Lecture 09

.title[
# Lecture 09
]
.subtitle[
## Carbon Tariffs
]
.author[
### Ivan Rudik
]
.date[
### AEM 4510
]

---

``` r
if (!require("pacman")) install.packages("pacman")
```

```
## Loading required package: pacman
```

``` r
pacman::p_load(
  tidyverse, xaringanExtra, rlang, patchwork, ragg
)
source("R/video_helpers.R")
source("R/09-carbon-tariffs-figures.R")
options(htmltools.dir.version = FALSE)
knitr::opts_hooks$set(fig.callout = function(options) {
  if (options$fig.callout) {
    options$echo <- FALSE
  }
  options
})
knitr::opts_chunk$set(
  cache = TRUE,
  cache.extra = list(
    tools::md5sum("R/09-carbon-tariffs-figures.R"),
    tools::md5sum("R/video_helpers.R")
  ),
  echo = TRUE,
  fig.align = "center",
  dev = "ragg_png",
  dpi = 220,
  fig.retina = 2
)
```

```
## Warning in xaringanExtra::style_panelset(panel_tab_color_active = "red"): 'xaringanExtra::style_panelset' is deprecated.
## Use 'style_panelset_tabs' instead.
## See help("Deprecated")
```

```
## Warning in style_panelset_tabs(...): The argument names of `style_panelset()`
## changed in xaringanExtra 0.1.0. Please refer to the documentation to update to
## the latest names.
```

```
## NULL
```

---

# Roadmap

1. What are carbon tariffs?
2. Basic trade theory: supply, demand, and tariffs
3. Adding pollution externalities to trade
4. Unilateral carbon taxes and leakage
5. Carbon tariffs to prevent leakage
6. Carbon tariffs alone
7. World carbon taxes
8. Different pollution intensities across countries

---

# What are carbon tariffs?

---

# Carbon tariffs

Carbon tariffs are tariffs imposed on imports based on their .hi[carbon content]

Why would we want carbon tariffs?

1. .hi[Leakage:] if country `$i$` imposes a carbon tax, production may shift to country `$j$` with no carbon tax

2. .hi[Competitiveness:] domestic firms face higher costs than foreign competitors

Carbon tariffs aim to "level the playing field" and reduce leakage

---

# Carbon tariffs in practice

.hi[EU Carbon Border Adjustment Mechanism (CBAM):]
- Reporting began in 2023, the definitive regime began in January 2026
- Covers cement, iron/steel, aluminum, fertilizers, electricity, hydrogen
- Importers must purchase certificates matching EU ETS price

???

Status checked October 27, 2026
EU CBAM definitive regime began January 1, 2026, with the financial obligation phased in alongside the removal of free EU ETS allowances
https://taxation-customs.ec.europa.eu/carbon-border-adjustment-mechanism/cbam-definitive-regime_en
https://www.gov.uk/government/publications/carbon-border-adjustment-mechanism-cbam-policy-summary/carbon-border-adjustment-mechanism-cbam-policy-summary
US bill status sources are in the following slides

---

# Clean Competition Act (CCA)

Senator Sheldon Whitehouse (D, RI) and Representative Suzan DelBene (D, WA)

Reintroduced December 2025, still in committee as of October 2026

Would cover goods such as steel, aluminum, cement, and fertilizer

???

S 3523 and HR 6787, introduced December 17, 2025, still in committee as of October 27, 2026
https://www.congress.gov/bill/119th-congress/senate-bill/3523/all-actions
https://www.congress.gov/bill/119th-congress/house-bill/6787/all-actions

---
count: false

# Clean Competition Act (CCA)

Covered domestic producers and importers would pay for emissions above an industry benchmark

- The benchmark starts at the US industry's average emissions intensity
- It tightens over time, encouraging cleaner production

- The charge starts at 60 dollars per metric ton of CO₂e above the benchmark
- Revenue supports cleaner industrial production

???

