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2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
Two questions on sustainability 
Geir B. Asheim 
Department of Economics, University of Oslo 
Joint IEA/ISI Strategic Forum 2014 and 
Workshop of the High-Level Expert Group 
on the Measurement of Economic Performance and Social Progress 
on Intra-generational and Inter-generational Sustainability 
Roma, 22-23 September 2014
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
The questions
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
The questions 
Q1 What is sustainability?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
The questions 
Q1 What is sustainability? 
Q2 Is sustainability good?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
Location in time and space
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
Location in time and space 
space 
(intragen. 
distr.) 
time 
(intergen. 
distr.)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
Location in time and space 
space 
(intragen. 
distr.) 
location 
time 
(intergen. 
distr.)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
Location in time and space 
Assume that each location is inhabited by a dierent individual 
space 
(intragen. 
distr.) 
location 
time 
(intergen. 
distr.)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
Location in time and space 
Assume that each location is inhabited by a dierent individual 
! Intergenerational perspective (time period: a generation) 
space 
(intragen. 
distr.) 
location 
time 
(intergen. 
distr.)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
Uncertain states
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
Uncertain states 
states 
location
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
Uncertain states 
Assume that each pair of location and resolved subset of 
uncertain states is inhabited by a dierent individual 
states 
location
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
Uncertain states 
Assume that each pair of location and resolved subset of 
uncertain states is inhabited by a dierent individual 
! No individual is subjected to risk/uncertainty 
states 
location
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
The questions 
Q1 What is sustainability? 
Q2 Is sustainability good?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
The questions 
Q1 What is sustainability? 
 Inequality along time only (intergenerational equity) 
Q2 Is sustainability good?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
The questions 
Q1 What is sustainability? 
 Inequality along time only (intergenerational equity) 
 Inequality along time and across space only 
(inter- and intragenerational equity / no uncertainty) 
Q2 Is sustainability good?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
The questions 
Q1 What is sustainability? 
 Inequality along time only (intergenerational equity) 
 Inequality along time and across space only 
(inter- and intragenerational equity / no uncertainty) 
 Inequality along time, across space and over states 
(inter- and intragenerational equity + uncertainty) 
Q2 Is sustainability good?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
The questions 
Q1 What is sustainability? 
 Inequality along time only (intergenerational equity) 
 Inequality along time and across space only 
(inter- and intragenerational equity / no uncertainty) 
 Inequality along time, across space and over states 
(inter- and intragenerational equity + uncertainty) 
 Inequality along time, across space and over states 
but not all location-state pairs are inhabited 
(endogenous population + positive prob. of extinction) 
Q2 Is sustainability good?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Conclusion 
References 
The questions 
Q1 What is sustainability? 
 Inequality along time only (intergenerational equity) 
 Inequality along time and across space only 
(inter- and intragenerational equity / no uncertainty) 
 Inequality along time, across space and over states 
(inter- and intragenerational equity + uncertainty) 
 Inequality along time, across space and over states 
but not all location-state pairs are inhabited 
(endogenous population + positive prob. of extinction) 
Q2 Is sustainability good? 
 Better to base goodness on social choice theory 
than attempt to extend sustainability as a primitive notion
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Question 1: What is sustainability?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Intergenerational equity
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Intergenerational equity 
De
nitions of sustainability
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Intergenerational equity 
De
nitions of sustainability 
A The present generation behaves in a sustainable manner if 
its wellbeing level can be the
rst element of a non-decrea- 
sing stream that satis
es techn.  institut. constraints.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Intergenerational equity 
De
nitions of sustainability 
A The present generation behaves in a sustainable manner if 
its wellbeing level can be the
rst element of a non-decrea- 
sing stream that satis
es techn.  institut. constraints. 
A1 The present generation behaves in a sustainable manner if 
the next generation can attain at least the same wellbeing 
level even if it behaves in a sustainable manner.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Intergenerational equity 
De
nitions of sustainability 
A The present generation behaves in a sustainable manner if 
its wellbeing level can be the
rst element of a non-decrea- 
sing stream that satis
es techn.  institut. constraints. 
A1 The present generation behaves in a sustainable manner if 
the next generation can attain at least the same wellbeing 
level even if it behaves in a sustainable manner. 
The stream is sustainable if all generations behave in a 
sustainable manner.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Intergenerational equity 
De
nitions of sustainability 
A The present generation behaves in a sustainable manner if 
its wellbeing level can be the
rst element of a non-decrea- 
sing stream that satis
es techn.  institut. constraints. 
A1 The present generation behaves in a sustainable manner if 
the next generation can attain at least the same wellbeing 
level even if it behaves in a sustainable manner. 
The stream is sustainable if all generations behave in a 
sustainable manner. 
B The stream is sustainable if the maximin value is 
non-decreasing, where the maximin value is sup, taken over 
the set of streams satisfying technical and institutional 
constraints, of inf of wellbeing along the stream.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Intergenerational equity 
De
nitions of sustainability 
A The present generation behaves in a sustainable manner if 
its wellbeing level can be the
rst element of a non-decrea- 
sing stream that satis
es techn.  institut. constraints. 
A1 The present generation behaves in a sustainable manner if 
the next generation can attain at least the same wellbeing 
level even if it behaves in a sustainable manner. 
The stream is sustainable if all generations behave in a 
sustainable manner. 
B The stream is sustainable if the maximin value is 
non-decreasing, where the maximin value is sup, taken over 
the set of streams satisfying technical and institutional 
constraints, of inf of wellbeing along the stream. 
C The present generation behaves in a sustainable manner if 
the genuine savings indicator, valued in terms an objective 
function along a stream implemented by a resource 
allocation mechanism, is non-negative.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Intergenerational equity 
De
nitions of sustainability 
A The present generation behaves in a sustainable manner if 
its wellbeing level can be the
rst element of a non-decrea- 
sing stream that satis
es techn.  institut. constraints. 
