  multi-period rotation.
•  Instead of 'rent' the value of a tree stand is
  usually referred to as its stumpage value, i.e.
  the value of the stand when it is logged, net of
  harvesting and transport costs.
• Stumpage value Vt (p - c)Qt, where Qt is the
  volume (e.g. m3 or cu. ft.) of wood cut, p is the
  price received at the mill ( per log or per
  tree), and c is harvesting costs plus any
  transport costs from the stand to the mill.

18
Stumpage value and single-rotation harvest

• Stumpage value depends explicitly on how old the
  stand of trees is. Value rises from the time of
  planting to some maximum point and thereafter
  declines. The time that passes before the tree
  is felled establishes the length of rotation, t
  T.

Stumpage value ()
Vt (p-c)Qt
Years (t)
T
19
Stumpage value and multiple rotation harvest

• If trees are harvested many times, then there is
  the possibility of many rotations. We want to
  choose the same harvest date, T, over many
  periods to maximize the overall stumpage value
  earned.

Stumpage value ()
VT (p c)QT
Years (t)
T
2T
3T
4T
5T
20
Maximum sustainable yield model

• The objective is to select a rotation period, T
  (e.g. in years) so as to maximize the average
  annual stumpage value, VT/T, over this rotation
  period from a timber stand.
• Average stumpage value is maximized at the stand
  age, T, where average annual stumpage value
  marginal stumpage value
• The average annual stumpage value is the
  equivalent to the net harvest price times the
  mean annual increment (MAI), i.e. VT/T (p
  c)QT/T. The marginal stumpage value is
  equivalent to the net harvest price times the
  current annual increment (CAI), i.e. dV(T)/dT
  (p c)(QT QT-1)/?T

21
Numerical example of MSY harvesting
22
Problems with the MSY harvesting rule

• Does not consider the opportunity cost of
  holding on to trees as an economic investment
• As we have to wait T years to harvest, there is
  an opportunity cost to this investment.
• Trees could be cut sooner and the timber proceeds
  invested in an alternative asset.
• For multi-rotation harvests, it does not consider
  the opportunity cost of alternative values of the
  land used for growing trees.
• Instead of growing trees, the land could be
  rented out or used for another land use
  (agriculture).
• There must be an implicit land rent cost of
  using the land to grow trees over several
  rotations.
• For forests with multiple (and non-timber)
  benefits, the inclusion of these additional
  values will affect the choice of harvest.
• These benefits are diverse recreational uses,
  wildlife and ecological preservation, global
  values, etc.

23
Nontimber values and multiple use forestry

• Nontimber values as a function of stand age, t,
  and rotation length, T.

(A) Water flow releases
Current Benefits ()
Present Values ()
Stand age (t)
Rotation length (T)
24
(B) Wildlife habitat, recreation, ecosystem
services
Current Benefits ()
Present Values ()
Stand age (t)
Rotation length (T)
(C) All nontimber values
Current Benefits ()
Present Values ()
Stand age (t)
Rotation length (T)
25
Multiple-use rotation combined values

• Because in this example water flow values
  dominate all nontimber values, including NTVs
  leads to a slightly shorter rotation.

All Forest Values ()
All forest values
Nontimber only
Timber only
Rotation length, T
T
T
26
Competing forest land uses
Net benefits per acre ()
Rents from agriculture
Stumpage value from forestry
Distance from market (x miles)
0
xmax
x