Checked October 27, 2026
S 3523 and HR 6787 were introduced December 17, 2025 and remain at the committee referral stage, neither has passed a chamber or become law
Senate sponsor Sheldon Whitehouse, House sponsor Suzan DelBene
https://www.congress.gov/bill/119th-congress/senate-bill/3523/all-actions
https://www.congress.gov/bill/119th-congress/house-bill/6787/all-actions
https://www.govinfo.gov/content/pkg/BILLS-119s3523is/html/BILLS-119s3523is.htm
https://www.epw.senate.gov/public/_cache/files/8/1/818a8365-fa0d-4e8d-b674-566a889a8fb3/217FD9365EBCD164038C604CF072701FD70A7EF0DE549E2D71790B3461220050.clean-competition-act-2025---1-pager.pdf
The 2025 version starts at $60 per metric ton CO2e and increases 6 percent plus inflation annually
The initial benchmark uses average 2025 industry emissions intensity, with tighter benchmarks thereafter
This is an intensity standard with a border charge, rather than the uniform tax on every unit of emissions in the simple model used later
Exports receive adjustments and there are exemptions and credits, so the slide describes the central mechanism
The schedule in the bill is proposed, it is not an implementation schedule for an enacted law
Revenue supports industrial decarbonization in the US and abroad

---

# Foreign Pollution Fee Act (FPFA)

Senators Bill Cassidy (R, LA) and Lindsey Graham (R, SC)

Reintroduced April 2025, still in committee as of October 2026

- Importers would pay a percentage of import value based on how much more emissions intensive a product is than the US benchmark
- Covers goods such as steel, aluminum, cement, and fertilizer
- The bill creates no carbon tax or fee on domestic production

Sponsors emphasize US manufacturing competitiveness and competition with China

This connects to the tariff alone case we will study later

???

Checked October 27, 2026
S 1325 was introduced April 8, 2025, with the latest listed action referral to Senate Finance on that date, it has not passed either chamber or become law
https://www.congress.gov/bill/119th-congress/senate-bill/1325
https://www.govinfo.gov/bulkdata/BILLSTATUS/119/s/BILLSTATUS-119s1325.xml
https://www.govinfo.gov/content/pkg/BILLS-119s1325is/html/BILLS-119s1325is.htm
https://www.cassidy.senate.gov/wp-content/uploads/2025/04/FPF_Section_by_Section_Summary_2025.pdf
The fee is a percentage of import value, with tiers linked to the pollution intensity gap and special treatment of nonmarket economies and foreign entities of concern
It is not a uniform dollar charge per ton equal to marginal damage
The bill expressly disclaims authority for any carbon tax or fee on domestically produced goods
The tariff alone description identifies the domestic versus import coverage, not every detail of the bill's fee formula
Competitiveness is the sponsors' stated motivation, not a claim that the proposal necessarily improves US welfare
https://www.cassidy.senate.gov/newsroom/press-releases/cassidy-graham-release-discussion-draft-on-trade-manufacturing-policy-to-hold-china-accountable/

---

# Comparing the two US proposals

<video width="900" height="506" controls playsinline preload="metadata" poster="videos/09-carbon-tariffs-cca-fpfa-poster.jpg" style="display:block;margin:auto;object-fit:contain;background:#000;" onplay="document.querySelectorAll('video').forEach(v => { if (v !== this) v.pause(); });">
<source src="videos/09-carbon-tariffs-cca-fpfa-playback.mp4" type="video/mp4"/>
<source src="videos/09-carbon-tariffs-cca-fpfa-playback.webm" type="video/webm"/>
</video>

???

Katarina Nehrkorn, Resources for the Future, In Focus: Carbon Border Adjustment Mechanisms, December 18, 2025
https://www.resources.org/in-focus/in-focus-carbon-border-adjustment-mechanisms-cca-fpfa/
https://www.youtube.com/watch?v=Z0bkGR6KCT4
This video compares the CCA and FPFA and discusses RFF's modeling of the proposed policies
Any modeled effects in the video are projections, not observed effects of enacted policies
The accompanying RFF webpage says December 18 for CCA reintroduction, but Congress records give December 17

---

# Understanding border carbon adjustments

<video width="900" controls preload="metadata" style="display:block;margin:auto;" onplay="document.querySelectorAll('video').forEach(v => { if (v !== this) v.pause(); });"><source src="videos/09-carbon-tariffs-bca-explained.mp4" type="video/mp4"><track kind="captions" src="videos/09-carbon-tariffs-bca-explained.en.vtt" srclang="en" label="English" default></video>

---

# This lecture

We will use a simple framework from Brunel and Levinson (2024) to understand:

1. How carbon tariffs work in theory

2. When they improve welfare

3. What complications arise in practice

The key insight: carbon tariffs are equivalent to a .hi[consumption tax] plus a .hi[production subsidy]

---

# Basic trade theory

---

# Tariffs are taxes on imports

A tariff is a .hi[tax on imports]

In this lecture we study the small open country case:
- Small: country `$i$` is too small to affect the world price
- Open: the country trades goods with the rest of the world
- Imports are available at the fixed world price `$P_W$`, regardless of how much this country imports
- This is what makes leakage especially transparent later on