A1 The present generation behaves in a sustainable manner if 
the next generation can attain at least the same wellbeing 
level even if it behaves in a sustainable manner. 
The stream is sustainable if all generations behave in a 
sustainable manner. 
B The stream is sustainable if the maximin value is 
non-decreasing, where the maximin value is sup, taken over 
the set of streams satisfying technical and institutional 
constraints, of inf of wellbeing along the stream. 
C The present generation behaves in a sustainable manner if 
the genuine savings indicator, valued in terms an objective 
function along a stream implemented by a resource 
allocation mechanism, is non-negative.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Inter- and intragenerational equity
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Inter- and intragenerational equity 
How to determine generational wellbeing 
when there is intragenerational inequality?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Inter- and intragenerational equity 
How to determine generational wellbeing 
when there is intragenerational inequality? 
Sustainable development is a development that meets the 
needs of the present without compromising the ability of 
future generations to meet their own needs
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Inter- and intragenerational equity  uncertainty
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Inter- and intragenerational equity  uncertainty 
How to determine generational wellbeing 
when there is intragenerational inequality and uncertainty?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Endogenous population 
+ positive prob. of extinction
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Inequality 
along time 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Q2 Is sust. 
good? 
Conclusion 
References 
Endogenous population 
+ positive prob. of extinction 
How to compare generational wellbeing 
when there is a positive probability 
that future generations might not exist?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Question 2: Is sustainability good?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Intergenerational equity 
space 
(intragen. 
distr.) 
location 
time 
(intergen. 
distr.)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Intergenerational equity 
How to impose impartiality? 
space 
(intragen. 
distr.) 
location 
time 
(intergen. 
distr.)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Intergenerational equity 
How to impose impartiality? 
Axiom of equal treatment: 
space 
(intragen. 
distr.) 
location 
time 
(intergen. 
distr.)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Intergenerational equity 
How to impose impartiality? 
Axiom of equal treatment: Strong/Finite Anonymity 
space 
(intragen. 
distr.) 
location 
time 
(intergen. 
distr.)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Intergenerational equity 
How to impose impartiality? 
Axiom of equal treatment: Strong/Finite Anonymity 
space 
(intragen. 
distr.) 
location 
time 
(intergen. 
distr.)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Intergenerational equity 
How to impose impartiality? 
Axiom of equal treatment: Strong/Finite Anonymity 
space 
(intragen. 
distr.) 
location 
time 
(intergen. 
distr.)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Buchholz: Impartiality + sensitivity leads to 
non-decreasing streams in productive economies
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Buchholz: Impartiality + sensitivity leads to 
non-decreasing streams in productive economies 
space 
(intragen. 
distr.) 
location 
time 
(intergen. 
distr.)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Buchholz: Impartiality + sensitivity leads to 
non-decreasing streams in productive economies 
space 
(intragen. 
distr.) 
location 
time 
(intergen. 
distr.)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Buchholz: Impartiality + sensitivity leads to 
non-decreasing streams in productive economies 
Justifying sustainability 
(Asheim, Buchholz  Tungodden, JEEM, 2001) 
space 
(intragen. 
distr.) 
location 
time 
(intergen. 
distr.)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Priority for the worse o
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Priority for the worse o 
Equal treatment of generations is compatible with 
with letting the welfare weights assigned to 
dierent generations' marginal well-being depend on
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Priority for the worse o 
Equal treatment of generations is compatible with 
with letting the welfare weights assigned to 
dierent generations' marginal well-being depend on 
their absolute level of well-being
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Priority for the worse o 
Equal treatment of generations is compatible with 
with letting the welfare weights assigned to 
dierent generations' marginal well-being depend on 
their absolute level of well-being 
their relative rank in well-being.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism 
xt A comprehensive measure of consumption indicating the 
well-being of generation t.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism 
xt A comprehensive measure of consumption indicating the 
well-being of generation t. Assume that unequal distribution 
of consumption is deemed undesirable in social evaluation.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism 
xt A comprehensive measure of consumption indicating the 
well-being of generation t. Assume that unequal distribution 
of consumption is deemed undesirable in social evaluation. 
u(xt ) Utility derived from xt , 
where u is an increasing and strictly concave function.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism 
xt A comprehensive measure of consumption indicating the 
well-being of generation t. Assume that unequal distribution 
of consumption is deemed undesirable in social evaluation. 
u(xt ) Utility derived from xt , 
where u is an increasing and strictly concave function. 
Under undiscounted utilitarianism, the weight on 
generation t's well-being is proportional to u0(xt ).
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism 
xt A comprehensive measure of consumption indicating the 
well-being of generation t. Assume that unequal distribution 
of consumption is deemed undesirable in social evaluation. 
u(xt ) Utility derived from xt , 
where u is an increasing and strictly concave function. 
Under undiscounted utilitarianism, the weight on 
generation t's well-being is proportional to u0(xt ). 
Since u is strictly concave, the weight on a worse o generation 
is higher than the weight on a better o generation.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism 
xt A comprehensive measure of consumption indicating the 
well-being of generation t. Assume that unequal distribution 
of consumption is deemed undesirable in social evaluation. 
u(xt ) Utility derived from xt , 
where u is an increasing and strictly concave function. 
Under undiscounted utilitarianism, the weight on 
generation t's well-being is proportional to u0(xt ). 
Since u is strictly concave, the weight on a worse o generation 
is higher than the weight on a better o generation. 
With n generations, the weight is 1n 
u0(xt )
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism 
xt A comprehensive measure of consumption indicating the 
well-being of generation t. Assume that unequal distribution 
of consumption is deemed undesirable in social evaluation. 
u(xt ) Utility derived from xt , 
where u is an increasing and strictly concave function. 
