Figure 2.3 Non-linearities and discontinuities in dose-response relationships
Magnitude of response to a
variable of interest
Sustainability: Figures etc.
Lectures in resource economics
Spring 2004, additional material 1
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G.B. Asheim, na re ad 1, updated 01.04.2004
(a)
The analogy of a sailing ship
Dose applied
per period
e
e = αy
T. Page, Conservation and Economic Efficiency, 1977, p. 14
Sustainability—being concerned with intergenerational distribution—
corresponds to the course of the ship.
If markets function in a perfectly competitive manner, then
development is efficient, implying that no generation can be made better
off without some other generation being made worse off.
In the analogy, a perfectly competitive equilibrium corresponds to the
sails being set in a balanced way given the chosen course.
If the course must be changed, say to benefit future generations, then
the position of the sails needs to be changed as well.
We still want the sails to be set in a balanced way, meaning that the
assumption of a perfectly competitive equilibrium can be maintained.
e
e = β0y - β1y2
y
Figure 2.8 Environmental impact and income
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Environmental
impact per
income unit
y
(b)
Figure 2.11 Two possible shapes of the
environmental Kuznets curve in the very longrun
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Case (a): Impact/Y → 0 as t → ∞
Environmental
Impact
Time, t
Environmental
Impact
Case (b): Impact/Y → k as t → ∞
b
k
a
0
Y*
Y1
G.B. Asheim, na re ad 1, updated 01.04.2004
Y2
Time, t
Income
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Figure 2.12 Two scenarios for the time profile of environmental impacts
G.B. Asheim, na re ad 1, updated 01.04.2004
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1
Figure 3.1 An indifference curve from a linear form of
social welfare function.
Figure 3.4 Rawlsian social welfare function indifference curve.
UB
UB
e•
W
Slope = -1
•
•
c
d
•
b
W = min{U A , U B }
W = UA + UB
45°
UA
0
UA
0
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Figure 4.2 Production functions with capital and natural resource inputs.
Kt
Kt
Q1 Q
2
Q3
Q3
Q2
Q1
(a)
Q3
Q2
Q1
0
Q1
Q2
Q3
Rt
0
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Rt
EDITOR: A copy of Figure 4.2 (Part (b)), in which the three curves have been drawn precisely.
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C
Figure 4.2 (Part (c))
Kt
Q1
Q2
Q3
Model (a):
One sector model
t
Q3
C
Q2
Model (b):
D-H-S model
Q1
t
0
Rt
R1
G.B. Asheim, na re ad 1, updated 01.04.2004
Figure 3.6 Optimal consumption growth paths
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Equity (Weak Anonymity)
Efficiency (Strong Pareto)
Utility
Utility
Time
Time
Utility
Utility
Time
Time
The two distributions are equally good.
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Dynamic consistency
Utility
The lower distribution is better.
Consider two distributions
with the same utility in the
first period.
Dynamic consistency (cont)
Utility
Time
Time
Utility
Utility
Time
Time
If the top is as good as the bottom, …
…, then the top is still as good after the first period.
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Unit comparability
Utility
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Consider two distributions with
the constant utility from the
second period.
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Unit comparability (cont)
Utility
Time
Time
Utility
Utility
Time
Time
…, then the top is still as good if the same constants
are added to (or subtracted from) both paths.
If the top is as good as the bottom, …
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Productivity
Utility
Productivity (cont) Consider a distribution
Consider a distribution
that is not non-decreasing.
Utility
that is not non-decreasing.
Time
Time
Utility
Utility
Time
Time
Then this distribution is feasible and inefficient.
Then this distribution is feasible and inefficient.
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Figure 4.1 Consumption paths over time.
Productivity (cont)
Ct
Utility
C(4)
C(3)
C(2)
Time
C(1)
Utility
C(5)
CMIN
C(6)
Time
CSURV
Hence, even this distribution is feasible.
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