---

# A simple trade model

Consider a small open economy (country `$i$`) that:
- Takes world prices `$P_W$` as given
- Can import or export a homogeneous good

Key curves:
- `$S$`: domestic supply
- `$D$`: domestic demand
- `$P_W$`: world price
    - The social marginal benefit of the good

Domestic suppliers can't charge more than `$P_W$`, and won't charge less

---

# Supply and demand refresher

In this market:

- `$D$` is .hi[marginal benefit] to domestic consumers

- `$S$` is .hi[marginal cost] to domestic producers

- If `$P_W$` is below the autarky (no trade) price, country `$i$` imports the good

- The gap between domestic demand and domestic supply is imports

---

# Free trade benchmark

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-free-trade-curves-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Start with domestic supply `$S$` and demand `$D$`

]

---
count: false
# Free trade benchmark

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-free-trade-world_price-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Free trade makes imports available at the world price `$P_W$`

]

---
count: false
# Free trade benchmark

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-free-trade-autarky-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Without trade (autarky), the price is `$P_A$`

Domestic supply equals domestic demand: there is no surplus or shortage

The world price `$P_W$` is lower, so the country imports with free trade

]

---
count: false
# Free trade benchmark

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-free-trade-quantities-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

At `$P_W$`:

- Consumers want to buy `$q_i^D$`
- Producers want to sell `$q_i^S$`

]

---
count: false
# Free trade benchmark

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-free-trade-shortfall-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

At `$P_W$`, consumers want more than domestic producers supply

The domestic shortfall is `$q_i^D - q_i^S$`

]

---
count: false
# Free trade benchmark

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-free-trade-imports-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Imports fill the domestic shortfall

`$$\text{Imports} = q_i^D - q_i^S$$`

Domestic production plus imports meets domestic demand

]

---
count: false
# The tariff

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-tariff-build-intro-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Suppose we add a tariff of `$\tau$` dollars per unit on top of the imported good's price `$P_W$`

]

---
count: false
# The tariff

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-tariff-build-import-price-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

It now costs `$P_W + \tau$` to buy the imported good

What do domestic producers do?

]

---
count: false
# The tariff

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-tariff-build-domestic-price-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Domestic producers can now raise their price to `$P_W + \tau$`

Imports no longer offer consumers a cheaper alternative

]

---
count: false
# The tariff

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-tariff-build-consumer-price-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Consumers face a price of `$P_W + \tau$` no matter who they buy from

The domestic price rises by `$\tau$`

]

---
count: false
# Quantity effects of a tariff

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-tariff-build-quantities-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

At the higher price:

- Domestic producers sell more
- Consumers buy less

]

---
count: false
# Quantity effects of a tariff

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-tariff-build-imports-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Imports shrink

More domestic production and less consumption both reduce imports

Reducing imports is often the stated purpose of tariffs, as in Trump's focus on trade deficits

]

???

Policy motivation example: Trump's April 2, 2025 tariff order explicitly targets
large and persistent US goods trade deficits.
https://www.whitehouse.gov/presidential-actions/2025/04/regulating-imports-with-a-reciprocal-tariff-to-rectify-trade-practices-that-contribute-to-large-and-persistent-annual-united-states-goods-trade-deficits/

This diagram shows imports falling in one market. It does not establish that
the economy's aggregate trade deficit falls: exports and other markets can
also respond. The slide describes a stated policy goal.

---
count: false
# Tariff revenue

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-tariff-build-revenue-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

The government collects the tariff on each unit imported

`$$R = \tau \times \left(q_{i\tau}^D - q_{i\tau}^S\right)$$`

The shaded rectangle is tariff revenue: the tariff per unit times imports

]

---
count: false
# Consumer surplus refresher

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-consumer-surplus-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Consumer surplus is the area below demand and above price

- Blue rectangle: consumers pay more on the units they still buy
- Orange triangle: consumers stop buying units they still valued above `$P_W$`

]

---
count: false
# Producer surplus refresher

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-producer-surplus-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Producer surplus is the area above supply and below price

- Blue rectangle: producers receive a higher price on their original output
- Orange triangle: producers gain extra surplus when they expand output to `$q_{i\tau}^S$`

]

---
count: false
# Consumer loss and redistribution

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-tariff-stage3.05-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

- `$-\Delta CS = a + b + c + d + e$`
- The whole shaded area is the .hi[consumer surplus loss]
- But `$a+b$` reappear as part of .hi[producer surplus gain]
- And `$d$` reappears as .hi[tariff revenue]