Under undiscounted utilitarianism, the weight on 
generation t's well-being is proportional to u0(xt ). 
Since u is strictly concave, the weight on a worse o generation 
is higher than the weight on a better o generation. 
With n generations, the weight is 1n 
u0(xt ) 
But what with 1 generations?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism 
Resolving a con
ict between the present and the future 
Well -being 
Time
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism 
Resolving a con
ict between the present and the future 
Well -being 
Time
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism 
Resolving a con
ict between the present and the future 
Well -being 
The blue stream is always preferred 
Time
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism 
Mirrlees (1967) computed optimal well-being streams in 
economic models under undiscounted utilitarianism and 
observed that present generations should save up to 50 % 
of their net income for the sake of future generations.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism 
Mirrlees (1967) computed optimal well-being streams in 
economic models under undiscounted utilitarianism and 
observed that present generations should save up to 50 % 
of their net income for the sake of future generations. 
Rawls (1971, p. 287) reluctantly pointed out that 
[t]his consequence can be to some degree corrected by 
discounting the welfare of those living in the future
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Weights depending on levels of well-being only: 
Undiscounted utilitarianism 
Mirrlees (1967) computed optimal well-being streams in 
economic models under undiscounted utilitarianism and 
observed that present generations should save up to 50 % 
of their net income for the sake of future generations. 
Rawls (1971, p. 287) reluctantly pointed out that 
[t]his consequence can be to some degree corrected by 
discounting the welfare of those living in the future 
Arrow (1999, p. 16) concluded that the strong ethical 
requirement that all generations be treated alike, itself 
reasonable, contradicts a very strong intuition that it is not 
morally acceptable to demand excessively high savings rates 
of any one generation, or even of every generation.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Welfare weights depending on rank only: 
Lexicographic maximin
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Welfare weights depending on rank only: 
Lexicographic maximin 
Maximize the well-being of the worst-o generation
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Welfare weights depending on rank only: 
Lexicographic maximin 
Maximize the well-being of the worst-o generation 
To break ties 
(if the worst-o generation has the same well-being) 
maximize the well-being of the second worst-o generation
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Welfare weights depending on rank only: 
Lexicographic maximin 
Maximize the well-being of the worst-o generation 
To break ties 
(if the worst-o generation has the same well-being) 
maximize the well-being of the second worst-o generation 
Etc.
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Welfare weights depending on rank only: 
Lexicographic maximin
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Welfare weights depending on rank only: 
Lexicographic maximin 
Resolving a con
ict between the present and the future 
Well -being 
Time
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Welfare weights depending on rank only: 
Lexicographic maximin 
Resolving a con
ict between the present and the future 
Well -being 
Time
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Welfare weights depending on rank only: 
Lexicographic maximin 
Resolving a con
ict between the present and the future 
Well -being 
The blue stream is never preferred 
Time
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
With absolute priority only, 
no weight on any
nite subset of generations
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
With absolute priority only, 
no weight on any
nite subset of generations 
With relative priority only, 
no weight on any generation but the worst o
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
With absolute priority only, 
no weight on any
nite subset of generations 
With relative priority only, 
no weight on any generation but the worst o 
How to avoid these extreme conclusions 
while treating generations equally?
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Combining absolute and relative priority 
With absolute priority only, 
no weight on any
nite subset of generations 
With relative priority only, 
no weight on any generation but the worst o 
How to avoid these extreme conclusions 
while treating generations equally? 
Combine absolute and relative priority!
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Time-discounted utilitarianism: (1
) 
P1 
t=1
t1u(xt ) 
where t is time and
2 (0; 1) is a time utility disc. factor
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Time-discounted utilitarianism: (1
) 
P1 
t=1
t1u(xt ) 
where t is time and
2 (0; 1) is a time utility disc. factor 
(1
) 
P1 
r=1
r1u(x[r ]) 
where (x[1]; x[2]; : : : ; x[r ]; : : : ) is a reordering of 
(x1; x2; : : : ; xt ; : : : ) such that x[1]  x[2]      x[r ]
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Time-discounted utilitarianism: (1
) 
P1 
t=1
t1u(xt ) 
where t is time and
2 (0; 1) is a time utility disc. factor 
(1
) 
P1 
r=1
r1u(x[r ]) 
where (x[1]; x[2]; : : : ; x[r ]; : : : ) is a reordering of 
(x1; x2; : : : ; xt ; : : : ) such that x[1]  x[2]      x[r ]     
Hence, r is rank and
2 (0; 1) is a rank utility disc. factor
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Zuber: Rank-discounted utilitarianism (RDU) 
Time-discounted utilitarianism: (1
) 
P1 
t=1
t1u(xt ) 
where t is time and
2 (0; 1) is a time utility disc. factor 
Rank-discounted utilitarianism: (1
) 
P1 
r=1
r1u(x[r ]) 
where (x[1]; x[2]; : : : ; x[r ]; : : : ) is a reordering of 
(x1; x2; : : : ; xt ; : : : ) such that x[1]  x[2]      x[r ]     
Hence, r is rank and
2 (0; 1) is a rank utility disc. factor 
Proposed by Stephane Zuber and analyzed in 
Justifying social discounting: The RDU approach 
(Zuber and Asheim, JET 2012)
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Zuber: Rank-discounted utilitarianism (RDU) 
Time-discounted utilitarianism: (1
) 
P1 
t=1
t1u(xt ) 
where t is time and
2 (0; 1) is a time utility disc. factor 
Rank-discounted utilitarianism: (1
) 
P1 
r=1
r1u(x[r ]) 
where (x[1]; x[2]; : : : ; x[r ]; : : : ) is a reordering of 
(x1; x2; : : : ; xt ; : : : ) such that x[1]  x[2]      x[r ]     
Hence, r is rank and
2 (0; 1) is a rank utility disc. factor 
Proposed by Stephane Zuber and analyzed in 
Justifying social discounting: The RDU approach 
(Zuber and Asheim, JET 2012) 
Utility discounting becomes a mere expression of 
intergenerational inequality aversion
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Consequence of RDU in present-future con
icts
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Consequence of RDU in present-future con
icts 
Resolving the con
ict between the present and the future 
Well -being 
Time
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Consequence of RDU in present-future con
icts 
Resolving the con
ict between the present and the future 
Well -being 
Time
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Consequence of RDU in present-future con
icts 
Resolving the con
ict between the present and the future 
Well -being 
The black stream is never preferred 
Time
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Consequence of RDU in present-future con
icts 
Resolving the con
ict between the present and the future 
Well -being 
Time
2 questions 
on sustain- 
ability 
G.B. Asheim 
Outline 
Q1 What is 
sust.? 
