Environmental Economics

Need to sum the private MC curves horizontally

1 Solve for qi in terms of MCi : MC1 = 6q1 → q1 = 1 6MC1 MC2 = 3q2 → q2 = 1 3MC2 2 Calculate aggregate emission reductions q as a function of aggregate marginal costs MC. Q = q1 + q2 = 1 6MC1 + 1 3MC2 3 Under a cost effective allocation, we know that marginal costs are equal across sources. So we'll drop the subscripts. Q = 1 6MC + 1 3MC = 1 2MC Now solve for aggregate marginal costs as a function of Q: Q = 1 2MC → MC(Q) = 2Q This is the aggregate cost curve for pollution reductions

Do hybrids improve efficiency?

Advantage: cost containment Disadvantage: emissions no longer capped Roberts & Spence (1976) showed that the ex post efficiency loss from imperfect MC estimation is smaller using a hybrid instrument than using either prices or quantities alone. Safety valves and price floors are very common: Bingaman-Specter (2007), Waxman-Markey, etc

Multi-sigma events

Although we're conditioned to think of the normal distribution, we have experienced enough costly 4 or 5 sigma events to know that other distributions must be considered Example: US stock prices fell 23% on October 19, 1987 Daily s.d. from 1950-1986: σ ≈ 1% This is the equivalent of an 11 foot tall woman If stock returns were normal, even a 5% crash would only be observed once every 14,000 years

Tradeable permits: solution

As with taxes, firms choose q to minimize TOTAL policy compliance costs. Total Cost = C(q) | {z } Abatement Cost + A(u − q − e¯) | {z } Net Permit Cost Solution (FOC): MC(q ⋆ ) − A = 0 This says firms reduce pollution until it is cheaper to buy permits This is the same exact condition at the tax solution, with the permit price A replacing the tax in the FOC.

How to set the tax?

Best answer is the Pigouvian approach: set τ equal to marginal benefits (ie Social Cost of Carbon) But we are rarely in a "first best" world either don't know what the benefit function is or can't achieve the social optimum politically So we often have some target Q¯ in mind instead US Paris Pledge: 50% below 2005 levels by 2030 How can we choose τ to achieve a total of Q¯ reductions across all sources?

Example: Clean Air Act NAAQS

CAA of 1970 — beginning of major involvement by Federal government in air pollution control. Two categories of air pollutants Criteria pollutants: thought to be safe at low levels, and common throughout the country SO2 NOx CO Particulates Lead Ozone (formed from NOx and VOCs in sunlight) Hazardous air pollutants: thought to be dangerous at any level, and found in only a few places

National Ambient Air Quality Standards (NAAQS)

CAA requires EPA to set standards for criteria pollutants at levels that protect the public's health with an adequate margin of safety. must consider most sensitive members of population, such as children with asthma, or people who work and exercise outdoors standards to be set without regard to cost of attainment (court interpretation) EPA required to revisit these standards frequently and update as the science changes Where does econ fit in? Health experts pick the NAAQS targets that are safe. We will ask if that target is being met at the lowest possible social cost

Safety-Valve Problem - Part A

Calculate the statically efficient level of emissions reductions, Q*, and the marginal cost of emissions reductions at this level, P*. What are the static net benefits of this policy if the regulator chooses this level? 22 Efficient policy sets MC = MB. So, • 3+Q = 9 - .5Q • Q* = 4 • P*=7. Net benefits are the area under the MB curve and above the MC curve up to the point of the policy. Total benefits = 9Q - .25*(Q)^2= 32. Total costs = 3Q + .5*(Q)^2 = 20. • So, net benefits, NB =12.

The Weitzman Rule

Coasean logic suggests that defining property rights should be equivalent to Pigouvian taxation [absent transaction costs & market power] Weitzman (1974) showed that the instruments are no longer equivalent in the face of cost uncertainty • If |Slope MC| > |Slope MB|, a price instrument (tax) will have lower expected DWL If |Slope MC| < |Slope MB|, a quantity instrument (cap and trade) will have lower expected DWL What's the intuition for this? Benefit uncertainty does not matter Since it's the marginal cost curve that determines outcomes under market based instruments

Policy options

Command and control - Technology standards - Uniform emission standards Market based - Taxes / Subsidies - Cap-and-trade tradeable permits Voluntary measures - [Not covered in this class] How should we choose between these? - legal constraints / justice / rights - political constraints - economic pros and cons

Social Cost of Carbon Summary

Conceptually, the efficient Pigouvian tax should be set at marginal social (external) damages Computing this number for carbon dioxide is incredibly challenging. Mapping each step individually is complex and uncertain, and these interact over decades 2010 US IAWG presented an important first step in computing this number, and that in turn informed the Obama admin SCC Since then, the SCC has played a central role in climate policy both domestically and internationally. For example, as of 2017 the federal government had used the SCC to assess the value of over eighty regulations with a combined $1 trillion in estimated gross benefits.

