Assignment: The Economics of Global Warming

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L7_MAC MD Worksheet Answers Ruth Forsdyke

1a) List some benefits of net GHG emissions? 1 ) P r o d u c e r s ’ R e v e n u e f r o m s e l l i n g G H G i n t e n s i v e g o o d s . 2 ) U t i l i t y / h a p p i n e s s / w e l l b e i n g d e r i v e d f r o m n e e d s a t t a i n e d f r o m c o n s u m i n g G H G i n t e n s i v e

g o o d s ( m e a s u r e d i n m o n e y u n i t s a s m a r g i n a l W T P ) . E x . T r a n s p o r t e n e r g y ( p u b l i c a n d t r a n s p o r t ) , f o o d , h o m e a p p l i a n c e s , c o m p u t e r s , l i g h t s , h e a t f o r h o m e s , n e w c l o t h i n g , m o v i e s , f u r n i t u r e , w o o d f r o m u n s u s t a i n a b l y l o g g e d f o r e s t s a n d f i s h f r o m u n s u s t a i n a b l y f i s h e d s e a s , t h e l o c a t i o n a l c o m p o n e n t o f h u m a n s e t t l e m e n t s w h i c h h a v e d i s p l a c e d n a t u r a l c a r b o n s i n k s , e d u c a t i o n .

b) List some costs of carbon dioxide emissions? D r o u g h t s , f l o o d s , b l e a c h i n g o f c o r a l r e e f s , c o a s t l i n e e r o s i o n , l o s s o f c o a s t a l l a n d f o r f a r m s , r e s i d e n t i a l a r e a s , i n d u s t r i e s a n d e c o s y s t e m s d u e t o s e a l e v e l r i s e , d a m a g e f r o m i n t e n s e w e a t h e r e v e n t s l i k e h u r r i c a n e s a n d t o r n a d o s , s p r e a d o f d e s s e r t s , s h r i n k a g e o f a r c t i c h a b i t a t ( e x . r i n g e d s e a l s a n d p o l a r b e a r s ) , l o s s o f c o r a l s a n d h a r m t o o c e a n e c o s y s t e m s d u e t o w a r m e r w a t e r , h a r m t o o c e a n e c o s y s t e m s a n d f i s h i n g i n d u s t r y d u e t o m o r e a c i d i c w a t e r s c a u s i n g s h e l l s o f s h e l l f i s h a n d c r u s t a c e a n s ( e x . c r a b s a n d l o b s t e r s ) t o d i s s o l v e , f o r e s t f i r e s d u e t o d r y i n g o u t , b e e t l e a n d m o t h d a m a g e s t o t r e e s d u e t o m o t h s a n d b e e t l e s h a b i t a t m o v i n g p o l e w a r d s , i n c r e a s e d d i s e a s e s i n p o l e w a r d r e g i o n s d u e t o s p r e a d o f d i s e a s e v e c t o r s l i k e M a l a r i a m o s q u i t o s .

2) a) At socially efficient allocation, find: Economic allocation i) Socially efficient (QSE) ii) Privately efficient (QM) I)Total social surplus ($) 225 225 – 625 = - 400 II) Total private surplus 975 80*40 = 1600 Total external costs 50* 15 = 750 50 * 40 = 2000 b) Graph 1: Total Social Surplus, Private Surplus and External Costs: Comparison with Market and Money Socially Efficient Level. I) Total Social Surplus (consumers, producers and third parties) i) Socially Efficient Level ii) Perfectly Competitive Market Level

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II) Total Private Surplus: (consumers and producers) i) Socially Efficient Level ii) Perfectly Competitive Market Level

III) Total net external Costs (positive externalities netted out & I have just called these “external costs”) ) Socially Efficient Level ii) Perfectly Competitive Market Level

• We can see that the total external costs are much larger at the market level than at the SE level. • The top pink total social surplus graphs are attained by subtracting the mustard total external

costs from the blue total private costs.

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3) Plot the marginal private surplus (marginal consumer benefits – marginal producer costs) and the marginal external costs ($50/unit) on the graph below. Table to help with plotting the marginal private surplus curve: Quantity of good (units)

Marginal private benefit

Marginal private cost

Marginal private surplus

Will private surplus increase or decrease if output is increased by one unit?