Q2 Is sust. 
good? 
Inequality 
along time 
Buchholz 
Zuber 
acr. location 
acr. location 
and states 
w/uninhab. 
locations 
Conclusion 
References 
Consequence of RDU in present-future con
icts 
Resolving the con
ict between the present and the future 
Well -being 
Time

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HLEG thematic workshop on "Intra-generational and Inter-generational Sustainability", Geir Asheim

  • 1. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Two questions on sustainability Geir B. Asheim Department of Economics, University of Oslo Joint IEA/ISI Strategic Forum 2014 and Workshop of the High-Level Expert Group on the Measurement of Economic Performance and Social Progress on Intra-generational and Inter-generational Sustainability Roma, 22-23 September 2014
  • 2. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References The questions
  • 3. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References The questions Q1 What is sustainability?
  • 4. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References The questions Q1 What is sustainability? Q2 Is sustainability good?
  • 5. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Location in time and space
  • 6. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Location in time and space space (intragen. distr.) time (intergen. distr.)
  • 7. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Location in time and space space (intragen. distr.) location time (intergen. distr.)
  • 8. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Location in time and space Assume that each location is inhabited by a dierent individual space (intragen. distr.) location time (intergen. distr.)
  • 9. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Location in time and space Assume that each location is inhabited by a dierent individual ! Intergenerational perspective (time period: a generation) space (intragen. distr.) location time (intergen. distr.)
  • 10. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Uncertain states
  • 11. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Uncertain states states location
  • 12. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Uncertain states Assume that each pair of location and resolved subset of uncertain states is inhabited by a dierent individual states location
  • 13. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Uncertain states Assume that each pair of location and resolved subset of uncertain states is inhabited by a dierent individual ! No individual is subjected to risk/uncertainty states location
  • 14. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References The questions Q1 What is sustainability? Q2 Is sustainability good?
  • 15. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References The questions Q1 What is sustainability? Inequality along time only (intergenerational equity) Q2 Is sustainability good?
  • 16. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References The questions Q1 What is sustainability? Inequality along time only (intergenerational equity) Inequality along time and across space only (inter- and intragenerational equity / no uncertainty) Q2 Is sustainability good?
  • 17. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References The questions Q1 What is sustainability? Inequality along time only (intergenerational equity) Inequality along time and across space only (inter- and intragenerational equity / no uncertainty) Inequality along time, across space and over states (inter- and intragenerational equity + uncertainty) Q2 Is sustainability good?
  • 18. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References The questions Q1 What is sustainability? Inequality along time only (intergenerational equity) Inequality along time and across space only (inter- and intragenerational equity / no uncertainty) Inequality along time, across space and over states (inter- and intragenerational equity + uncertainty) Inequality along time, across space and over states but not all location-state pairs are inhabited (endogenous population + positive prob. of extinction) Q2 Is sustainability good?
  • 19. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References The questions Q1 What is sustainability? Inequality along time only (intergenerational equity) Inequality along time and across space only (inter- and intragenerational equity / no uncertainty) Inequality along time, across space and over states (inter- and intragenerational equity + uncertainty) Inequality along time, across space and over states but not all location-state pairs are inhabited (endogenous population + positive prob. of extinction) Q2 Is sustainability good? Better to base goodness on social choice theory than attempt to extend sustainability as a primitive notion
  • 20. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Question 1: What is sustainability?
  • 21. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Intergenerational equity
  • 22. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Intergenerational equity De
  • 24. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Intergenerational equity De
  • 25. nitions of sustainability A The present generation behaves in a sustainable manner if its wellbeing level can be the
  • 26. rst element of a non-decrea- sing stream that satis
  • 27. es techn. institut. constraints.
  • 28. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Intergenerational equity De
  • 29. nitions of sustainability A The present generation behaves in a sustainable manner if its wellbeing level can be the
  • 30. rst element of a non-decrea- sing stream that satis
  • 31. es techn. institut. constraints. A1 The present generation behaves in a sustainable manner if the next generation can attain at least the same wellbeing level even if it behaves in a sustainable manner.
  • 32. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Intergenerational equity De
  • 33. nitions of sustainability A The present generation behaves in a sustainable manner if its wellbeing level can be the
  • 34. rst element of a non-decrea- sing stream that satis
  • 35. es techn. institut. constraints. A1 The present generation behaves in a sustainable manner if the next generation can attain at least the same wellbeing level even if it behaves in a sustainable manner. The stream is sustainable if all generations behave in a sustainable manner.
  • 36. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Intergenerational equity De
  • 37. nitions of sustainability A The present generation behaves in a sustainable manner if its wellbeing level can be the
  • 38. rst element of a non-decrea- sing stream that satis
  • 39. es techn. institut. constraints. A1 The present generation behaves in a sustainable manner if the next generation can attain at least the same wellbeing level even if it behaves in a sustainable manner. The stream is sustainable if all generations behave in a sustainable manner. B The stream is sustainable if the maximin value is non-decreasing, where the maximin value is sup, taken over the set of streams satisfying technical and institutional constraints, of inf of wellbeing along the stream.