Safety-Valve Problem - Part C

Congress chooses to use a quantity instrument, mandating emissions reductions equal to the efficient level, Q*. Calculate the expected net benefits of this policy, taking into consideration the fact that marginal costs are uncertain. Assume that there is a 50% chance MC = MCL, and a 50% chance MC = MCH. At Q*=4 • In both cases: Total benefits = 9Q - .25*(Q)^2= 32. • Start with the MCL = Q. Total costs = .5*(Q)^2 = 8 • NB = 32 - 8 = 24. Now take the MCH . = 6 + Q • Total costs = 6Q + .5*(Q)^2 = 32 • NB = 0. So, expected net benefits, ENB = .5*24 +.5*0 = 12

Safety-Valve Example - Setup

Congress is considering a policy to reduce emissions of gunk. Although this pollutant is currently unregulated, an independent review of the issue has found that marginal costs and marginal benefits of pollution control follow the following schedule: MC = 3 + Q • MB = 9 - .5Q Where Q is the quantity of gunk emission reductions.

MBI Benefit #3: More Green Innovation

Consider a polluter with baseline emissions u and abatement costs mc0 (q). Imagine a command and control standard that requires the firm to reduce pollution by x. Now imagine some new "green" technology is available, which, if adopted, reduces the firms marginal abatement costs to mc1 (q) < mc0 (q). How much would the firm be willing to pay for this technology? How much would it reduce emissions if adopted? Now imagine if the policy was implemented as a tax, rather than a command and control standard. How much would the firm be willing to pay for this technology now? Does it abate more now?

Hot spot example

Consider two firm example from first lecture: - MC1 = 6q1 - MC2 = 3q2 Now imagine that these two firms are in two different cities The pollutant is a local pollutant (i.e. non uniformly mixing) Marginal benefit function same in both cities - MB1 = 28 − q1 - MB2 = 28 − q2

Getting to cost-effectiveness in practice

Controlling pollution in a cost-effective way sounds like a good idea. . . . . . but how do we actually do it? Historically, most regulation was "command and control" Technology standards require all polluters to install a piece of pollution control technology Example: CAA required that all cars have catalytic converters Performance standards allow the level of pollution to vary across polluters, but require all polluters achieve the same level of pollution per unit. Example: Car inspection stickers

Steps for finding a cost-effective allocation

Convert total costs to marginal costs 2 Solve a system of equations: Cost-effectiveness Policy constraint 3 Plug the cost-effective quantities back into the MC equations, make sure they are all equal. 4 Integrate or return back to to the total cost equation to calculate the total cost paid by each polluter. Note: marginal costs will be equal but total costs generally won't!

More generally, revenue raised can be useful

Double dividend Reduce labor taxes Pay down debt Build political consensus (most cap-and-trade programs give permits away to politically important polluters) Achieve distributional equity goals Carbon taxes are regressive Invest in R&D that could lower the long run policy cost (?)

MBIs may not be a good idea when the pollutant is highly local

Efficient point: MB = MC Cost effective point: MC equal for all polluters. If some polluters have higher costs than others (which is the motivation for MBIs), then under a cost-effective policy they will pollute more. This means that the areas around those firms will have more pollution than the areas around firms with low costs. If pollution is characterize by increasing marginal damages (typical shape), this will not be efficient. This is the "hot spot" problem

MBIs make sense when a pollutant is uniformly mixing

Efficient point: MB = MC MBI's achieve cost effectiveness by allowing some firms to pollute more than others If the pollutant is uniformly mixing, then it doesn't matter where it's emitted (or which firms pollute): Since the pollution mixes perfectly, MB is the same everywhere. Will also not be a problem if damages are linear (ie if MB is constant) This is the case for greenhouse gases

Tradeable permits: Polluter's problem

Emissions (e) = Baseline (u) - Abatement (q) Firms must provide a permit for every unit of emissions (e) the price of a pollution allowance (permit) is A Firms are given e¯ permits to start Total costs of the policy to the firm are: 1 Abatement costs: C(q) 2 The net cost of permits: A(e − e¯) = A(u − q − e¯)

Can also show this analytically

Emissions(E) = Baseline pollution(U) − Abatement(Q) Notation for these problems Let ui be the "unconstrained" (baseline) emissions at firm i U denotes aggregate baseline emissions, summed over all polluters. Let qi be the emissions abatement at firm i, under some policy Q denotes aggregate policy emission reductions Let ei be the resulting policy emissions at firm i E denotes aggregate policy emissions

A cost-effective solution must satisfy 2 conditions

Eq 1: Cost-Effectiveness Constraint q ⋆ 1 and q ⋆ 1 equate marginal costs: MC1(q ⋆ 1 ) = MC2(q ⋆ 2 ) ie the marginal cost of abatement must be equal for all firms Eq 2: Policy Constraint Total reductions hit the policy target Q¯ = q ⋆ 1 + q ⋆ 2

What happens if we use cap and trade requiring 11 units of emission reductions TOTAL?

