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Social Choice and Welfare

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13-06-2016 | Original Paper

Sustainable growth

Author: Geir B. Asheim

Published in: Social Choice and Welfare | Issue 3-4/2017

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Abstract

This paper explores the view that a criterion of intergenerational equity serves to make choices according to ethical intuitions on a domain of relevant technological environments. In line with this view I first calibrate different criteria of intergenerational equity in the AK model of economic growth, with a given productivity parameter A, and then evaluate their performance by mapping the consequences of the criteria in various technological environments. The evaluation is based on the extent to which they yield social choice mappings satisfying four desirable properties. The Calvo criterion as well as sustainable discounted utilitarianism and rank-discounted utilitarianism yield sustainable growth in the AK model, the Ramsey technology and the Dasgupta–Heal–Solow–Stiglitz technology for any specifications of these technological environments.

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I use the term ‘wellbeing’ for what Roemer and his co-authors refer to as ‘welfare’. It is meant to indicate the current living situation and thus includes more than material consumption. Sentiments like altruism is, however, assumed not to be included in this indicator. In the technological environments considered in the current paper, net production is split between wellbeing and investment in reproducible capital, implying that wellbeing is measured in the same cardinal scale as capital.

The analysis of the sustainable growth criterion in Llavador et al. (2010) is based on a conjectured ‘turnpike’ result, entailing that such an efficient balanced growth path is approached when the inputs initially are not in the proportions needed for efficient balanced growth. In Llavador et al. (2011) there is in addition a stock of CO\(_2\) in the atmosphere which is constant along the efficient balanced growth path.

Asheim and Mitra (2010, Section 2) use the construction presented here to establish the existence of a SDU welfare function, while using their requirements (W.1)–(W.4) as the primitive definition.

Hence, the RDU criterion combines an “absolute” Priority View with a “relative” one; see Fleurbaey (2015) and Buchak (2015).

Conditions (2) and (3) of Asheim and Mitra (2010, Proposition 3) are satisfied since \(p_{t}/p_{t-1} = 1/A \ge \rho \) for all \(t \ge 1\), writing \(p_0 = 1\), and \({\sum }_{t=1}^\infty p_t x_t^e = k_0 = {\sum }_{t=1}^\tau p_t \tilde{x}_t + p_\tau \tilde{k}_\tau \ge {\sum }_{t=1}^\infty p_t \tilde{x}_t\) for any feasible stream \(_1 \tilde{x}\) and for all \(\tau \ge 1\).

Zuber and Asheim (2012, Proposition 10) is based on Asheim (1991, Proposition 6), where the proof of Case 2 must be adapted to the AK model to show that \(_1 x^e\) maximizes \(w_\rho ^T(_1 x^+)\) over all non-decreasing streams \(_1 x^+\) when \(A \le 1/\rho \).

Asheim and Mitra (2010, Lemma 1) is a formal demonstration of this result, as \(\sum _{t=1}^\tau \rho ^{t-1} \Lambda (1+g)^{t-1}\) would diverge for any \(\rho \) satisfying \(1/(1+g) \le \rho < 1\) if a wellbeing stream defined by \(x_t = \Lambda (1+g)^{t-1}\) for all t were feasible with \(\Lambda > 0\) and \(g > 0\).

Use (7) combined with \(f(k) = k^\alpha \) and \(\dot{k} = sf(k)\) to obtain \(\dot{x}/x = s \alpha k^{\alpha - 1}\) and insert in (8).

Mitra et al. (2013) do likewise in the continuous time version of the model.

Asheim and Mitra (2010, Lemma 2) is a formal demonstration of this result, as \(\sum _{t=1}^\tau \rho ^{t-1} \Lambda (1+g)^{t-1}\) would diverge for any \(\rho \) satisfying \(1/(1+g) \le \rho < 1\) if a wellbeing stream defined by \(x_t = \Lambda (1+g)^{t-1}\) for all t were feasible with \(\Lambda > 0\) and \(g > 0\).

The two parameters can be calibrated independently if there are two different combinations of gross productivity and growth rate, \((A^*, g^*)\) and \((A^{**}, g^{**})\), that appeal to ethical intuitions in the AK model.

