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

1. 2 questions on sustainability 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 sustainability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References The questions

3. 2 questions on sustainability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References The questions Q1 What is sustainability?

4. 2 questions on sustainability 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 sustainability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Location in time and space

6. 2 questions on sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Uncertain states

11. 2 questions on sustainability G.B. Asheim Outline Q1 What is sust.? Q2 Is sust. good? Conclusion References Uncertain states states location

12. 2 questions on sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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

23. nitions of sustainability

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-decreasing stream that satis

27. es techn. institut. constraints.

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.

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.

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.

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.

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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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?

80. 2 questions on sustainability 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 sustainability 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 sustainability 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

84. 2 questions on sustainability 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 sustainability 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 sustainability 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.

88. 2 questions on sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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

97. 2 questions on sustainability 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

100. nite subset of generations With relative priority only, no weight on any generation but the worst o

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 sustainability 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!

106. 2 questions on sustainability 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

107. ) P1 t=1

108. t1u(xt ) where t is time and

109. 2 (0; 1) is a time utility disc. factor

111. ) P1 t=1

113. 2 (0; 1) is a time utility disc. factor (1

114. ) P1 r=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 ]

117. ) P1 t=1

119. 2 (0; 1) is a time utility disc. factor (1

120. ) P1 r=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 sustainability 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

124. ) P1 t=1

126. 2 (0; 1) is a time utility disc. factor Rank-discounted utilitarianism: (1

127. ) P1 r=1

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 sustainability 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

131. ) P1 t=1

133. 2 (0; 1) is a time utility disc. factor Rank-discounted utilitarianism: (1

134. ) P1 r=1

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 sustainability 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 sustainability 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 sustainability 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

143. 2 questions on sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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 sustainability 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.

169. cation for time utility discounting. Policy (e.g. concerning climate change) may lead to dierent people living in the future.

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.

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:

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

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.)

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 sustainability 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

181. t, 1984)

183. t, 1984) For any egalitarian allocation with very high positive wellbeing, wellbeing population size

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

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

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 sustainability 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 sustainability 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 sustainability 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

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

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)

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 sustainability 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 sustainability 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 sustainability 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?

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?

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?

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

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 sustainability 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 variable 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

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