Eq1 (Policy Constraint): q1 + q2 = 11 q2 = 11 − q1 Eq2 (Cost effectiveness): MC1 = MC2 2q1 = q2 Solution: - q ′ 1 = 11/3 - q ′ 2 = 33/3 − 11/3 = 22/3 Too much pollution in city 1; too little in 2

How should the government allocate permits?

Example allocation 1: e¯1 = 35 ; e¯2 = 35 To solve C&T problem, two conditions: 1 Cost-effectiveness MC1(q ⋆ 1 ) = MC2(q ⋆ 2 ) 2 policy constraint (cap) condition e ⋆ 1 + e ⋆ 2 = 70 = (u1 − q ⋆ 1 ) + (u2 − q ⋆ 2 ) (u1 + u2) − 70 = (q ⋆ 1 + q ⋆ 2 ) = 30 Since these are the same as the tax case, solution is the same! - q ⋆ 1 = 10 and q ⋆ 2 = 20

Numeric example: Solution

Find q1 and q2 that minimize total cost of reducing emissions by 30. Know the cost effective solution must satisfy two conditions: 1 Cost effectiveness: MC1(q ⋆ 1 ) = MC2(q ⋆ 2 ) 2 Policy target: q ⋆ 1 + q ⋆ 2 = 30 We have two equations and two variables. Simplify and solve: 1 6q1 = 3q2 → 2q1 = q2→ 2 q1 + 2q1 = 30 → Solution: q ⋆ 1 = 10 and q ⋆ 2 = 20

Example: Impose a $60 tax on the firms above

Firm 1's problem: minqTC1 = C1(q1) + τ (u1 − q1) minqTC1 = 3(q1) 2 + 60(60 − q1) FOC: 6q1 − 60 = 0→q ⋆ 1 = 10 Firm 2's problem: minqTC2 = 3 2 (q2) 2 + 60(40 − q2) FOC: 3q2 = 60→q ⋆ 2 = 20 Same solution as above!

How taxes work

Firm has baseline emissions u, and choses emission abatement q Government implements a tax τ for every unit of pollution emitted (e = u − q) If firm does nothing to respond, it's costs are u × τ But firms can respond by reducing emissions at total cost C(q) Question: How much should the firm abate? [draw graph] What are its costs if it sets q = 0? What are its costs if it sets q = u?

Pollution taxes: Polluter's problem

Firm's problem: pick abatement (q) to minimize TOTAL policy compliance costs: Total Cost = C(q) | {z } Abatement Cost + τ (u − q) | {z } Tax Bill Costs of the policy to the firm are: - Abatement costs: C(q) - PLUS taxes on emissions not abated: τ (u − q) First order condition: MC(q) − τ = 0 Implication: the firm want's to reduce pollution up until the point where it is cheaper to pay the tax

Review cap-and-trade and tax equivalence

Firms minimize costs of complying with policy Total costs = Abatement costs + Tax/Permit Costs • Under a tax, cheaper to abate if MC < T • This gives us emissions E(T) = U - Q(T) • Under a cap, a maximum of E emissions allowed • Firms with highest compliance costs buy permits • If we set E = E(T), we'll get Q(T) reductions • Permit price A = T = MC(Q(T))

Safety-Valve Problem - Part D (Solution)

First check the prices at Q* to see if either case binds • MCH = 6 + Q = 10 > 8 • MCL = Q = 4 < 8 The low case is unaffected (P=4, is below the safety valve). In the high case, P=10, so the safety valve will bind in this case. i.e. polluters will prefer to pay the penalty of 8 instead of buying permits at 10 • At the safety valve price, emissions reductions are less than 4 MCH(Q) = 8 = 6 + Q, so Q =2. • Total benefits = 9Q - .25*(Q)^2 = 17. • Gross costs are 6Q + .5Q^2 + 6*2 = 14. So Net Benefits = 3. So, under the safety valve, expected net benefits, ENB = .5*24 + .5*3 = 13.5. • Expected emissions reductions are .5*2 + .5*4 = 3.

Can combine price and quantity instruments into a hybrid instrument

For example, in the context of a cap-and-trade system: Imagine the government announces in advance that it is willing to sell (an unlimited number of) additional allowances at a specific price SV (the trigger price). Sometimes referred to as a "safety-valve" This effectively caps the allowance price A <= SV Once it is reached, this trigger price acts like a tax on additional pollution, fixing marginal abatement costs but expanding the original cap on aggregate emissions. The government can also institute a price floor (PF) --- ie the government commits to buy permits at a fixed minimum price.

Challenge is to combine all these micro estimates into one global damage calculation

For now the all of the IAMs rely on a single (black box) function translating temperature changes to dollars.

The government wants to reduce pollution

How many reductions (q) should come from firm 1 (q1) and how many should come from firm 2 (q2)? add second axis to impose 100 unit target What are the total costs of this policy if firm 1 does everything? (q1 = 100,q2 = 0) What are the total costs of this policy if both firms share the burden equally? (q1 = q2 = 50) What level minimizes costs?

