Transcript Lecture 2 - Illinois State University

 Homework
 Quiz
#9 Due Wednesday
#4 Wednesday
 Group
 Exam
Outline Due Wednesday
#4 – Nov. 28th
 Group
Presentations – Dec. 3 & 5
 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?
 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 Net Benefit = $10 million
• Sustainable Management = $500,000 per year
 Clear
cutting
• r=4%
• PVNB = $400,000/ 0.04 =$10mil.
• r=6%
• PVNB = $600,000/ 0.06 =$10mil.
 Sustainable
Management
• PVNB = $500,000/0.04=$12.5mil.
• PVNB = $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
13-8
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 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.
A
higher discount rate implies a shorter
harvest period.
 Increasing
the planting cost or harvest
cost will not affect the optimal harvest
age.
 With
a high discount rate, replanting
may not be efficient.

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