Forest Production
Forest Production
1,HARVESTING COSTS IN THE
SOUTH
2,PRODUCTION THEORY
3,PRODUCTION AND COST OF
HARVESTING SOUTHERN
TIMBER
4,CONCLUSION
HARVESTING COSTS IN THE SOUTH
? Cubbage(1983) Harvesting System
Simulator (Stuart 1981)
? Wang et al.(1998) GIS modelling framework
? Kluender et al.(1998) removal intensity and
tree size on harvesting costs and
profitability
PRODUCTION THEORY
?Production Functions
?Cost Functions
?Revenue Functions
?Profit Functions
?Input-Input Relationships
?Product-Product Relationships
PRODUCTION THEORY
?Production Functions
?A production function is a basic input-
output relationship that describes a
biophysical relationship or production
process
)( xfy ?
PRODUCTION THEORY
Average Product
Marginal Product
Elasticity of Production
xi
yA P xi ?
xi
yM P xi
?
??
y
xi
xi
yi
?
???
PRODUCTION THEORY
?Cost Functions
?Cost functions represent the minimum
cost of producing a good or service at
given input prices.
wxywc m i n),( ?
PRODUCTION THEORY
Firm’s supply curve
PRODUCTION THEORY
?Revenue Functions
?Revenue functions represent the
maximum revenue that can be derived
from given output prices and a set of
inputs.
pyxpR m a x),( ?
PRODUCTION THEORY
y
TRAR ?
y
TRMR
?
??
pMRAR ??
PRODUCTION THEORY
?Profit Functions
? Economic theory postulates that the objective
of the firm is to maximize profits,which are
defined as the difference between the firm’s
revenue and costs.
?? wxxpfwp ??? )(m ax),(
? ?),(m ax ywcpy ??
PRODUCTION THEORY
pMPxi = wxi or MPxi = wxi/p
p-MC = 0 or p = MC
MC = MR
PRODUCTION THEORY
?Input-Input Relationships
? The relationship between two inputs
and one output is determined by the
productivities of the individual
inpputs and their interaction,
PRODUCTION THEORY
? e.g,The volume of timber that can be harvested
with varying combinations of labor and
machinery,Inputs are typically substitutes,and
thus in our example,a given volume of timber
can be produced with various combinations of
labor and machinery,A logger may decrease
machinery use by replacing it with more labor
and still be able to harvest the same amount of
timber,
PRODUCTION THEORY
?Product-Product Relationships
? The production possibilities frontier
represents the maximum amounts of two
outputs that can be produced from a given
amount of a single input.
PRODUCTION THEORY
Most forestry operations involve multiple
outputs and multiple inputs,In the case of two
inputs,the efficiency conditions are that the
MRTS must be equal across the two outputs,
These marginal conditions generalize to the N
output-N input case.
2
1
1
2
p
p
y
y ??
?
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CASE STUDY
Technology class 1979production 1987production
Cords
Per class
Cords
Per crew
Cost
($/cord)
Cords
Per class
Cords
Per crew
Cost
($/cord)
shortwood
Manual bobtail 20813 20.8 43.7 3233 26.9 43.5
Manual bigstick 124777 27.0 44.0 26365 26.8 51.4
Manual/skidder 35806 36.3 52.9 13655 38.8 60.5
Forwarder 27629 70.2 44.8 7858 86.1 48.6
Cable-skidder 36334 69.4 52.0 8494 59.8 54.9
Grapple-skidder 25763 189.3 32.2 16189 160.5 31.1
Total(shortwood) 270763 34.4 45.4 75794 41.7 48.9
longwood
Cable-skidder 145222 143.1 36.3 155290 127.8 30.0
Grapple-skidder 229958 254.9 32.3 556233 294.7 25.4
Total(longwood) 384180 190.7 34.0 711523 227.7 26.4
Total(all classes) 654943 66.1 38.7 787317 154.3 28.8
CONCLUSION
?The aggregate timber harvesting analysis
?The results suggest that there has not
been significant change for this
technology class,except for the increased
influence of the scale of operations on
total cost.