Step 3: Mapping Temperature to Damages

How would you go about doing this? We discussed measuring benefits from environmental protection earlier in the course What were some of those methods? How would you go about applying that in this context? There is a growing body of evidence showing wide ranging effects of climate change (in many different MICRO contexts)

Integrated Assessment Models (IAMs)

IAMS combine insights from science and economics Emissions →GHG concentrations →Temperature →Economic Damages Come at the cost of simplification The 2010 IWG used three IAMs Dynamic Integrated model of Climate & the Economy (DICE) William Nordhuas (2018 Nobel Winner) Climate Framework for Uncertainty, Negotiation and Distribution (FUND) Richard Tol and David Antoff Policy Analysis of the Greenhouse Effect (PAGE) Chris Hope

Price path with a hybrid instrument

If A(QQ ) > safety valve, the government issues more permits • Q < QQ • If A(QQ ) < price floor, the government buys back permits • Q > Q The set of possible prices under this hybrid policy is • PF< A

Firms respond by trading permits (and reducing their emissions)

If a firm's marginal cost is less than the market permit price, then it could make money by reducing its emissions by one unit and selling one of its emissions permits. If its marginal cost is greater than the permit price, then it could reduce its costs by emitting an extra unit and purchasing a permit to cover those emissions. So firm's buy and sell permits until their marginal cost of pollution control is equal to the market price of permits. Since everyone faces the same permit price, the result is cost effectiveness!

What matters in economics is opportunity cost

If you have tickets to the Red Sox tonight, you're willingness to sell them on Stubhub should not depend on how much you paid for them. This is the independence property of tradeable permits: Firms' abatement decisions do not depend on how permits are awarded.

Can't the EPA just set polluter-specific standards at the cost-effective levels?

Imagine the EPA sets separate pollution control requirements for each individual source of emissions. If these requirements are chosen such that all firms have equal marginal costs, the policy will be cost effective In previous example, can mandate q1 = 10 and q2 = 20 How realistic is this? Problem: The government needs to know the exact marginal cost function of every polluter. This is near-impossible for the regulator to observe. Why? can look at accounting data to observe outlays on environmental compliance. but in the relevant economic cost is opportunity cost

Finding a cost-effective allocation graphically

Imagine there are two firms: firm 1 and firm 2 Both produce 100 units of pollution They can reduce pollution at cost C(q), where q is the amount of pollution abatement. It is cheaper for firm 1 to reduce pollution than firm 2 It costs firm 2 50% more to abate: MC2(q) = 1.5MC1(q) The marginal cost of abatement for the 50th unit of pollution at firm 1 is MC1(50) = 100. So MC2(50) = 150

Thus, there is a one to one mapping across the two

Imagine we pick some tax τ ′ . can use the social marginal cost curve to find the resulting abatement Q′ = Q(τ ′ ) emissions under the tax are E(τ ′ ) = U − Q(τ ′ ) If we had instead issued a fixed number of pollution permits E¯ = E ′ We would have gotten Q¯ = U − E ′ reductions by construction We can plug Q¯ into the aggregate marginal cost curve to figure out what the resulting permit price would be Since we picked Q¯ = Q(τ ′ ), the resulting permit price would have been A = τ ′ Implication: Little economic distinction between tax and equivalently strict cap-and-trade (in this simple model)

Policy choice and fat tails

Implication: If things are normally distributed, we will never really be that surprised. However, if the problem has fat tails, we may experience surprise shocks orders of magnitude larger than anything we've every experienced before Why does this matter? When the probability of infinite damages is nonzero, the expected BCA framework breaks down Even a small possibility of infinite damages causes us to spend infinite amount on abatement today At this point expected utility and cost benefit analysis not such a useful framework Economists are still working on this problem

In 2017, Trump admin applied an SCC of just $7

In rolling back the Obama CAFE standards, the Trump admin applied a "domestic" social cost of carbon, essentially excluding costs outside of the United States What do people think of this? Think about the international cooperation problem set

We want to choose the policy with the lowest expected DWL

In this example, DWLP < DWLQ Since MB and MC are linear: Can see this by simply noticing that QP is closer to Q* than QQ So a tax is preferable in this example

Safety-Valve Problem - Part D

Industry is worried about price spikes if emission reductions turn out to be expensive. In order to allay these fears, Congress writes a "safety valve" in to the law. As an alternative to purchasing permits for their emissions, polluters can pay a penalty of $8 for each unit of gunk that they emit. Calculate the expected emissions reductions and net benefits.

Safety-Valve Problem - Part B

It turns out that the estimated marginal cost schedule is actually an average of two competing reports, a high cost estimate and a low cost estimate, which the independent agency considers equally likely. MCH = 6 + Q MCL = Q Given this uncertainty in costs, would you recommend that the regulator use a price or a quantity instrument to regulation gunk? Explain the intuition for your answer.