]

---
count: false
# Tariff welfare accounting

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-tariff-stage3.1-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

- `$\Delta PS = a + b$`
- `$\Delta CS = -(a + b + c + d + e)$`
- `$R = d$` is tariff revenue
- `$\Delta W_i = \Delta PS + R + \Delta CS$`
- So for a .hi[small country], `$\Delta W_i = -c - e$`
- The only net welfare losses are the two deadweight loss regions `$c$` and `$e$`

]

---
count: false
# Production distortion

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-tariff-stage4-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Triangle `$c$`: producing in the more expensive country

- The tariff shifts production from cheaper foreign producers to more costly domestic producers
- The extra production cost is deadweight loss

]

---
count: false
# Consumption distortion

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-tariff-stage5-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Triangle `$e$`: consuming too little of the good

- Consumers stop buying units they value more than the world price `$P_W$`
- These lost gains from consumption are deadweight loss

]

---

# Why start with ordinary tariffs?

In a .hi[small open economy], an ordinary tariff is a private welfare loss: it transfers surplus around inside the country but leaves deadweight loss `$c+e$`

- Consumer surplus falls by `$a+b+c+d+e$`
- Producer surplus rises by `$a+b$`
- Government revenue is `$d$`, so the private net loss is the deadweight loss `$c+e$`

Carbon tariffs are only potentially useful because there is .hi[another distortion] missing from this diagram: production creates pollution

So next we add the environmental externality to this standard tariff benchmark

---

# Adding pollution

---

# Production creates pollution

Now suppose production of this good creates pollution

Let `$e$` = emissions per unit of output (same everywhere for now)

Let `$d$` = marginal damage from emissions (global pollutant)

The .hi[social marginal cost (SMC)] of production is: `$SMC = S + e \times d$`

SMC lies above the private supply curve by the external cost `$e \times d$`

---

# Free trade with pollution

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig2a-pollution-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Free trade output is pinned down by domestic demand and supply at the world price

]

---
count: false
# Free trade with pollution

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig2a-pollution-stage2-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Country `$i$`'s SMC curve lies above its private supply curve

The vertical gap is the external cost: `$e \times d$`

]

---
count: false
# Free trade with pollution

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig2a-pollution-stage3-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

The green region shows the welfare loss from excessive domestic production, counting global environmental damages and holding foreign production fixed

]

---
count: false
# Free trade with pollution

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig2a-pollution-stage4-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

At the world price `$P_W$`, marginal benefit is pinned down by world demand, while marginal social cost is given by `$SMC$`

That triangle is the set of units for which marginal benefit exceeds private supply cost but is below marginal social cost

]

---

# Global perspective

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig2b-world-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

From a global perspective:
- Free trade output is where `$D = S$`
- Efficient output is where `$D = SMC$`
- The green region is the global welfare gain from cutting output from `$Q_W$` to `$Q_W^*$`

]

---

# Country and global perspectives

Global DWL on the right is the sum of each country's DWL on the left

---

# The externality problem

With a global pollutant like `$CO_2$`:

- Same marginal damages occur regardless of where emissions happen
- No country has incentive to fully internalize the externality
- Unpriced emissions lead to .hi[too much production] globally, with or without trade

A global carbon tax `$= e \times d$` would achieve efficiency

But what if only .hi[one country] acts?

---

# Unilateral carbon tax

---

# Country `$i$` imposes a carbon tax

Suppose country `$i$` imposes a carbon tax `$t = e \times d$` on domestic production

This shifts country `$i$`'s supply curve up by `$t$`

But the .hi[world price doesn't change] (small open economy)

So the carbon tax reduces the net price domestic producers receive from `$P_W$` to `$P_W - t$`

---

# Effects of unilateral carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig3-unilateral-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Before the tax, producers receive `$P_W$` and supply `$q_i^S$`

Their marginal production cost equals the price they receive

]

---
count: false
# Effects of unilateral carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig3-unilateral-shift-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

First view: shift supply up by the tax `$t = e \times d$`

Firms need a price that covers production cost plus tax

`$$S_i(q) + t = P_W$$`

Output falls to `$q_{it}^S$`

]

---
count: false
# Effects of unilateral carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig3-unilateral-net_price-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Equivalent view: keep the original supply curve

Producers receive `$P_W$` but pay `$t$`, leaving `$P_W - t$`

`$$S_i(q) = P_W - t$$`

The same output `$q_{it}^S$` results

]

---
count: false
# Effects of unilateral carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig3-unilateral-stage2-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

After the tax:
- Consumers still face the world price `$P_W$`
- But with a tax `$t$`, producers receive the net of tax price `$P_W - t$`
- Domestic output falls to `$q_{it}^S$`

]

---
count: false
# Effects of unilateral carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig3-unilateral-question-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

.hi[Leakage] comes next:
- Consumers in country `$i$` still demand `$q_i^D$` at price `$P_W$`
- Imports rise enough to offset the fall in domestic output
- Foreign production replaces home production: that is leakage

So what happens to production and emissions globally?