0 100 20 80 increase 15 8 5 3 5 5 0 I n c r e a s e 40 6 0 6 0 0 N o c h a n g e 60 4 0 8 0 - 4 0 D e c r e a s e 80 2 0 1 0 0 - 8 0 D e c r e a s e 100 0 1 2 0 - 1 2 0 D e c r e a s e Q 100- Q 20+Q ( 1 0 0 - Q ) – ( 2 0 + Q )

= 8 0 – 2 Q Depends on Q

4) The area under the $ marginal private surplus curve from 0 to Q represents the t o t a l p r i v a t e s u r p l u s from production and consumption of Q goods. 5) The area under the $ marginal external cost curve from 0 to Q represents the t o t a l p r i v a t e s u r p l u s of production and consumption of Q goods. 6) Now we modify the framework to enable us to focus directly on emissions. Assume that each unit of output produces one tonne of GHG emissions (E) such that Q = E, where E represents GHG emissions in CO2e/year. a) Marginal private surplus of Q goods = 80 – 2Q (eqn. 1 from table) Now substitute E for Q, where E = Q into equation 1 to get:

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b) Marginal private Surplus (E) = 8 0 – 2 E ( i n $ / t o n n e G H G s ) ( a l s o c a l l e d t h e M a r g i n a l A b a t e m e n t c o s t a s p r i v a t e p a r t i e s g i v e u p s u r p l u s d u e t o a b a t e m e n t ) . MAC(E) = 8 0 – 2 E . c) Recall that Marginal external cost (Q) = 50 $/ unit of good ( c o n s t a n t a n d h e n c e i n d e p e n d e n t o f Q i n o u r e x a m p l e ) . Since Q = E, and each additional good produced causes external costs of 50 $/unit (the marginal external cost), it follows that each additional tonne of GHGs (in CO2e) causes external damages of $ 50 to the third parties called marginal damages. MD (E) = $ 5 0 p e r t o n n e o f G H G s ( t h i s i s c a l l e d t h e “ m a r g i n a l d a m a g e ” ) 7) a) Plot MAC and MD curves on the graph below. Note that the units on the vertical axis are $/tonne while those on the horizontal axis are tonnes per year. Graph 3: MAC-MD Framework 8) What area represents the total private surplus of producing 15 tonnes CO2e/year? A + B = $ 9 7 5 ( t h i s i s t h e t o t a l p r o d u c e r a n d c o n s u m e r s u r p l u s f r o m t h e G H G s — i f c o n s u m e r s w e r e f o r c e d t o a b a t e t o E = 0 f r o m t h e S o c i a l l y e f f i c i e n t l e v e l , t h e y w o u l d l o s e t h i s ! )

9) What area represents the total damages to 3rd parties of producing 15 tonnes CO2e/year? B = $ 7 5 0 ( a g a i n i f t h e p r i v a t e p a r t i e s h a d t o a b a t e f r o m S E l e v e l t o 0 , t h e t h i r d p a r t i e s w o u l d s a v e t h e s e d a m a g e s w h i c h w o u l d b e a n e t b e n e f i t t o t h e m ) . 10) What area represents the loss of net total private surplus due to abating emissions from the competitive market equilibrium “Business as usual” (“BAU”) level of EBAU = 40 tonnes/yr to the $ socially efficient (SE) level of 15 tonnes/yr? C = $ 6 2 5 , t h i s i s t h e p r i v a t e p a r t y ’ s t o t a l a b a t e m e n t c o s t s f r o m B A U e m i s s i o n s t o t h e s o c i a l l y e f f i c i e n t l e v e l ( w h i c h w o u l d o c c u r u n d e r e n f o r c e d “ i d e a l ” r e g u l a t i o n s ) .

80

100

0

20

40

60 A = $225

D= $625

C = $625

B = $750

Emissions (tonnes CO2e/year)

$ / tonne

Marginal Private Surplus of emissions = MAC

Marginal Damages

7b) At s o c i a l l y e f f i c i e n t q u a n t i t y of 15 tonnes: T o t a l p r i v a t e s u r p l u s = Area A+ B = $ 975 T o t a l e x t e r n a l c o s t s = Area B = $ 750 T o t a l s o c i al s u r p l u s = Area (A+B) – A = A = $ 225/ year c) At p r i v a t e l y e f f i c i e n t q u a n t i t y of 40 tonnes: T o t a l p r i v a t e s u r p l u s = Area A+B+C = $ 1600 T o t a l e x t e r n a l c o s t s = Area B+C+D = $ 2000 T o t a l s o c i al s u r p l u s = Area_(A+B+C)- (B+C+D) = A-D = $ 225 - $625 = - $400