How does each firm's total cost compare? I

Just showed that we can achieve cost-effectiveness by either: 1 requiring q ⋆ 1 = 10 and q ⋆ 2 = 20 2 taxing firms at $60 per unit of emissions e What are the firm's total costs under these approaches? Command and control: TC1 = 3(q1) 2 = 3(10) 2 = 300 TC2 = 3 2 (q2) 2 = 3 2 (20) 2 = 600$60 emission tax: TC1 = 3(q1) 2 + τ (u1 − q1) = 3(10) 2 + 60(50) = 3300 TC2 = 3 2 (q2) 2 + τ (u2 − q2) = 3 2 (20) 2 + 60(20) = 1800 Why are these so different? - The tax penalizes emissions, C&C just mandates abatement - This has important dynamic implications (next week)

Cost-effectiveness of Pigouvian taxes

Just showed: Each firm responds by reducing its emissions until its marginal cost of pollution control is equal to the tax. If we charge every firm the same tax, this will ensure that the marginal cost of abatement is the same for all firms Necessary condition for cost-effectiveness Note that the government does not need to know MC1 and MC2! Key Result: Any policy that charges firms the same tax will be cost effective

Tradeable permits: Independence property

Lets return to the solution polluter's problem: Total Cost = C(q) | {z } Abatement Cost + A(u − q − e¯) | {z } Net Permit Cost Solution (FOC): MC(q ⋆ ) − A = 0 Firms abate until marginal costs are equal to the permit price Note that the firm's first order condition does not depend on the number of permits it is allocated (e¯) Why not?

What if costs ended up being lower than expected?

MCE > MCR Now Q* > QE * This means that QP is now too high And QQ is now too low But QP is still closer to Q* than QQ This tells us that DWLP < DWLQ

We can check to see if our solution is cost effective

Marginal costs should be equal at the two firms: MC1(q ⋆ 1 ) = 6q ⋆ 1 = 6 · 10 = $60 MC2(q ⋆ 2 ) = 3q ⋆ 2 = 3 · 20 = $60 (yes!) And the pollution constraint should be satisfied: q ⋆ 1 + q ⋆ 2 = 10 + 20 = 30 (yes!) Plug back in to cost curves to get total policy cost (900) C1(q1) = 3(q1) 2 = 300 C2(q2) = 3 2 (q2) 2 = 600

*Properties of Cost-Effective Allocations

Marginal private costs are equal at every firm: MCi(qi) = MCj(qj) ∀i, j. Intuition: arbitrage condition This implies that the marginal social cost of pollution reduction is equal to the marginal private cost of pollution reduction at any firm: MCs(Q⋆ ) = MCi(q ⋆ i ) ∀i Intuition: since they're all equal by construction, we only need to know one firm's marginal cost As a result, the marginal social cost curve is equal to the horizontal sum of the marginal private cost curves.

What happens if we set an emissions cap and realized costs end up higher than expected?

New social optimum Q* MB = MCR Since the government set a cap, the quantity of emissions reduction is still fixed at QQ = QE * But since costs are higher, QE * > Q* Under these costs, the marginal cost at MC(QE *) = A > T What DWL now? - Since QQ > Q*, DWL is the social cost of excessive emissions reductions achieved by the policy

What happens if we set a tax and realized costs end up higher than expected?

New social optimum Q* • MB = MCR If the government chose to use a tax, firms still abate until MCR = T Since T was chosen under MCE < MCR , this will result in too few emission reductions What DWL here? Since Q < Q*, DWL is the social value of beneficial emissions reductions not achieved by the policy

Where does the permit price come from?

Permits allow firms to pollute. Imagine you're a polluter, with enough permits to fully cover your baseline emissions (e¯ = u) - Your marginal cost of reducing pollution is zero for the first unit. - And if you reduce, you can sell that permit to another polluter with positive willingness to pay If the market is "competitive" (ie firms are small), trades like this will occur until the marginal abatement costs of all firms is equal. At that point, the price to buy a permit is equal to the marginal cost of reducing pollution: A = MC(U − E¯ ).

Price and quantity instruments are equivalent in the absence of uncertainty

Policymaker wants to achieve an expected efficient level of pollution QE * • Knows MB and the expected MC Option 1: Price instrument (P) • Set tax T = MC(QE *) Firms abate until MC =T • QP = QE * Option 2: Quantity instrument (Q) • Issue emission permits: # Permits = Baseline - QE * Firms buy permits if MC > A; sell if MC < A • Expected price A = MC(QE *) If MCE is correct, both the tax and the tradeable permit system max net benefits. (Max expected net benefits.)

Taxes and cap-and-trade are both cost-effective

Polluters seek to minimize their cost of complying with the regulation Under a tax, this means they abate until MC = τ ; Under cap-and-trade they abate until MC = A (the permit price) Since ALL polluters face the same marginal cost of polluting, both policies are cost effective Under a cost-effective allocation, the aggregate marginal cost of abatement (across all firms) is simply the horizontal sum of all firms marginal costs So the aggregate marginal cost curve for both policies is the same

MBI Benefit #1: Cost-effectiveness

Primary motivation was cost effectiveness: —Does the policy achieve the environmental goal at the lowest possible cost? Necessary condition: Command-and-control might be cost-effective if: 1 The cost of abatement is the same for all polluters (then you can simply tell them all to do the same thing) 2 OR the cost of pollution at every polluter is known to the regulator (can then figure out how much each firm should abate) If either of these is true, MBI's might be less important. But there are two additional reasons to like them.