]

---
count: false
# Effects of unilateral carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig3-unilateral-stage3-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

]

---
count: false
# Effects of unilateral carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig3-unilateral-stage4-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

From country `$i$`'s perspective:
- Consumer surplus does not change: they still pay `$P_W$` and consume `$q_i^D$`
- The government gains revenue `$R_t$`

]

---
count: false
# Effects of unilateral carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig3-unilateral-stage6-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

From country `$i$`'s perspective:
- Producers lose producer surplus equal to `$R_t + d$`

]

---
count: false
# Effects of unilateral carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig3-unilateral-stage7-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Why do producers lose `$R_t + d$`?
- Blue rectangle: they receive a lower net of tax price on the units they still sell
- Orange triangle: they also stop selling the units between `$q_{it}^S$` and `$q_i^S$` for which their PMC `$< P_W$`

]

---
count: false
# Effects of unilateral carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig3-unilateral-stage8-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Why is `$d$` the country's deadweight loss?
- `$R_t$` is only a transfer from producers to the government, so it stays inside country `$i$`
- Net national effect: `$+R_t - (R_t + d) = -d$`

]

---
count: false
# Effects of unilateral carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig3-unilateral-stage9-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Why does leakage make `$d$` the relevant national loss?
- The triangle `$d$` is the pure private loss left after netting out the transfer `$R_t$`
- Consumers in country `$i$` are unaffected and imports replace the lost domestic output/emissions

]

---
count: false
# Effects of unilateral carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig3-unilateral-stage10-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Why does leakage make `$d$` the relevant national loss?
- The tax reduces home production, but foreign production rises 1-for-1: that is leakage
- The environmental gain is offset abroad, so country `$i$` is left with the private DWL `$d$`

]

---

# Unilateral carbon tax effects

The increase in imports means .hi[foreign production increases]

This is .hi[carbon leakage]: emissions shift abroad rather than being reduced

- Country `$i$` raises its marginal production costs through the carbon tax

- Country `$i$` producers supply less at any price with a higher MC

- World price is unchanged at `$P_W$` so quantity demanded domestically for the good does not change

- Imports from abroad fill in the difference

- Production and emissions increase abroad

---

# Leakage undermines the tax

With identical carbon intensities and a small country implementing the tax (so `$P_W$` is fixed):
- 1 unit fewer domestic production = 1 unit more foreign production
- .hi[Net global emissions unchanged!]

The carbon tax:
- Generates tax revenue `$R_t$` (rectangle)
- Creates deadweight loss `$d$` (triangle) from production distortion
- Achieves .hi[zero environmental benefit]

Country `$i$` bears costs but gets no environmental gain

---

# Leakage is a rate, not a constant

Economists often summarize leakage with the .hi[leakage rate]:

$$
\text{Leakage rate} = \frac{\Delta E_j}{-\Delta E_i}
$$

where `$\Delta E_i < 0$` is the change in home emissions and `$\Delta E_j > 0$` is the change in foreign emissions

---

# Leakage is a rate, not a constant

$$
\text{Leakage rate} = \frac{\Delta E_j}{-\Delta E_i}
$$

Benchmarks:
- `$0$`: no foreign offset
- Between `$0$` and `$1$`: global emissions still fall, but less than the domestic reduction
- `$1$`: one for one offset, as in this small open economy example with identical intensities
- Greater than `$1$`: possible if output shifts to dirtier foreign producers

---

# What determines leakage?

Leakage is .hi[larger] when the world price moves less in response to the tax:

- The taxing country is small in world markets, so its supply cut hardly changes the world price

- With little price movement, domestic demand doesn't change and imports replace the lost domestic output

---
count: false
# What determines leakage?

Leakage is .hi[larger] when foreign replacement is elastic or dirty:

- Foreign supply is elastic and trade costs are low, so firms abroad can expand output quickly when home production falls

- Foreign production is more emissions intensive than home production (`$e_j > e_i$`), so each unit shifted abroad offsets more of the home emissions reduction

---
count: false
# What determines leakage?

