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Social Choice and Welfare

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13.06.2016 | Original Paper

Sustainable growth

verfasst von: Geir B. Asheim

Erschienen in: Social Choice and Welfare | Ausgabe 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.

Vorheriger Artikel Peripheral diversity: transfers versus public goods

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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.

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Titel: Sustainable growth
verfasst von: Geir B. Asheim
Publikationsdatum: 13.06.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 3-4/2017
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-016-0977-9

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