  • 40. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Intergenerational equity De
  • 41. nitions of sustainability A The present generation behaves in a sustainable manner if its wellbeing level can be the
  • 42. rst element of a non-decrea- sing stream that satis
  • 43. es techn. institut. constraints. A1 The present generation behaves in a sustainable manner if the next generation can attain at least the same wellbeing level even if it behaves in a sustainable manner. The stream is sustainable if all generations behave in a sustainable manner. B The stream is sustainable if the maximin value is non-decreasing, where the maximin value is sup, taken over the set of streams satisfying technical and institutional constraints, of inf of wellbeing along the stream. C The present generation behaves in a sustainable manner if the genuine savings indicator, valued in terms an objective function along a stream implemented by a resource allocation mechanism, is non-negative.
  • 44. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Intergenerational equity De
  • 45. nitions of sustainability A The present generation behaves in a sustainable manner if its wellbeing level can be the
  • 46. rst element of a non-decrea- sing stream that satis
  • 47. es techn. institut. constraints. A1 The present generation behaves in a sustainable manner if the next generation can attain at least the same wellbeing level even if it behaves in a sustainable manner. The stream is sustainable if all generations behave in a sustainable manner. B The stream is sustainable if the maximin value is non-decreasing, where the maximin value is sup, taken over the set of streams satisfying technical and institutional constraints, of inf of wellbeing along the stream. C The present generation behaves in a sustainable manner if the genuine savings indicator, valued in terms an objective function along a stream implemented by a resource allocation mechanism, is non-negative.
  • 48. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Inter- and intragenerational equity
  • 49. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Inter- and intragenerational equity How to determine generational wellbeing when there is intragenerational inequality?
  • 50. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Inter- and intragenerational equity How to determine generational wellbeing when there is intragenerational inequality? Sustainable development is a development that meets the needs of the present without compromising the ability of future generations to meet their own needs
  • 51. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Inter- and intragenerational equity uncertainty
  • 52. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Inter- and intragenerational equity uncertainty How to determine generational wellbeing when there is intragenerational inequality and uncertainty?
  • 53. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Endogenous population + positive prob. of extinction
  • 54. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Inequality along time acr. location acr. location and states w/uninhab. locations Q2 Is sust. good? Conclusion References Endogenous population + positive prob. of extinction How to compare generational wellbeing when there is a positive probability that future generations might not exist?
  • 55. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Question 2: Is sustainability good?
  • 56. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Intergenerational equity space (intragen. distr.) location time (intergen. distr.)
  • 57. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Intergenerational equity How to impose impartiality? space (intragen. distr.) location time (intergen. distr.)
  • 58. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Intergenerational equity How to impose impartiality? Axiom of equal treatment: space (intragen. distr.) location time (intergen. distr.)
  • 59. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Intergenerational equity How to impose impartiality? Axiom of equal treatment: Strong/Finite Anonymity space (intragen. distr.) location time (intergen. distr.)
  • 60. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Intergenerational equity How to impose impartiality? Axiom of equal treatment: Strong/Finite Anonymity space (intragen. distr.) location time (intergen. distr.)
  • 61. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Intergenerational equity How to impose impartiality? Axiom of equal treatment: Strong/Finite Anonymity space (intragen. distr.) location time (intergen. distr.)
  • 62. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Buchholz: Impartiality + sensitivity leads to non-decreasing streams in productive economies
  • 63. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Buchholz: Impartiality + sensitivity leads to non-decreasing streams in productive economies space (intragen. distr.) location time (intergen. distr.)
  • 64. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Buchholz: Impartiality + sensitivity leads to non-decreasing streams in productive economies space (intragen. distr.) location time (intergen. distr.)
  • 65. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Buchholz: Impartiality + sensitivity leads to non-decreasing streams in productive economies Justifying sustainability (Asheim, Buchholz Tungodden, JEEM, 2001) space (intragen. distr.) location time (intergen. distr.)
  • 66. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Priority for the worse o
  • 67. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Priority for the worse o Equal treatment of generations is compatible with with letting the welfare weights assigned to dierent generations' marginal well-being depend on
  • 68. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Priority for the worse o Equal treatment of generations is compatible with with letting the welfare weights assigned to dierent generations' marginal well-being depend on their absolute level of well-being
  • 69. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Priority for the worse o Equal treatment of generations is compatible with with letting the welfare weights assigned to dierent generations' marginal well-being depend on their absolute level of well-being their relative rank in well-being.
  • 70. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References
  • 71. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism
  • 72. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism xt A comprehensive measure of consumption indicating the well-being of generation t.
  • 73. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism xt A comprehensive measure of consumption indicating the well-being of generation t. Assume that unequal distribution of consumption is deemed undesirable in social evaluation.
  • 74. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism xt A comprehensive measure of consumption indicating the well-being of generation t. Assume that unequal distribution of consumption is deemed undesirable in social evaluation. u(xt ) Utility derived from xt , where u is an increasing and strictly concave function.
  • 75. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism xt A comprehensive measure of consumption indicating the well-being of generation t. Assume that unequal distribution of consumption is deemed undesirable in social evaluation. u(xt ) Utility derived from xt , where u is an increasing and strictly concave function. Under undiscounted utilitarianism, the weight on generation t's well-being is proportional to u0(xt ).
  • 76. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism xt A comprehensive measure of consumption indicating the well-being of generation t. Assume that unequal distribution of consumption is deemed undesirable in social evaluation. u(xt ) Utility derived from xt , where u is an increasing and strictly concave function. Under undiscounted utilitarianism, the weight on generation t's well-being is proportional to u0(xt ). Since u is strictly concave, the weight on a worse o generation is higher than the weight on a better o generation.
