Green accounting: Green NNP and genuine savings
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1 Green accouning: Green NNP an genuine savings Lecures in resource economics Spring 2, Par G.B. Asheim, na.res., upae Naional accouning gives a isore picure of savings if changes in socks of naural an environmenal resources are no inclue in naional accouns evelopmen of proucive capaciy if changes in environmenal ameniies are no inclue. Problems: How o measure genuine (or comprehensive savings an wha oes i inicae? How o measure green (or comprehensive ne naional prouc an wha oes i inicae? G.B. Asheim, na.res., upae Solow claims in An almos pracical sep owars susainabiliy (1992/1993: laim 1: Properly efine naional prouc measures he maximum curren level of consumer saisfacion ha can be susaine forever [an is herefore] a measure of susainable income given he sae of he economy. laim 2: Properly efine an properly calculae, his year s ne naional prouc can always be regare as his year s ineres on sociey s oal sock of capial. G.B. Asheim, na.res., upae
2 Hence, wo quesions: Quesion 1: Does Green NNP measure susainable income (he maximum level of consumpion ha can be susaine forever? Answer: Yes, approximaely. Alhough Green NNP ens o overesimae susainable income. Quesion 2: an Green NNP be regare as ineres on sociey s genuine wealh? Answer: No. hange in Green NNP can be regare as ineres on genuine savings. G.B. Asheim, na.res., upae Two moels of opimal growh Moel (a: One secor moel Moel (b: Dasgupa-Heal-Solow moel Dasgupa Heal (197, Solow (197 Q( K Q( K, R S R S R Assumpions on he echnology: Q K, R ( onsequences of iscoune uiliarianism. G.B. Asheim, na.res., upae NNP in he one secor moel (moel (a Green NNP a ime : Y Q( K K Ne prouc Expeni ure - Response o quesion 1: A consumpion level equal o Q( K is susainable by keeping K for all imes. Q Q(K Response o quesion 2: Ineres rae: i QK ( K ( < Q( K / K Ineres on capial: ik QK ( K K < Q( K 123 Green NNP Q K K K G.B. Asheim, na.res., upae
3 Savings in he one secor moel (moel (a Genuine savings a ime : K Even hough Green NNP is no ineres on capial (if he proucion funcion exhibis ecreasing reurns o scale, i hols ha: Y { QK ( K i { K change in green NNP Ineres on genuine savings This is a general resul, holing in all moels uner comprehensive accouning. G.B. Asheim, na.res., upae NNP in he D-H-S moel (moel (b Ineres rae: i Q ( K, K Resource price: p QR ( K, p Hoelling s rule: i p Green NNP a ime : Y Q( K, R pr K ps Ne Expeniprouc ure Response o quesion 1: I will reurn o his. G.B. Asheim, na.res., upae Response o quesion 2: NNP as ineres on wealh in he D-H-S moel (moel (b? Assume for his page only ha he proucion funcion exhibis consan reurns o scale (RS: Q( K, Q K Q R ik pr K R Green NNP Y Q( K, pr ik < i( K ps 123 Wealh Observaion: Green NNP nee no be equal o ineres on wealh, even uner RS. Query: If ne prouc income, is ik naional income (so ha no income accrues o resource owners?. G.B. Asheim, na.res., upae
4 Savings in he D-H-S moel (moel (b Genuine savings a ime : ps pr ( p ( Q( K, p Y QK QR R pr pr i ipr (since QK i, Q i( p Inepenenly of wheher RS is impose, i hols ha: ( ( K pr i K pr change in green NNP R p, an p ip Ineres on genuine savings G.B. Asheim, na.res., upae Genuine savings PV of fuure changes in consumpion ( p R i ( p R τ e ( τ p R e By inegraing: 1 τ K pr 23 e Genuine 123 savings Presen value of fuure changes in consumpion Observaion: If evelopmen is susaine (non-ecr. cons., hen genuine savings is non-negaive, an Green NNP is non-ecreasing since Y. i ( pr This hols uner comprehensive accouning. G.B. Asheim, na.res., upae Response o quesion 1: Wha abou Green NNP as a measure of susainable income? Assume iscoune uiliarianism: Then: Since p R ρ τ ( e U ( e Or equivalenly: i ρ U e τ, ρ max U ( e ( U ( U ( ( K p R ( U ( ρ i follows ha U ( 1 23 e Genuine savings 12 3 in uiliy erms Presen value of fuure changes in uiliy G.B. Asheim, na.res., upae
5 Wha abou Green NNP as a measure of susainable income (con? ρ ρ ρ ( U ( e ρu ( e ( U ( e By inegraing, i follows ha: ρ ρ ( ( U e ρu ( e ( ( ρ pr ( U ( e U ( Since U i follows ha ( p R ρ U ( U ( ρ ( U e Uiliy NNP 1 23 This is Weizman s (1976 main resul. Uiliy ineres on uiliy wealh (M.L. Weizman, On he welfare significance of naional prouc in a ynamic economy, QJE, 1976 G.B. Asheim, na.res., upae Wha abou Green NNP as a measure of susainable income (con? ρ Since e 1/ ρ i follows ha Weizman s resul can be rewrien as: ( U U ( ( ρ pr e ( ρ U ( e Inerpreaion: Uiliy NNP is he saionary equivalen of fuure uiliy. S Le enoe he max. susainable consumpion a ime. If acual consumpion equals max. susainable consumpion a ime ; i.e., S, an is he unique opimal ( pah, hen genuine savings are posiive: K p R. Why? > G.B. Asheim, na.res., upae onclusions (on Green NNP as a measure of susainable income Genuine savings can be posiive, i.e, K pr >, even hough consumpion excees max. susainable consumpion. Y pr > oes no imply ha consumpion is susainable since he resource price epens on he pah ha will be followe. (G.B. Asheim, Ne naional prouc as an inicaor of susainabiliy, SJE, 199 Uner iscoune uiliarianism posiive genuine savings K pr > posiive NNP growh Y i( pr > is a necessary, bu no sufficien, coniion for susainable evelopmen. (J..V. Pezzey, One-sie Susainabiliy Tess wih Ameniies an Shifs in Technology, Trae an Populaion, forhcoming in JEEM G.B. Asheim, na.res., upae
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