Leakage is .hi[smaller] when policy reduces quantity demanded by increasing the world price:

- The taxing country is large in world markets, so its supply cut changes the world price

- With price increases, domestic quantity demanded falls

- Then fewer imports are needed to fill the gap, so there is less of an emissions increase abroad, and greater global emissions reductions

---
count: false
# What determines leakage?

Leakage is .hi[smaller] when foreign expansion is constrained or cleaner:

- If foreign producers supply is inelastic, firms abroad are limited in how much they can increase production

- If home production is dirtier than foreign production (`$e_i > e_j$`), shifting output abroad offsets less of the domestic abatement and can even lower global emissions

---

# Carbon tax + carbon tariff

---

# Adding a carbon tariff

The problem with the carbon tax was that consumers can easily switch to importing the dirty good from another country not subject to the carbon tax

One potential way to address this is a .hi[carbon tariff] of rate `$\tau$`: a tax on imports proportional to their carbon content

Here we will tax imports at the same rate as domestic production: `$$\tau = t = e \times d$$`

---
count: false

# Adding a carbon tariff

A carbon tax reduces the net price producers receive by `$t$`

A carbon tariff raises the price producers receive by `$\tau = t$`,

so producers get `$P_W - t + \tau = P_W$`, the price without a tax or tariff

A carbon tariff raises the price consumers pay by `$\tau = t$`, so consumers pay `$P_W + \tau$`

So tax + tariff works like a consumption tax in the end

---

# Adding a carbon tariff

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig4-tax-only-stage1-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Start from the carbon tax alone:
- Producers net `$P_W - t$`
- Home output is `$q_{it}^S$`
- Consumers still pay `$P_W$` and buy `$q_i^D$`
- Country `$i$` imports `$q_i^D - q_{it}^S$`

]

---
count: false

# Adding a carbon tariff

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig4-tax-only-stage2-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Why is leakage a problem here?
- Imports replace the lost domestic output
- So home emissions fall, but foreign production rises
- The tax changes domestic supply, not consumption
- Since consumption doesn't change, there must be more imports

]

---
count: false

# Adding a carbon tariff

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig4-tax-tariff-stage2-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Now add a carbon tariff `$\tau = t$` on imports:
- Consumers pay `$P_W + \tau$`
- Domestic quantity demanded falls from `$q_i^D$` to `$q_{i\tau}^D$`
- Domestic producers receive `$P_W + \tau - t = P_W$`
- So domestic supply returns to `$q_i^S$`

]

---
count: false

# Adding a carbon tariff

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig4-tax-tariff-stage2.1-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Post tariff imports equal `$q_{i\tau}^D - q_i^S$`

- Higher domestic production and lower consumption reduce imports relative to the carbon tax alone
- Domestic production returns to its unregulated level, while consumption falls: .hi[global production and emissions fall]

]

---
count: false

# Adding a carbon tariff

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig4-tax-tariff-stage3-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Revenue effects:
- The domestic carbon tax still raises `$R_t$`
- The tariff raises `$R_\tau$` on remaining imports
- Both are transfers inside country `$i$`: tax `$R_t$` paid by producers, tariff `$R_\tau$` paid by consumers

]

---
count: false

# Adding a carbon tariff

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig4-tax-tariff-stage4-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

- `$b$` is the consumption deadweight loss from the higher price
- Reduced consumption where the private benefit `$D[i]$` was greater than the PMC of production `$P_W$`

]

---
count: false

# Adding a carbon tariff

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig4-tax-tariff-stage4.1-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Since `$\tau = t = e \times d$`

- The price `$P_W + \tau$` includes the external damage cost
- `$b+f$` is the environmental gain from lower world output and emissions of `$q_i^D - q_{i\tau}^D$`
- Tax + tariff improves social welfare by `$f$`

]

---

# Recap

With only a tax:
- Domestic production/emissions become more expensive
- Consumers can easily switch to imports: "leakage"
- We taxed production but received no environmental benefits

Adding a carbon tariff:
- We are now making foreign production/emissions more expensive for our domestic consumers
- Consumers can no longer as easily switch to imports
- Emissions fall because they are correctly priced (good!)
- Consumption falls (bad!)