  • 77. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism xt A comprehensive measure of consumption indicating the well-being of generation t. Assume that unequal distribution of consumption is deemed undesirable in social evaluation. u(xt ) Utility derived from xt , where u is an increasing and strictly concave function. Under undiscounted utilitarianism, the weight on generation t's well-being is proportional to u0(xt ). Since u is strictly concave, the weight on a worse o generation is higher than the weight on a better o generation. With n generations, the weight is 1n u0(xt )
  • 78. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism xt A comprehensive measure of consumption indicating the well-being of generation t. Assume that unequal distribution of consumption is deemed undesirable in social evaluation. u(xt ) Utility derived from xt , where u is an increasing and strictly concave function. Under undiscounted utilitarianism, the weight on generation t's well-being is proportional to u0(xt ). Since u is strictly concave, the weight on a worse o generation is higher than the weight on a better o generation. With n generations, the weight is 1n u0(xt ) But what with 1 generations?
  • 79. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism
  • 80. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism Resolving a con ict between the present and the future Well -being Time
  • 81. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism Resolving a con ict between the present and the future Well -being Time
  • 82. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism Resolving a con ict between the present and the future Well -being The blue stream is always preferred Time
  • 83. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism
  • 84. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism Mirrlees (1967) computed optimal well-being streams in economic models under undiscounted utilitarianism and observed that present generations should save up to 50 % of their net income for the sake of future generations.
  • 85. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism Mirrlees (1967) computed optimal well-being streams in economic models under undiscounted utilitarianism and observed that present generations should save up to 50 % of their net income for the sake of future generations. Rawls (1971, p. 287) reluctantly pointed out that [t]his consequence can be to some degree corrected by discounting the welfare of those living in the future
  • 86. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Weights depending on levels of well-being only: Undiscounted utilitarianism Mirrlees (1967) computed optimal well-being streams in economic models under undiscounted utilitarianism and observed that present generations should save up to 50 % of their net income for the sake of future generations. Rawls (1971, p. 287) reluctantly pointed out that [t]his consequence can be to some degree corrected by discounting the welfare of those living in the future Arrow (1999, p. 16) concluded that the strong ethical requirement that all generations be treated alike, itself reasonable, contradicts a very strong intuition that it is not morally acceptable to demand excessively high savings rates of any one generation, or even of every generation.
  • 87. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References
  • 88. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Welfare weights depending on rank only: Lexicographic maximin
  • 89. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Welfare weights depending on rank only: Lexicographic maximin Maximize the well-being of the worst-o generation
  • 90. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Welfare weights depending on rank only: Lexicographic maximin Maximize the well-being of the worst-o generation To break ties (if the worst-o generation has the same well-being) maximize the well-being of the second worst-o generation
  • 91. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Welfare weights depending on rank only: Lexicographic maximin Maximize the well-being of the worst-o generation To break ties (if the worst-o generation has the same well-being) maximize the well-being of the second worst-o generation Etc.
  • 92. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Welfare weights depending on rank only: Lexicographic maximin
  • 93. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Welfare weights depending on rank only: Lexicographic maximin Resolving a con ict between the present and the future Well -being Time
  • 94. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Welfare weights depending on rank only: Lexicographic maximin Resolving a con ict between the present and the future Well -being Time
  • 95. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Welfare weights depending on rank only: Lexicographic maximin Resolving a con ict between the present and the future Well -being The blue stream is never preferred Time
  • 96. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References
  • 97. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References With absolute priority only, no weight on any
  • 98. nite subset of generations
  • 99. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References With absolute priority only, no weight on any
  • 100. nite subset of generations With relative priority only, no weight on any generation but the worst o
  • 101. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References With absolute priority only, no weight on any
  • 102. nite subset of generations With relative priority only, no weight on any generation but the worst o How to avoid these extreme conclusions while treating generations equally?
  • 103. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Combining absolute and relative priority With absolute priority only, no weight on any
  • 104. nite subset of generations With relative priority only, no weight on any generation but the worst o How to avoid these extreme conclusions while treating generations equally? Combine absolute and relative priority!
