Lecture 05

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# Roadmap

1. What are the different kinds of price instruments in theory and the real world?
2. What happens under a tax?

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# Taxes

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# Emission taxes

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# Emission taxes

The main tax we will focus on is an .hi[emission tax]

When a polluter faces an emission tax, it must pay a fee `$\tau$` to the regulator for each unit of emissions `$E$`

It is as if the government claimed the property rights to the air on behalf of the citizens, and then sold the rights to pollute back to the firm at price `$\tau$`

Solves the two big problems with externalities:

1. Poorly defined property rights (assigned to the regulator)
2. High transactions costs (pay a flat fee)

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# Emission taxes

What is the socially optimal tax?

The `$\tau$` that minimizes total social cost: abatement cost + damages (ignore tax payments since they're just a transfer from firms to the regulator)

Let `$C(E)$` be abatement cost of emissions level `$E$` and `$D(E)$` be damages at `$E$`

We know abatement costs are decreasing in emissions and damages are increasing in emissions

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# Emission taxes

To figure out the socially optimal tax we need to know how the firm and regulator make decisions

First lets set up the firm problem: they want to minimize the cost of satisfying the policy

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# Emission taxes: firm

The firm's problem is then:
$$ \min_E C(E) + \tau E$$

The firm's first-order condition to minimize costs is:
`$$\underbrace{-C'(E^*)}_{\text{MAC}} = \tau$$`

The firm minimizes costs by choosing emissions `$E^*$` so that its MAC equals the tax

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# Emission standards: firm

The firm minimizes costs by choosing emissions so that its MAC equals the tax

This makes sense!

The tax is the PMC of emitting, the MAC is the PMB of emitting (reduced abatement cost)

Costs are minimized when these two things are equal

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# Emission taxes: regulator

The regulator's problem is to maximize social welfare / minimize total costs of abatement and damages

We already know this occurs when:
`$$-C'(E^*) = D'(E^*)$$`
--

but we know that firms select `$E^*$` so that:
`$$-C'(E^*) = \tau$$`

This means that the regulator's optimal tax is given by:
`$$\tau^* = D'(E^*)$$`

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# Emission taxes: regulator

The optimal tax is equal to the MD .hi[at the optimal emission level]

This also makes a lot of sense

We want the firm to act as if they are bearing the damage costs on the margin

The tax actually makes them bear a cost exactly equal to marginal damage

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# Emission taxes: graphical

![taxes](05-slides-taxes_files/figure-html/tax-1.png)
]

The optimal tax equals MD at `$E^*$`

You can think of this as the firm being forced to pay for damages equal to the cost of the last unit of emissions

In addition to paying abatement cost equal to the red area `$B$`, the firm also has a tax payment equal to the blue area `$F+G$`

]

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# Emission taxes: real world

Australia started carbon tax on July 1, 2012

$23 AUD per ton of carbon emitted for large emitters as a response to the Copenhagen Accord of 2009

Australia hopes to reduce carbon emissions by 80% below 2000 levels by 2050

Started by Julia Gillard government and revoked by Tony Abbott government in July 2014

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# Emission taxes: real world

In 2008, the province of British Columbia implemented North America’s first broad-based carbon tax

The carbon tax applies to the purchase and use of fossil fuels and covers approximately 70% of provincial greenhouse gas emissions

Beginning April 1, 2018, B.C.'s carbon tax rate is $35 per tonne of carbon dioxide equivalent emissions

To improve affordability, government increased the Climate Action Tax Credit

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# Subsidies

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# Abatement subsidies

What is the socially optimal abatement subsidy `$s$`?

The `$s$` that minimizes total social cost: abatement cost + damages (ignore tax payments since they're just a transfer from firms to the regulator)

Let `$C(E)$` be abatement cost of emissions level `$E$` and `$D(E)$` be damages at `$E$`

First lets set up the firm problem: they want to minimize the cost of satisfying the policy

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# Abatement subsidies: firm

The firm's problem is then:
$$ \min_E C(E) - s(E_0-E)$$
where we are substituting in `$E_0-E$` for `$A$`

The firm's first-order condition to minimize costs is:
`$$-C'(E^*) = s$$`

The firm minimizes costs by choosing emissions `$E^*$` so that its MAC equals the subsidy rate!

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# Abatement subsidies: firm

The firm minimizes costs by choosing emissions so that its MAC equals the subsidy rate

This makes sense!

The subsidy is the MC of emitting: the forgone abatement subsidy

The MAC is the marginal benefit of emitting (reduced abatement cost)

Costs are minimized when these two things are equal

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# Abatement subsidies: firm

The regulator's problem is to minimize the social cost of emissions, we know they want to set:
`$$-C'(E^*) = D'(E^*)$$`
--

but we know that firms set:
`$$-C'(E^*) = s$$`

This means that the regulator wants to set:
`$$s^* = D'(E^*)$$`

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# Emission taxes: regulator

The optimal subsidy is equal to the MD at the optimal emission level

This also makes a lot of sense

We want the firm to act as if they are bearing the damage costs on the marginal

The subsidy actually makes them bear a cost exactly equal to marginal damage

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# Abatement subsidies: graphical

![subsidies](05-slides-taxes_files/figure-html/subsidies-1.png)
]

The optimal subsidy equals MD at `$E^*$`

You can think of this as the firm being forced to pay for damages equal to the cost of the last unit of emissions

In addition to paying abatement cost equal to the red area `$B$`, the firm also has subsidy **revenues** equal to the red+blue area `$B+F$`

]

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# Abatement subsidies

It is as if the government claimed the property rights to the air on behalf of the firm, and then pays the firm for the right to clean air on behalf of the citizens

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# Taxes vs Standards
<center>
<img src="files/05-bakken.png" width="80%" />
</center>

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# Taxes vs Standards

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# Emission taxes

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# Unconventional oil

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# Unconventional oil

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# Unconventional oil

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# Flaring regulations in North Dakota

North Dakota Industrial Commission established firm-level flaring limits beginning in October 2014

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# Flaring regulations in North Dakota

This is a .hi-blue[standard]: a mandate on the quantity of gas captured

It was applied uniformly across firms

We know that means it'll be inefficient

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# Real world MACs

Firms appear to be cost-minimizing to comply

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# Real world MACs

But this doesn't mean total costs are minimized given the quantity of gas captured

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# What if we used a tax?

What if we set a tax instead of a standard?

Suppose we just used the existing *public* lands royalty rate

We could capture 99% of the gas as the regulation, but 50% of the cost

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# Almost everyone is better off

The majority of firms are better off with a tax