Transcript Lecture 2 - Illinois State University

 Homework
 Quiz
#9 Due Wednesday
#4 Wednesday
 Group
 Exam
Outline Due Wednesday
#4 – next Wednesday
 Group
Presentations – Dec. 2 & 4
 Now
assume that we can translate this
population/yield relationship into an
economic relationship between fishing
boats and total product.
Boats
0
1
2
3
4
5
6
7
8
9
Total
0
Product
12
22
28
30
28
24
16
8
0
Stock
100
90
80
70
60
50
40
30
20
10
Growth
0
12
22
28
30
28
22
12
8
0
A
natural state with no fishing industry
A
fishing industry obtaining the MSY from
the fishery
A
fishing industry operating under an
efficient management plan, with
economically optimal returns
A
fishing industry characterized by open
access.
 Fish
prices average $10 per fish and the
cost to operate a fishing boat for a year is
$40.
 Construct
a graph showing total revenue
and total costs in the fishery.
 TR
= P*Q
 TC= AC of Boat * Number of Boats
Boats
Prod
uct
0
1
2
3
4
5
6
7
8
9
0
12
22
28
30
28
24
16
8
0
TR
0
120 220 280 300 280 240 160 80
0
TC
0
40
NB
0
80 140 160 140 80
80 120 160 200 240 280 320 360
0 -120 -240 -360
400
350
300
250
Total Revenue
Total Cost
200
150
100
50
0
1
2
3
4
5
6
7
8
9
 Derive
graphs showing marginal and
average revenue and marginal cost.
 AR
= TR/Q
 MR
= ∆TR/ ∆Q
 MC
= ∆TC/ ∆Q
Boats
0
1
2
3
4
5
6
7
8
9
Product
0
12
22
28
30
28
24
16
8
0
TR
0
120
220
280
300
280
240
160
80
0
TC
0
40
80
120
160
200
240
280
320
360
NB
0
80
140
160
140
80
0
-120
-240
-360
MR
#VALUE
120
100
60
20
-20
-40
-80
-80
-80
AR
#DIV/0!
120
110
93.33
75
56
40
22.86
10
0
MC
#VALUE
40
40
40
40
40
40
40
40
40
 What
is the optimal policy for cutting
trees?
 What
is the optimal harvest age for a
stand of trees?
 What
is the optimal rotation age for a
stand of trees?
 Timber
Characteristics
• Output and capital good
• Clear cutting – logging practice where most or all
trees are uniformly cut down.
• Sustainable management – Selective harvesting
around old growth tree, who durability provide
habitats for plant and animals.
 Imagine
you own a
stand of trees with
100,000 cubic feet
of standing timer.
 And
an annual
growth rate of 5,000
cubic feet.
 At
a price of $100 per cubic foot
• Clear cutting = $10 million
• Sustainable Management = $500,000 per year
 Clear
cutting
• r=4%
• PV= $400,000/ 0.04 =$10mil.
• r=6%
• PV = $600,000/ 0.06 =$10mil.
 Sustainable
Management
• PV = $500,000/0.04=$12.5mil.
• PV = $500,000/0.06=$8.33mil.
 Timber
Characteristics
• Output and capital good
• Time from investment (planting) to recovery of
investment (harvesting) is long, 25 year or greater
 Growth
of a tree
• Measured in volume
• Biologists can track the growth of a tree
 Small initial volume
 Experiences considerable growth early on
 But growth rate declines as it gets older
13-17
Copyright © 2009 Pearson AddisonWesley. All rights reserved.
 Weather
 Soil
 Insects, diseases
 Tree
types
 Care
 Forest
fires
 Air pollution
 Trees
have two kinds of value.
• Stumpage value - the sales of timber or other
products.
• In theory the stumpage value of a timber tree
equals the value of lumber that can be sawed
out, minus the costs of harvest, transport, and
conversion to lumber.
 Tree
grows at rate shown in above figure
 Cost to plant is $1,000
 Price of pulp wood $1 per cubic feet
 Cost to harvest $0.30 per cubic feet
• Benefits are measured using the potential volume of
wood given the growth rate and the price of the
lumber. The annual incremental growth represents the
marginal growth.
• Planting costs are immediate and thus are not
discounted while harvesting costs are discounted
because they are paid in the future.
 The
optimal time to harvest from a profit
maximization perspective would be the age
that maximizes the present value of net
benefits from the wood.
 Net
benefits are calculated by subtracting the
present value of costs from the value of the
timber at harvest age.
 The
discount rate will affect the
harvest decision.
 When
undiscounted
• Opportunity cost = 0
 When
discounted
• r>0 implies there is an opportunity cost
 Harvesting
costs are discounted and are
proportional to the amount of timber
harvested.
 The
net benefit of a unit of wood
harvested at any age is the price of the
wood minus the marginal cost of that unit.
A
tax levied on each cubic foot of wood
harvested would simply raise the
marginal cost of harvesting by the
amount of the tax.

Environmental Value – the value generated from
increased biodiversity, reduced climate change,
and existence of the tree.
 Benefits
• Materials for housing, paper, wood products
• Fuel
• Cleanse the air (CO2 to O2)
• Mitigates climate change
• Provides shelter and habitat for wildlife
• Increased biodiversity
• Maintain the watersheds that supply drinking
water
A
higher discount rate implies a shorter
harvest period.
 Increasing
the planting cost or harvest
cost will not affect the optimal harvest
age.
 Including
environmental values, and the
positive externalities of the forest,
changes the optimal harvest age.