---

# The key insight

With identical carbon intensities everywhere:

Why?
- Tax on domestic production raises domestic costs
- Tariff on imports raises import costs
- Both domestic and imported goods consumed at home face the same carbon price
- Equivalent to taxing domestic consumption of the carbon intensive good

---

# Numerical example: setup

Use the same simple market for both equivalence results:

`$$Q_D = 100 - P,\qquad Q_S = P - 20,\qquad P_W = 40$$`

--
Definitions:
- `$Q_D$` = domestic quantity demanded
- `$Q_S$` = domestic quantity supplied
- `$M = Q_D - Q_S$` = imports
- `$P_W$` = world price

---
count: false

# Numerical example: setup

Carbon and policy terms:
- `$e_H$` and `$e_F$` = home and foreign emissions per unit
- `$d$` = damage per unit of emissions
- `$t$` = domestic carbon tax on home production
- `$\tau$` = carbon tariff on imports
`$$e_H = e_F = 1,\qquad d = 10,\qquad t = \tau = 10$$`

---
count: false

# Numerical example: setup

Start from the free trade benchmark:

Step 1: under free trade, the domestic price equals the world price
`$$P = P_W = 40$$`

Step 2: plug `$P_W$` into demand and supply
`$$Q_D = 100 - 40 = 60$$`
`$$Q_S = 40 - 20 = 20$$`
`$$M = Q_D - Q_S = 60 - 20 = 40$$`

---

# Numerical example: tax + tariff

Under a domestic carbon tax and equal tariff, work in three steps:

Step 1: solve for prices

Here `$P_c$` is the price paid by consumers and `$P_p$` is the net price received by domestic producers
`$$P_c = P_W + \tau = 40 + 10 = 50$$`
`$$P_p = P_c - t = 50 - 10 = 40$$`

---
count: false

# Numerical example: tax + tariff

Step 2: plug those prices into demand and supply
`$$Q_D = 100 - P_c = 100 - 50 = 50$$`
`$$Q_S = P_p - 20 = 40 - 20 = 20$$`
`$$M = Q_D - Q_S = 50 - 20 = 30$$`

---
count: false

# Numerical example: tax + tariff

Step 3: compute government revenue

Here `$R_t$` is domestic carbon tax revenue and `$R_\tau$` is tariff revenue
`$$R_t = t \times Q_S = 10 \times 20 = 200$$`
`$$R_\tau = \tau \times M = 10 \times 30 = 300$$`
`$$R = R_t + R_\tau = 200 + 300 = 500$$`

---

# Numerical example: equivalent consumption tax

Now replace tax + tariff with a pure consumption tax of 10:

Step 1: solve for prices

Consumers pay the tax, so `$P_c$` rises, but producers still receive the world price
`$$P_c = P_W + 10 = 40 + 10 = 50$$`
`$$P_p = P_W = 40$$`

---

# Numerical example: equivalent consumption tax

Step 2: plug those prices into demand and supply
`$$Q_D = 100 - P_c = 100 - 50 = 50$$`
`$$Q_S = P_p - 20 = 40 - 20 = 20$$`
`$$M = Q_D - Q_S = 50 - 20 = 30$$`

---

# Numerical example: equivalent consumption tax

Step 3: compute government revenue

`$$R_c = 10 \times Q_D = 10 \times 50 = 500$$`

So tax + tariff and a consumption tax generate the same outcome:
- same consumer price: `$P_c = 50$`
- same producer price: `$P_p = 40$`
- same domestic demand: `$Q_D = 50$`
- same domestic supply: `$Q_S = 20$`
- same imports: `$M = 30$`
- same total revenue: 500

---

# Carbon tariff alone

---

# What if we only use a tariff?

Some proposals call for carbon tariffs .hi[without] a domestic carbon tax

What does this accomplish?

---
count: false

# What if we only use a tariff?

A carbon tariff raises the price producers receive by `$\tau$`, which is the same thing as a production subsidy of `$\tau$`

A carbon tariff raises the price consumers pay by `$\tau$`, which is the same thing as a consumption tax of `$\tau$`

So tariff alone works like a consumption tax plus a production subsidy in the end

---

# Carbon tariff alone in practice

<video width="900" controls preload="metadata" style="display:block;margin:auto;" onplay="document.querySelectorAll('video').forEach(v => { if (v !== this) v.pause(); });"><source src="videos/09-carbon-tariffs-tariff-alone-practice.mp4" type="video/mp4"><track kind="captions" src="videos/09-carbon-tariffs-tariff-alone-practice.en.vtt" srclang="en" label="English" default></video>

---

# Carbon tariff alone

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig5-tariff-alone-stage1-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Start from free trade:
- Consumers and producers in country `$i$` both face `$P_W$`
- Domestic output is `$q_i^S$` and consumption is `$q_i^D$`
- Imports fill the gap `$q_i^D - q_i^S$`