Steps for solving a cap and trade problem

Profitable trades will exist whenever MC1 ̸= MC2 Writ large this says that trading will continue until MCs are equal across all firms This no profitable trades condition is identical to the cost effectiveness condition under taxation We also know that the total amount of emissions is capped at E¯ Permits capped: e1 + e2 ≤ E¯ This gives us two equations and two unknowns, just like last time. 1 Cost-effectiveness: MC1(q ⋆ 1 ) = MC2(q ⋆ 2 ) 2 Policy constraint (cap): (u1 − q1) + (u2 − q2) = U − Q = E¯

Under tradeable permits, government locks in a quantity

Quantity of allowable emissions set before MC is known. • U = Q + E, so this is same as setting emissions reductions (QQ ) Firms buy and sell permits based on the realized permit price A = MCR at QQ . We showed in class that permits go to highest value (highest MC) users until MC is the same for all covered firms. Since there is a cap on reductions, permit price A floats to clear the market. If MC is higher than expected, A will be higher than the expected A; If MC is lower than expected, A will be lower. Thus under tradable permits, government locks in quantity of emissions, and let's the price of emission reductions float

This is a key result

Question: How should the government allocate permits (e¯1 and e¯2) to the two firms? Answer: It doesn't matter for cost effectiveness - as long as we assume zero transaction costs. . . . This is just the Coase Theorem! As long as property rights are clearly defined and there are no transaction costs, the efficient allocation is obtained. Note that formally we also need the emitters to all be small ie price takers

Discount rate wrapup

Question: Why don't we invest in capital markets now, earn those returns, and then use that money to abate the carbon problem later? Put differently: We are going to leave a stock of capital to our children. Should we invest in the market or invest in carbon abatement? Many social investments involve large up front costs and long term benefits - education, poverty alleviation, disease eradication Ethically tempting to set a low discount rate for GCC However we need to be consistent - can't invest in everything

Ramsey Formula

Ramsey (1928) inter-generational discount rate formula: r = ηg + ρ g is the growth in per capita consumption (g ≈ 2%) η is the absolute value of the marginal utility of consumption η = 0 → marginal utility of $ does not change w/ income η = 1 → 1% increase income reduces marginal utility by 1% Common Assumptions: .05 < η < 3 ρ is the pure rate of time preference ρ = 2% →person born in 2035 = .5 person born in 2000 Common Assumptions: 0 < ρ < 3 Why not zero?

Intuition for why taxes are cost effective

Remember that a firm's marginal costs increase as it reduces its emissions When the firm's marginal cost of is less than the tax, then it is cheaper for the firm to reduce its emissions by one unit than to pay a tax on that unit. However, when its marginal cost is greater than the tax, then it is cheaper for the firm just to pay the tax and emit the unit of pollution. Optimal firm response: Abate until MC = tax If all firms face the same tax, MC1 = tax = MC2 (etc)

Simultaneous Benefit and Cost Uncertainty and the Choice of Policy Instrument

Same MCE , MCR , MBE , and MBR as before Set policies at T and QQ where MBE = MCE • Positive correlation: MBR > MBE → MCR > MCE Q* now closer to QP than QQ So, result has switched: deadweight loss with tax is now greater than with permits Stavins (1992) Rule: Positive Correlation favors Quantity Instrument (Q) Negative Correlation favors Price Instrument (P)

What is the economically efficient tax?

Scientists have identified 1.5 - 2 degrees of warming as important targets, and the UN reports measure progress relative to the target. The economically efficient Pigouvian tax would be set equal to the marginal damages of CO2 pollution. In 2009 the US formed an inter-agency working group (IAWG) to come up with a number for the social cost of carbon (SCC).

Takeaway from graph

Should be able to show the total costs under any allocation of effort Unless marginal costs are equal, arbitrage lowers total costs. Arbitrage argument: if the the marginal costs of abatement at the two firms weren't equal, then we could shift one unit of abatement from the higher marginal cost firm to the lower marginal cost firm. This would lower the overall cost without changing the quantity of pollution reduced.

Four key steps in calculating SCC

Socioeconomic emissions and pathway Climate model Damage function Discounting

How much does this cost each firm?

Solution gives us implied emissions: e1 = 60 − 10 = 50 and e2 = 40 − 20 = 20 We know permit price is equal to marginal costs: A = MC1(q ⋆ 1 ) = MC2(q ⋆ 2 ) = 60 Total costs = Abatements costs + Permit Costs TC(q ⋆ ) = C(q ⋆ ) + A(e ⋆ − e¯) Firm 1: TC1 = 3(10) 2 + 60(50 − 35) = 1200 Firm 2: TC2 = 3 2 (20) 2 + 60(20 − 35) = −300

Caveat to all of these properties

Some firms (with fixed costs or high marginal costs) might not have any reductions. Remember: firms can't reduce more than baseline emissions.

