Assignment: The Economics of Global Warming

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L7_Marginal Abatement Cost Marginal Damage Worksheet (MAC MD) Ruth Forsdyke

The MAC-MD model is used estimate the social benefits and costs of the net GHG emissions in order to estimate socially efficient (SE) trajectories and prices of greenhouse gas emissions, that is those that maximize the total social surplus from the GHG emissions over time. The MAC(E) and MD (E) equations in units of happiness units/tonne CO2e can be derived “top down” as outputs from dynamic optimization models (called IAMs) in which there is a benevolent social planner, the objective of whom is to maximize the happiness (utility) of the greatest number of people and other organisms over time; The social planner takes the utilitarian objective as the criteria the evaluation of “social welfare” in the model. The models are then calibrated using money estimates of abatement costs and net damages from emissions where money units can be converted into theoretical typical consumption units by dividing money world income by the price of an “average basket of goods and services”. More detail will be provided when we discuss IAMs. The MAC and MD curves can also be estimated from the “bottom up” by estimating costs of abating GHGs given the technological options and monetary estimates of damages. The MAC is the demand equation of the private parties for emissions while the MD is the supply equation. This worksheet shows how the MAC MD framework relates to the Pigouvian goods, services and output framework developed in L3 to L5. Note that the following interpretation assumes that the objective is to maximize the total money social surplus over time and not the utility of the greatest number as in the IAMs model. The social welfare criteria of the planner in our worksheet model hence corresponds to a situation of money social efficiency in which the total money private surplus from emissions – net negative externalities from emissions (valued in money) is maximized. This would be the case in which the externalities were paid for, i.e. “internalized” by the private parties such that they have to pay the third parties for the net damages inflicted, i.e. the producers’ MC curve would correspond to the social supply curve in the Pigou model. The private party surplus (net benefits) from emissions is derived indirectly through the surplus from the thneeds, the output of which creates the residual GHG byproducts. The framework divides parties up into two groups instead of 3 as in the Pigou model. This makes the model simpler to analyze but at a cost of information about how private surplus is divided up between consumers and producers. The two parties are:

1) Private parties = consumers and producers (get consumer and producer surplus) 2) “Third parties” who experience the net negative externalities.

This work sheet is designed to be guided discovery, letting you discover the concepts on your own. Try answering the questions. As you go, you can check your answers with the answer key or use them to help you out if you get stuck. You may find that there is a lot to keep track of right now!—with practice, the concepts should become clear.

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1a) List some benefits of net GHG emissions?

b) List some costs of net GHG emissions?

2) Next, we will develop the MAC-MD framework from Pigou’s market framework focusing on one particular good, service of input (thneed). Graph 1: Market for Thneeds with Externalities:

a) At socially efficient allocation, find: Economic allocation socially efficient (QSE) Privately efficient (QM) Total social surplus Total private surplus Total external costs b) Label on your graph. * Recall that marginal benefit private is equal to the consumers’ marginal willingness to pay = MBPrivate = 100 – Q. This is also equal to the marginal social benefit because we assumed no positive externalities such that MBSocial = MBPrivate + 0 (more realistically, think of MCexternal as having netted out the positive externalities.

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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. Use the table to help you. Quantity of good (units)

Marginal private benefit

Marginal private cost

Marginal private surplus

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

0 100 20 80 increase 15 40 60 80 100 Q 100- Q 20+Q (eq’n 1) Depends on Q Graph 2: Marginal Private Surplus for Thneeds and External Costs 4) The area under the $ marginal private surplus curve from 0 to Q represents the _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ from production and consumption of Q goods. 5) The area under the $ marginal external cost curve from 0 to Q represents the _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ of production and consumption of Q goods.

80

100

QMarket = 40

QSE = 15

0

20

40

60

3) At s o c i a l e ff i c ie n t q u a n t it y of 15 goods: T o t a l p r iv a te s u r p l u s = area __________= $________________ T o t a l e x te r n a l c o s t s = area ___________ = $__________________ T o t a l so c ia l s u r p lu s = T o t a l p r i v a t e s u r p l u s – to t a l e x te r n a l c o s ts = Area __________________ - Area ______________ = Area _______________= $__________________ 4) At p r i v a t e l y e ff i c ie n t q u a n t it y of 40 goods: T o t a l p r iv a te s u r p l u s = area ________= $_____________ T o t a l e x te r n a l c o s t s = area _________ = $ ________________ T o t a l so c ia l s u r p lu s = Area _______________ - Area _____________ = Area ______________ = $_______________

Quantity thneeds (units/ year).

$ /good

Notice how the new graphical framework is simpler due to aggregating the benefits and costs of the private parties to get the marginal private surplus. The framework is simpler, but with a cost in terms of loss of information. Note: The external costs are really “net external costs” whereby external benefits like lower winter heating bills have been subtracted out. Adding the external benefit curve to the graph would make it more complicated and hence more difficult to learn.

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6) Now we modify the framework to focus directly on emissions. Assume that each unit of output causes one tonne of GHG emissions (E) such that Q = E, where E represents GHG emissions in CO2e/year.1 a) Marginal private surplus of Q goods = _________________ (eqn. 1 from table above) Now substitute E for Q, where E = Q into equation 1 to get: b) Marginal private Surplus (E) = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ( 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) = __________________ 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) = __________________ 7) 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/ year. These are unrealistic numbers for simplicity.

1 Note that if the relationship between Q and E changes, the translation between our two graphical set ps will not be as simple.

- If we increase emissions by one unit (left to right on graph), the private parties gain marginal private surplus (a net benefit), while the third parties experience a net marginal external cost (a net cost) of $50/tonne. - If we decrease emissions by one unit (right to left on graph), the private parties loose the marginal private surplus and hence incur a net cost (loss of producer and consumer surplus) while the third parties make a net gain equal to the marginal damages saved ($50/tonne). - Economists, call the marginal private surplus of emissions the marginal cost of abatement [MAC(E)] -- taking the right to left perspective.

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Graph 3: The Market for Greenhouse Gases (MAC-MD) 8) What area represents the total private surplus of producing 15 tonnes CO2e/year? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

9) What area represents the total damages to 3rd parties of producing 15 tonnes CO2e/year? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

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? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 11) What area represents the total damages reduced to third parties by abating emissions from the competitive market equilibrium level of 40 tonnes to 15 tonnes? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

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 _____________(demand or supply) for/of emissions equation while the MD represents the minimum willingness to accept (minWTA) for emissions and is hence the ____________ (demand or supply) for/of emissions 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)= 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 given E emissions?

80

100

EMarket = 40

ESE = 15

0

20

40

60

7b) At s o c i a l 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 __________ = $_____________ T o t a l e x t e r n a l c o s t s =___________ Area ___________ = $ ____________ T o t a l s o c i al s u r p l u s = Area (A+B) – A = A = $ 225/ year 7c) 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 _______________= $ ____________ T o t a l e x t e r n a l c o s t s = Area _____________ = $ _____________ T o t a l s o c i al s u r p l u s = Area ______________________________= $ _____________________________

Emissions (tonnes of CO2e/year

$ / tonne CO2e

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17) a) What marginal tax on emissions (carbon tax) will induce firms to abate to money socially efficient level? b) Find total carbon tax collected. (Show on a graph)

18) What quota on emissions (emissions standard) will induce firms to abate to the money socially efficient level? (Show on a graph) 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? (Show on a graph). b) How could the subsidy be financed? 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? 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?