Price CO2e = 50

ESE = 15

EMarket = 40

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11) What area represents the total damages reduced to third parties by abating emissions from the competitive market equilibrium level of 40 tonnes (BAU) to 15 tonnes? D + C = $ 1 2 5 0 ( t h i s w i l l i n c l u d e b o t h d a m a g e s a v o i d e d ( e x c r o p l o s s d u e t o d r o u g h t s ) a n d a d a p t a t i o n c o s t s a v o i d e d ( e x . U S f a r m e r s a v o i d i n s t a l l i n g e x p e n s i v e w a t e r s t o r a g e a n d i r r i g a t i o n s y s t e m s / e x . c o a s t a l h o m e s d o n o t h a v e t o b e m o v e d i n l a n d ) .

12) The MAC represents the maximum marginal willingness to pay (max WTP) of the private parties to emit an additional tonne of GHG emissions and is hence the D E M A N D for/of emissions equation while the MD represents the minimum willingness to accept (minWTA) for emissions and is hence the D E M A N D (demand or supply) for/of emissions (IF private parties are made to pay the third parties for the damages). 13) For each emissions level (E) in the table, find the MAC and MD and indicate whether decreasing emissions by one additional tonne causes total social surplus to rise or fall. Emissions (tonnes CO2e/year) = E

MAC = loss marginal private surplus emissions due to reducing emissions by one unit = 80 – 2E

MD = marginal surplus gain due to reduced external costs to 3rd parties = $50/ tonne CO2e

Marginal social surplus change = MD - MAC

Will total social surplus from emissions rise or fall if emissions are abated by one unit?

0 8 0 5 0 - 3 0 D e c r e a s e 1 0 6 0 5 0 - 1 0 d e c r e a s e 1 5 5 0 5 0 0 N o c h a n g e 4 0 0 5 0 5 0 I n c r e a s e 17) a) What marginal tax on emissions (carbon tax) will induce firms to abate to money socially efficient level? Graph 4: Carbon Tax in the MAC-MD Framework - T h e m a r g i n a l c a r b o n t a x i s $ 5 0 / t o n n e .

80

100

EMarket = 40

ESE = 15

0

20

40

1

Price CO2e = 50

B = $750

Emissions (tonnes CO2e/year)