What happens if costs are uncertain?

Specifically, what if the intercept of MC is unknown? What would cause MC to be higher or lower?

Skinny vs. fat tails

Standard deviation "sigma" captures the likelihood of tail outcomes Typically think in terms of normal distribution: p(> 1σ) ≈ .32 p(> 2σ) ≈ .05 p(> 3σ) ≈ .0027 Example: height of US women is well approximated by a normal distribution with mean 64 inches and s.d. of 3 inches a 6 foot tall woman is 2.66 sigma event 1 out of every 100 women you see

Steps for solving a hybrid problem

Start with the emissions reductions implied by the cap (Qe) • Use the realized marginal cost curve MCr to determine the permit price Ae at that level of emissions reductions. If Ae > SV, firms will save money by paying SV instead. By paying SV, they are able to emit more pollution than the cap would imply. • Set MCr = SV to figure out the implied emission reductions, Qsv < Qe. Compute net benefits by plugging Qsv into the total benefit and cost curves. If Ae > PF, the government reduces the supply of permits. Specifically, they tell firms they must pay the max of either (Ae or PF). Set MCr = PF to figure out the implied emission reductions, Qpf > Qe. Compute net benefits by plugging Qpf into the total benefit and cost curves. If PF < Ae < SV, it's as if the price collar doesn't exist. The price floats to clear the market. Q = Qe.

Example: Acid Rain Program

Sulfur dioxide emissions (primarily from coal) projected high into the atmosphere cause acid rain 1990 Clean Air Act Amendments capped sulfur dioxide emissions from US power plants Emissions capped nationally at 50% (10 million tons) below 1980 by 2000 First large scale cap-and-trade system in the world. Widely regarded as an incredible success Acid rain declined by 70% Net benefits of more than $100 billion

Possible trades under cap-and-trade

Take the graphical example from last class. Wanted 100 units of abatement from firms 1 and 2. Both firms initially produce 100 units of pollution What happens if we give firm 1 has all 100 permits?

Under a tax, government locks in a price

Tax (T) set before MC is known. Firms always abate until realized MCR = T. Thus under at tax, government locks in the marginal price of emissions, and let's the quantity of emission reductions float. If MC ends up being higher, then reductions will be lower than expected • If MC ends up being lower, then reductions will end up being higher than expected

Context: Non-Pigouvian taxes create DWL

The government needs to raise money for a variety of activities (infrastructure, defense, education, etc) Even if everyone agrees these expenditures are net beneficial, raising revenue to pay for them creates deadweight loss Example: Labor taxation Conversely, Pigouvian taxation internalizes an environmental externality, and there reduces deadweight loss in the taxed market. Thus we can use the tax revenue or auctioned permit revenue to reduce other distortionary taxes, while keeping government expenditure fixed. This win-win tax policy is referred to as the "Double Dividend"

Step 2: Map emissions to climate changes

The physical systems that make up our climate are incredibly complex. There are very sophisticated models being developed to improve our ability to answer this question. The models used in these IAMs are no where near that frontier. Instead these models typically reduce all that complexity to single climate sensitivity parameter: the average surface warming resulting from a doubling of CO2, in equilibrium There is enormous uncertainty about this parameter (will get to this later). But it's also inherently simplistic, relative to how complex the climate is.

*Properties of Cost-Effective Allocations

The total social cost curve is always below (or equal to) the lowest total private cost curve: Cs(Q) ≤ Ci(Q) ∀i, Q Intuition: The social planner assigns emissions reductions to the lowest cost firms. So by spreading emissions out, the social cost can't be higher than the lowest cost firm's costs of achieving the same target

Also need put damages in present value terms

These benefits tell us the damages each year in the future. Present Value = Future Value (1 + r) t What is the "right" discount rate r to use? Two reasons to discount across generations: 1 future generations will be better off 2 we value current generation more

An alternative approach is to use incentives

This is a "market based" approach For example, rather than prescribing how much every firm must abate, instead make firms pay a tax for every unit of pollution they emit. How does this curb pollution? What was the analogy in the Hausman video?

Alternatively, the government can auction off the permits

This sets e¯ = 0 for all firms This is equivalent to a vertical supply curve at Q¯ . While the demand curve for permits is just the reflection of the marginal abatment cost curve (graph this) Polluters will bid up to their marginal abatement costs in the auction. The highest bidders get selected until the permits run out. At this point, the price of the auction is the marginal cost of the last bidder, ie A = MC(U − E¯ ). The benefit is that the government raises A ∗ E¯ dollars in revenue.

Cap-and-trade (tradable permits)

To solve the previous problem, government still needed to know the aggregate MC curve An alternative would be for the government to just set the pollution level directly by issuing pollution permits, and requiring firms to relinquish one permit for every unit of pollution they emit.