  • 105. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References
  • 106. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Time-discounted utilitarianism: (1
  • 108. t1u(xt ) where t is time and
  • 109. 2 (0; 1) is a time utility disc. factor
  • 110. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Time-discounted utilitarianism: (1
  • 112. t1u(xt ) where t is time and
  • 113. 2 (0; 1) is a time utility disc. factor (1
  • 115. r1u(x[r ]) where (x[1]; x[2]; : : : ; x[r ]; : : : ) is a reordering of (x1; x2; : : : ; xt ; : : : ) such that x[1] x[2] x[r ]
  • 116. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Time-discounted utilitarianism: (1
  • 118. t1u(xt ) where t is time and
  • 119. 2 (0; 1) is a time utility disc. factor (1
  • 121. r1u(x[r ]) where (x[1]; x[2]; : : : ; x[r ]; : : : ) is a reordering of (x1; x2; : : : ; xt ; : : : ) such that x[1] x[2] x[r ] Hence, r is rank and
  • 122. 2 (0; 1) is a rank utility disc. factor
  • 123. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Zuber: Rank-discounted utilitarianism (RDU) Time-discounted utilitarianism: (1
  • 125. t1u(xt ) where t is time and
  • 126. 2 (0; 1) is a time utility disc. factor Rank-discounted utilitarianism: (1
  • 128. r1u(x[r ]) where (x[1]; x[2]; : : : ; x[r ]; : : : ) is a reordering of (x1; x2; : : : ; xt ; : : : ) such that x[1] x[2] x[r ] Hence, r is rank and
  • 129. 2 (0; 1) is a rank utility disc. factor Proposed by Stephane Zuber and analyzed in Justifying social discounting: The RDU approach (Zuber and Asheim, JET 2012)
  • 130. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Zuber: Rank-discounted utilitarianism (RDU) Time-discounted utilitarianism: (1
  • 132. t1u(xt ) where t is time and
  • 133. 2 (0; 1) is a time utility disc. factor Rank-discounted utilitarianism: (1
  • 135. r1u(x[r ]) where (x[1]; x[2]; : : : ; x[r ]; : : : ) is a reordering of (x1; x2; : : : ; xt ; : : : ) such that x[1] x[2] x[r ] Hence, r is rank and
  • 136. 2 (0; 1) is a rank utility disc. factor Proposed by Stephane Zuber and analyzed in Justifying social discounting: The RDU approach (Zuber and Asheim, JET 2012) Utility discounting becomes a mere expression of intergenerational inequality aversion
  • 137. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Consequence of RDU in present-future con icts
  • 138. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Consequence of RDU in present-future con icts Resolving the con ict between the present and the future Well -being Time
  • 139. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Consequence of RDU in present-future con icts Resolving the con ict between the present and the future Well -being Time
  • 140. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Consequence of RDU in present-future con icts Resolving the con ict between the present and the future Well -being The black stream is never preferred Time
  • 141. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Consequence of RDU in present-future con icts Resolving the con ict between the present and the future Well -being Time
  • 142. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Consequence of RDU in present-future con icts Resolving the con ict between the present and the future Well -being Time
  • 143. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Consequence of RDU in present-future con icts Resolving the con ict between the present and the future Well -being Time The blue stream is sometimes preferred
  • 144. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity space (intragen. distr.) location time (intergen. distr.)
  • 145. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity How to impose impartiality? space (intragen. distr.) location time (intergen. distr.)
  • 146. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity How to impose impartiality? Axiom of equal treatment: space (intragen. distr.) location time (intergen. distr.)
  • 147. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity How to impose impartiality? Axiom of equal treatment: Strong/Finite Anonymity space (intragen. distr.) location time (intergen. distr.)
  • 148. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity How to impose impartiality? Axiom of equal treatment: Strong/Finite Anonymity space (intragen. distr.) location time (intergen. distr.)
  • 149. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity How to impose impartiality? Axiom of equal treatment: Strong/Finite Anonymity space (intragen. distr.) location time (intergen. distr.)
  • 150. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Consequence of RDU in intragenerational con icts
  • 151. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Consequence of RDU in intragenerational con icts Well -being Time
  • 152. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Consequence of RDU in intragenerational con icts Well -being Rich countries Poor countries Time Ti
  • 153. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Consequence of RDU in intragenerational con icts The red stream is always preferred Well -being Rich countries Poor countries Time Ti
  • 154. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Consequence of RDU in intragenerational con icts The red stream is always preferred Well -being Time
  • 155. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity + uncertainty states location
  • 156. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity + uncertainty How to impose impartiality? states location
  • 157. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity + uncertainty How to impose impartiality? Consider equally likely states states location
  • 158. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity + uncertainty How to impose impartiality? Consider equally likely states states 2 equally likely states location
  • 159. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity + uncertainty How to impose impartiality? Consider equally likely states and impose equal treatment between locations in equally likely states states 2 equally likely states location
  • 160. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity + uncertainty How to impose impartiality? Consider equally likely states and impose equal treatment between locations in equally likely states states 2 equally likely states location
  • 161. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity + uncertainty How to impose impartiality? Consider equally likely states and impose equal treatment between locations in equally likely states states 2 equally likely states location
  • 162. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Inter- and intragenerational equity + uncertainty How to impose impartiality? Consider equally likely states and impose equal treatment between locations in equally likely states states 2 equally likely states location
  • 163. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction
  • 164. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation:
  • 165. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation: There is a positive probability of human extinction.
  • 166. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation: There is a positive probability of human extinction. Stern Review's justi
  • 167. cation for time utility discounting.
  • 168. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation: There is a positive probability of human extinction. Stern Review's justi
  • 169. cation for time utility discounting. Policy (e.g. concerning climate change) may lead to dierent people living in the future.
  • 170. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation: There is a positive probability of human extinction. Stern Review's justi
  • 171. cation for time utility discounting. Policy (e.g. concerning climate change) may lead to dierent people living in the future. So we need to be able to evaluate alternatives with dierent sets of potential people.
  • 172. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation: There is a positive probability of human extinction. Stern Review's justi
  • 173. cation for time utility discounting. Policy (e.g. concerning climate change) may lead to dierent people living in the future. So we need to be able to evaluate alternatives with dierent sets of potential people. Result:
  • 174. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation: There is a positive probability of human extinction. Stern Review's justi
  • 175. cation for time utility discounting. Policy (e.g. concerning climate change) may lead to dierent people living in the future. So we need to be able to evaluate alternatives with dierent sets of potential people. Result: The RDU approach generalized to
  • 176. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation: There is a positive probability of human extinction. Stern Review's justi
  • 177. cation for time utility discounting. Policy (e.g. concerning climate change) may lead to dierent people living in the future. So we need to be able to evaluate alternatives with dierent sets of potential people. Result: The RDU approach generalized to variable population (Asheim and Zuber, TE forth.)