$ /tonne CO2e

Marginal Private Surplus of emissions = MAC

Marginal Damages = Marginal Carbon Tax

2

D

C

Total carbon tax = B

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- F o r E > 1 5 , p o l l u t e r s w i l l s a v e m o r e t a x o n e a c h u n i t a b a t e d t h a n i t w i l l c o s t t h e m t o a b a t e ( i n t e r m s o f p r i v a t e s u r p l u s l o s s ) . H e n c e , t h e y w i l l a b a t e a t o n n e . T h e y w i l l s t o p a b a t i n g a t E = 1 5 b e c a u s e t h e m a r g i n a l t a x s a v e d w i l l b e e q u a l t o t h e m a r g i n a l p r i v a t e s u r p l u s l o s t . T h e y w i l l n o t a b a t e f u r t h e r t h a n 1 5 t o n n e s b e c a u s e t h e t a x s a v e d p e r t o n n e i s l e s s t h a n t h e m a r g i n a l p r i v a t e s u r p l u s l o s t . - M a r g i n a l t a x l i n e i s s a m e a s M D b u t o n l y h o l d s b e c a u s e t h e M D i s c o n s t a n t . - A c o n s t a n t M D i s r e a s o n a b l e o v e r a s h o r t t i m e f r a m e l i k e 1 y e a r b e c a u s e e a c h a d d i t i o n a l t o n n e o f e m i s s i o n s c a u s e s a b o u t t h e s a m e d a m a g e s . I n t h e l o n g e r r u n ( s a y 1 c e n t u r y ) t h e M D c u r v e i s e x p e c t e d t o s l o p e u p w a r d a s m o r e d a m a g e s a r e e x p e c t e d t o b e i n f l i c t e d b y l a t e r e m i s s i o n s a s t h e G H G s c o n t i n u e t o b u i l d u p i n t h e a t m o s p h e r e . b) Find total carbon tax collected. (Draw on your graph) - T h e t o t a l c a r b o n t a x i s $ 5 0 / t o n n e * 1 5 t o n n e s / y e a r = $ 7 5 0 / y e a r - T h i s c o r r e s p o n d s t o t h e a r e a u n d e r t h e M D c u r v e f r o m 0 t o 1 5 t o n n e s ( B ) - I f t h e p r i v a t e p a r t i e s d i d n o t a b a t e a t a l l , t h e y w o u l d h a v e t o p a y 4 0 * 5 0 = $ 2 0 0 0 o f c a r b o n t a x , s o t h e y s a v e a r e a D + C . 18) What quota on emissions (emissions standard) will induce firms to abate to the money socially efficient level? (Draw on your graph) T h e g o v e r n m e n t s e t s a n e m i s s i o n s s t a n d a r d o f 1 5 t o n n e s p e r y e a r a n d t h e f i r m s a r e f i n e d i f t h e y e m i t m o r e t h a n 1 5 t o n n e s p e r y e a r . G r a p h i c a l l y , d r a w a v e r t i c a l l i n e a t 1 5 t o n n e s / y e a r . 19) a) What marginal abatement subsidy could be used to get the firm to abate to the money socially efficient level? b) What is the total subsidy if government correctly estimates business as usual emissions? (Draw on your graph). T h e m a r g . a b a t e m e n t s u b s i d y i s $ 5 0 / t o n n e — i . e f o r e a c h t o n n e a b a t e d b e l o w B A U , t h e g o v e r n m e n t p a y s t h e f i r m $ 5 0 . T h e t o t a l s u b s i d y i s ( 4 0 - 1 5 ) * 5 0 = $ 1 2 5 0 ( A r e a C + D ) . Graph 5: Marginal Abatement Subsidy in the MAC-MD Framework

80

100

$ /tonne CO2e

Marginal Private Surplus of emissions = MAC

Marginal Damages = Marginal Abatement Subsidy

C

D

ESE = 15

EMarket = 40

Total carbon subsidy = B

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b) How could the subsidy be financed? T h e s u b s i d y i s f i n a n c e d b y t a x e s o r t h e g o v e r n m e n t i s s u e s b o n d s t o b o r r o w t h e m o n e y i n w h i c h c a s e , i t l a t e r p a y s t h i s m o n e y b a c k t o l e n d e r s o u t o f f u t u r e t a x e s . c) Suppose that the government overestimates the business as usual (BAU) level of emissions to be . Will the government pay less or more subsidy than it needs to? T h e g o v e r n m e n t w o u l d p a y t o o m u c h s u b s i d y . F o r e x a m p l e , s u p p o s e t h e g o v e r n m e n t i n c o r r e c t l y e s t i m a t e s t h e B A U e m i s s i o n s l e v e l t o b e 4 5 t o n n e s / y e a r . I t w i l l e n d o u t p a y i n g ( 4 5 – 1 5 ) * 5 0 = $ 1 5 0 0 o f t o t a l s u b s i d y ( m o r e t h a n i n p a r t a ) . 20) Why should we be concerned about using monetary social efficiency as a social wellbeing criterion to determine optimal carbon taxes, abatement subsidies, emissions standards or sink photosynthesis floors in a world, which has a very unequal income distribution? - T h e p o l i c i e s a r e s e t t o m a x i m i z e t h e T o t a l s o c i a l s u r p l u s ( = m o n e t a r y t o t a l p r i v a t e s u r p l u s m i n u s t h e t o t a l d a m a g e s t o t h e t h i r d p a r t i e s ) . T h e u s e o f m o n e y p u t s m o r e w e i g h t o n h i g h i n c o m e v s . l o w i n c o m e p e o p l e ’ s b e n e f i t s a n d c o s t s a n d s o t h e f i n a l a l l o c a t i o n m a y n o t m a x i m i z e t h e t o t a l s o c i a l s u r p l u s w e r e i t t o i n s t e a d b y m e a s u r e d i n h a p p i n e s s o r u t i l i t y u n i t s ( u t i l s ) . I t i s q u e s t i o n a b l e w h e t h e r u t i l i t y c a n b e m e a s u r e d i n t h e o r y a n d i n p r a c t i c e .