Numerical Example

Two firms, with 100 units of aggregate baseline pollution baseline emissions for firm 1: u1 = 60 baseline emissions for firm 2: u2 = 40 Total costs (C) of abatement for each firm: C1(q1) = 3(q1) 2 C2(q2) = 3 2 (q2) 2 where q are units of emission reduction Government would like to reduce overall emissions by 30 units. What is the cost-effective allocation of emissions reductions to achieve this goal?

Numerical Example Revisited

Two firms, with 100 units of aggregate baseline pollution baseline emissions for firm 1: u1 = 60 baseline emissions for firm 2: u2 = 40 Total costs (C) of abatement for each firm: C1(q1) = 3(q1) 2 C2(q2) = 3 2 (q2) 2 where q are units of emission reduction Government would like to reduce overall emissions by 30 units. What tax on emissions cost-effectively achieves this target?

Why do we care about permit price uncertainty?

Uncertain prices make it very difficult for firms to make investment decisions This may cause them to delay investments If risk averse, could reduce investments • Carbon tax eliminates price risk... Which type of pollutants does it make sense to smooth prices over time for?

MBI's provide greater incentives for innovation

Under C&C regulation, firms only care about meeting the regulation (costs just a function of reductions) Under the tax, a firm also cares about reducing its tax burden. Thus, even if the government has perfect information on cost curves, it will be more cost effective in the long run to use incentive based regulation.

What is the efficient amount of q1 and q2?

Want MB1 = MC1 and MB2 = MC2 Implies: 28 − q1 = 6q1 → q ∗ 1 = 4 28 − q2 = 3q2 → q ∗ 2 = 7

Step 1: Predicting baseline

What factors are important for determining CO2 emissions over the next 100 years? What factors are important for determining CO2 emissions over the next 100 years? Useful decomposition: Kaya Identity F = P × G P × E G × F E F is global CO2 emissions from human sources P is global population G is world GDP E is global energy consumption What will baseline emissions look like?

Banking and Borrowing

What happens if firms can bank/ borrow permits across years? With dynamic decisions (saving or borrowing), firms equate discounted marginal profits from each dynamic in put across years • Single year: FV=(1+r)PV • Hotelling rule: Permit prices will rise by the interest rate Absent uncertainty Price volatility will be mitigated by private incentives If costs are high this year, they will borrow permits from future and abate less If costs are low they will do more abatement and save permits for future high cost years

Algebraic solution

What is the cost-effective way to reduce pollution by Q¯ units? ie what choice of q1 and q2 will solve the problem: min q1,q2 [C1(q1) + C2(q2)] s.t. q1 + q2 ≥ Q

What do these properties imply for cost effective

What was the difference between Kyoto and Paris? Kyoto: Only Annex I countries (narrow and deep approach) Paris: Whole world (shallow but broad)

When are MBI's NOT a good idea?

When costs are homogenous across sources - For example if a single control technology is obviously ideal - [note gains from revenue and dynamic efficiency] When monitoring is costly - If number of regulated entities is very high - Example: tailpipe emissions When implementation involves costs that undermine the program - Remember the Coase Theorem! Cap and trade may not be cost effective when transaction costs are high and permits are not auctioned. When marginal benefits vary across sources

How much should we pay to reduce CO2

Would represent the efficient tax Even without that, necessary for conducting mandatory RIAs Overview Four steps in estimating the consequences of CO2 emissions Discuss uncertainty Discounting

The economic importance of tail events

[This section based on Nordhaus 2011] For some policy problems, our main concern is with very extreme outcomes Examples: - Hiroshima - 9/11 - Financial collapse In these situations, the shape/ tail of the distribution matters more than the mean Did those distributions of climate sensitivity look normal?

Why can't the government just ask firms to report their costs

in previous problem, firm 2 has lower costs. C1(q1) = 3(q1) 2 C2(q2) = 3 2 (q2) 2 as a result q ∗ 1 = 10 < q ∗ 2 = 20 C1(q1) = 3(q1) 2 = 300 C2(q2) = 3 2 (q2) 2 = 600 if firm 1 lied and reported the same cost function as firm 2, it would have only had to reduce pollution by 15, for a total cost of 337.5.

What matters is the relative slopes of MB and MC

steeper than MB Here we show that the situation is reversed if MC is flatter than MB Now the tradeable permit approach is more efficient than the tax: DWLP > DWLQ Weitzman (1974) Rule: MC Slope > MB Slope Price Instrument MC Slope MB Slope Quantity Instrument

Revisiting our numerical example using permits

two firms that emit 100 of baseline pollution: u1 = 60 u2 = 40 Total costs of abatement for each firm: C1(q1) = 3(q1) 2 C2(q2) = 3 2 (q2) 2 Government wants to reduce overall emissions by 30 units. Set the cap equal the baseline emissions minus the desired emissions reductions. E¯ = U − Q¯ = 100 − 30 = 70

What if the benefits are uncertain, not the costs?

• Now MBR > MBE • What matters for determining outcome of the policy is the marginal cost curve: • Under a tax, MC determines Q • Under a cap, MC determines P If only benefits are uncertain, then both instruments are equally inefficient • So, benefit uncertainty has no effect on which instrument is more efficient