  • 178. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation: There is a positive probability of human extinction. Stern Review's justi
  • 179. cation for time utility discounting. Policy (e.g. concerning climate change) may lead to dierent people living in the future. So we need to be able to evaluate alternatives with dierent sets of potential people. Result: The RDU approach generalized to variable population (Asheim and Zuber, TE forth.) avoids the repugnant conclusion
  • 180. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References The Repugnant Conclusion (Par
  • 182. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References The Repugnant Conclusion (Par
  • 183. t, 1984) For any egalitarian allocation with very high positive wellbeing, wellbeing population size
  • 184. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References The Repugnant Conclusion (Par
  • 185. t, 1984) For any egalitarian allocation with very high positive wellbeing, there is an allocation with very low positive wellbeing which is better. wellbeing population size
  • 186. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation: There is a positive probability of human extinction. Stern Review's justi
  • 187. cation for time utility discounting. Policy (e.g. concerning climate change) may lead to dierent people living in the future. So we need to be able to evaluate alternatives with dierent sets of potential people. Result: The RDU approach generalized to variable population (Asheim and Zuber, TE forth.) avoids the repugnant conclusion
  • 188. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation: There is a positive probability of human extinction. Stern Review's justi
  • 189. cation for time utility discounting. Policy (e.g. concerning climate change) may lead to dierent people living in the future. So we need to be able to evaluate alternatives with dierent sets of potential people. Result: The RDU approach generalized to variable population (Asheim and Zuber, TE forth.) avoids the repugnant conclusion and the very sadistic conclusion
  • 190. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References The Very Sadistic Conclusion (Arrhenius, 2014)
  • 191. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References The Very Sadistic Conclusion (Arrhenius, 2014) wellbeing population size
  • 192. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References The Very Sadistic Conclusion (Arrhenius, 2014) wellbeing c population size
  • 193. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation: There is a positive probability of human extinction. Stern Review's justi
  • 194. cation for time utility discounting. Policy (e.g. concerning climate change) may lead to dierent people living in the future. So we need to be able to evaluate alternatives with dierent sets of potential people. Result: The RDU approach generalized to variable population (Asheim and Zuber, TE forth.) avoids the repugnant conclusion and the very sadistic conclusion
  • 195. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation: There is a positive probability of human extinction. Stern Review's justi
  • 196. cation for time utility discounting. Policy (e.g. concerning climate change) may lead to dierent people living in the future. So we need to be able to evaluate alternatives with dierent sets of potential people. Result: The RDU approach generalized to variable population (Asheim and Zuber, TE forth.) avoids the repugnant conclusion and the very sadistic conclusion risk (Asheim and Zuber, 2014)
  • 197. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Inequality along time Buchholz Zuber acr. location acr. location and states w/uninhab. locations Conclusion References Endogenous population + positive prob. of extinction Motivation: There is a positive probability of human extinction. Stern Review's justi
  • 198. cation for time utility discounting. Policy (e.g. concerning climate change) may lead to dierent people living in the future. So we need to be able to evaluate alternatives with dierent sets of potential people. Result: The RDU approach generalized to variable population (Asheim and Zuber, TE forth.) avoids the repugnant conclusion and the very sadistic conclusion risk (Asheim and Zuber, 2014) handles pos. prob. of extinct. while ensuring equal treatment across uncertain states
  • 199. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Conclusion Q1 What is sustainability? Q2 Is sustainability good?
  • 200. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Conclusion Q1 What is sustainability? Q2 Is sustainability good?
  • 201. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Conclusion Q1 What is sustainability? Can be de
  • 202. ned in the case of inequality along time only (intergenerational equity) Q2 Is sustainability good?
  • 203. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Conclusion Q1 What is sustainability? Can be de
  • 204. ned in the case of inequality along time only (intergenerational equity) More dicult to de
  • 205. ne in the other cases (with inequality not only along time, but also across space and over uncertain states, and with uninhabited location-state pairs) Q2 Is sustainability good?
  • 206. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Conclusion Q1 What is sustainability? Can be de
  • 207. ned in the case of inequality along time only (intergenerational equity) More dicult to de
  • 208. ne in the other cases (with inequality not only along time, but also across space and over uncertain states, and with uninhabited location-state pairs) Q2 Is sustainability good?
  • 209. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Conclusion Q1 What is sustainability? Can be de
  • 210. ned in the case of inequality along time only (intergenerational equity) More dicult to de
  • 211. ne in the other cases (with inequality not only along time, but also across space and over uncertain states, and with uninhabited location-state pairs) Q2 Is sustainability good? Combining axiomatic analysis with productive technologies leads to sustainable streams with inequality along time only
  • 212. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Conclusion Q1 What is sustainability? Can be de
  • 213. ned in the case of inequality along time only (intergenerational equity) More dicult to de
  • 214. ne in the other cases (with inequality not only along time, but also across space and over uncertain states, and with uninhabited location-state pairs) Q2 Is sustainability good? Combining axiomatic analysis with productive technologies leads to sustainable streams with inequality along time only Such axiomatically based criteria can be used to determine goodness also in the other cases
  • 215. 2 questions on sustain- ability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References References Arrhenius G. 2014. Population Ethics. Oxford, UK: Oxford UP. Forthcoming Arrow KJ. 1999. Discounting, morality, and gaming. In Discounting and Inter- generational Equity ed. PR Portney, JP Weyant. Washington, DC: RFF Asheim GB, Buchholz W, Tungodden B. 2001. Justifying sustainability J Environ. Econ. Man. 41:252{268 Asheim GB, Zuber S. 2013. Escaping the repugnant conclusion: RDU with vari- able population. Forthcoming in Theor Econ Asheim GB, Zuber S. 2014. Probability adjusted RDU. CESifo WP No 4728 Mirrlees JA. 1967. Optimal growth when technology is changing. R. Econ. Stud. 46:32{37 Par
  • 216. t D. 1984. Reasons and Persons. Oxford: Oxford UP Rawls J. 1971. A Theory of Justice. Cambridge, MA: Harvard UP Zuber S, Asheim GB. 2012. Justifying social discounting: the rank-discounted utilitarian apporach. J. Econ. Theory 147:1572{1601