Arrow KJ (1974) Rawls’ principle of just saving. Swed J Econ 75:323–335CrossRef

Asheim GB (1988) Rawlsian intergenerational justice as a Markov-perfect equilibrium in a resource technology. Rev Econ Stud 55:469–483CrossRef

Asheim GB (1991) Unjust intergenerational allocations. J Econ Theory 54:350–371CrossRef

Asheim GB, Ekeland I (2016) Resource conservation across generations in a Ramsey–Chichilnisky model. Econ Theory 61:611–639CrossRef

Asheim GB, Mitra T (2010) Sustainability and discounted utilitarianism in models of economic growth. Math Soc Sci 59:148–169CrossRef

Asheim GB, Nesje F (2016) Destructive intergenerational altruism. Memorandum 22/2015, Department of Economics, University of Oslo, revised April 2016, J Assoc Environ Res Econ (forthcoming)

Asheim GB, Zuber S (2014) Escaping the repugnant conclusion: rank-discounted utilitarianism with variable population. Theor Econ 9:629–650CrossRef

Asheim GB, Zuber S (2016) Evaluating intergenerational risks. CESifo Working Paper No. 4728, revised April 2016, J Math Econ. doi:10.1016/j.jmateco.2016.05.005 (forthcoming)

Asheim GB, Buchholz W, Hartwick J, Mitra T, Withagen C (2007) Constant savings rates and quasi-arithmetic population growth under exhaustible resource constraints. J Environ Econ Manag 53:213–229CrossRef

Beals R, Koopmans TC (1969) Maximizing stationary utility in a constant technology. SIAM J Appl Math 17:1001–1015CrossRef

Buchak L (2015) Relative priority. Mimeo, University of California, Berkeley

Calvo G (1978) Some notes on time inconsistency and Rawls’ maximin criterion. Rev Econ Stud 45:97–102CrossRef

Cass D, Mitra T (1991) Indefinitely sustained consumption despite exhaustible natural resources. Econ Theory 1:119–146CrossRef

Chichilnisky G (1996) An axiomatic approach to sustainable development. Soc Choice Welf 13:231–57CrossRef

Dasgupta PS (1974) On some alternative criteria for justice between generations. J Public Econ 3:405–423CrossRef

Dasgupta PS (2008) Discounting climate change. J Risk Uncertain 37:141–169CrossRef

Dasgupta PS (2011) The ethics of intergenerational distribution: reply and response to John E. Roemer. Environ Resour Econ 50:475–493CrossRef

Dasgupta PS, Heal GM (1974) The optimal depletion of exhaustible resources. Rev Econ Stud (Symp) 41:3–28CrossRef

Dasgupta PS, Heal GM (1979) Economic theory and exhaustible resources. Cambridge University Press, Cambridge

Dasgupta S, Mitra T (1983) Intergenerational equity and efficient allocation of exhaustible resources. Int Econ Rev 24:133–153CrossRef

Dietz S, Asheim GB (2012) Climate policy under sustainable discounted utilitarianism. J Environ Econ Manag 63:321–335CrossRef

Fleurbaey M (2015) Equality versus priority. How relevant is the distinction? Econ Philos 31:203–217CrossRef

Gale D (1967) On optimal development in a multi-sector economy. Rev Econ Stud 34:1–18CrossRef

Koopmans TC (1960) Stationary ordinal utility and impatience. Econometrica 28:287–309CrossRef

Llavador H, Roemer JE, Silvestre J (2010) Intergenerational justice when future worlds are uncertain. J Math Econ 46:728–761CrossRef

Llavador H, Roemer JE, Silvestre J (2011) A dynamic analysis of human welfare in a warming planet. J Public Econ 95:1607–1620CrossRef

Llavador H, Roemer JE, Silvestre J (2013) Should we sustain? And if so, sustain what? Consumption or the quality of life? In: Fouquet R (ed) Handbook on energy and climate change. Edward Elgar, Cheltenham

Mitra T, Asheim GB, Buchholz W, Withagen C (2013) Characterizing the sustainability problem in an exhaustible resource model. J Econ Theory 148:2164–2182CrossRef

Nordhaus WD (2007) The Stern review on the economics of climate change. J Econ Lit 45:687–702CrossRef

Rawls J (1999) A theory of justice, revised edn. The Belknap Press of the Harvard University Press, Cambridge

Ray D (1987) Nonpaternalistic intergenerational altruism. J Econ Theory 41:112–132CrossRef

Roemer JE (2011) The ethics of intertemporal distribution in a warming planet. Environ Resour Econ 48:363–390CrossRef

Roemer JE (2013) Once more on intergenerational discounting in climate-change analysis: reply to Partha Dasgupta. Environ Resour Econ 56:141–148CrossRef

Sen A (1979) Utilitarianism and welfarism. J Philos 76:463–489CrossRef

Solow RM (1974) Intergenerational equity and exhaustible resources. Rev Econ Stud (Symp) 41:29–45CrossRef

Stern NH (2006) The Stern review of the economics of climate change. Cambridge University Press, Cambridge

Stiglitz J (1974) Growth with exhaustible natural resources: efficient and optimal growth paths. Rev Econ Stud (Symp) 41:123–137CrossRef

Weitzman ML (2007) The Stern review of the economics of climate change. J Econ Lit 45:703–724CrossRef

Zuber S, Asheim GB (2012) Justifying social discounting: the rank-discounted utilitarian approach. J Econ Theory 147:1572–1601CrossRef

Title: Sustainable growth
Author: Geir B. Asheim
Publication date: 13-06-2016
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 3-4/2017
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-016-0977-9

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