]

---
count: false

# Carbon tariff alone

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig5-tariff-alone-stage2-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Now impose a carbon tariff `$\tau$` with no domestic carbon tax:
- Consumers pay `$P_W + \tau$`
- Domestic producers also receive `$P_W + \tau$`
- So consumption falls and home output rises

]

---
count: false

# Carbon tariff alone

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig5-tariff-alone-stage3-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Why is this different from tax + tariff?
- The tariff alone taxes consumption but also protects domestic producers
- Output rises to `$q_{i\tau}^S$` and demand falls to `$q_{i\tau}^D$`
- Imports shrink because both margins move

]

---
count: false

# Carbon tariff alone

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig5-tariff-alone-stage4-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

- The government collects tariff revenue `$R_\tau$` on remaining imports
- The tariff pushes some production away from cheaper foreign suppliers

]

---
count: false

# Carbon tariff alone

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig5-tariff-alone-stage5-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

- `$a$` is the production DWL from replacing cheaper imports with costlier home output
- `$b$` is the consumption DWL from reduced consumption at the higher price
- Lower consumption has environmental benefits `$b+f$`: `$(q_i^D - q_{i\tau}^D)\times d$`

]

---
count: false

# Carbon tariff alone

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig5-tariff-alone-stage5.1-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Welfare and environment:
- Net social benefit is `$(b+f)-(b+a) = f-a$`
- Gains from real reductions in pollution
- Losses from inefficient subsidization of domestic production
- Net effect is ambiguous

]

---
count: false

# Numerical example: setup

For the tariff alone example, use the same market structure:

`$$Q_D = 100 - P,\qquad Q_S = P - 20,\qquad P_W = 40$$`

Definitions:
- `$Q_D$` = domestic quantity demanded
- `$Q_S$` = domestic quantity supplied
- `$M = Q_D - Q_S$` = imports
- `$P_c$` = price paid by consumers
- `$P_p$` = price received by domestic producers

Policy for this case:
`$$t = 0,\qquad \tau = 10$$`

---
count: false

# Numerical example: setup

Start from the free trade benchmark:

Free trade benchmark:
`$$P_c = P_p = P_W = 40$$`
`$$Q_D = 100 - 40 = 60$$`
`$$Q_S = 40 - 20 = 20$$`
`$$M = Q_D - Q_S = 40$$`

---
count: false

# Numerical example: tariff alone

With a tariff alone, work in three steps:

Step 1: solve for prices

Here both consumers and domestic producers face the tariff inclusive price
`$$P_c = P_W + \tau = 40 + 10 = 50$$`
`$$P_p = P_c = 50$$`

---
count: false

# Numerical example: tariff alone

Step 2: plug those prices into demand and supply
`$$Q_D = 100 - P_c = 100 - 50 = 50$$`
`$$Q_S = P_p - 20 = 50 - 20 = 30$$`
`$$M = Q_D - Q_S = 50 - 30 = 20$$`

---
count: false

# Numerical example: tariff alone

Step 3: compute tariff revenue
`$$R_\tau = \tau \times M = 10 \times 20 = 200$$`

---
count: false

# Numerical example: equivalent tax + subsidy

Now replace the tariff with a consumption tax of 10 and a production subsidy of 10:

Step 1: solve for prices

Consumers pay the consumption tax, and producers receive the world price plus the subsidy
`$$P_c = P_W + 10 = 40 + 10 = 50$$`
`$$P_p = P_W + 10 = 40 + 10 = 50$$`

---
count: false

# Numerical example: equivalent tax + subsidy

Step 2: plug those prices into demand and supply
`$$Q_D = 100 - P_c = 100 - 50 = 50$$`
`$$Q_S = P_p - 20 = 50 - 20 = 30$$`
`$$M = Q_D - Q_S = 50 - 30 = 20$$`

---
count: false

# Numerical example: equivalent tax + subsidy

Step 3: compute the government budget

Here `$R_c$` is consumption tax revenue
`$$R_c = 10 \times Q_D = 10 \times 50 = 500$$`
`$$\text{Subsidy cost} = 10 \times Q_S = 10 \times 30 = 300$$`
`$$R^{net} = R_c - \text{Subsidy cost} = 500 - 300 = 200$$`

---
count: false

# Numerical example: equivalent tax + subsidy

So tariff alone and a consumption tax plus production subsidy generate the same outcome:
- same consumer price: `$P_c = 50$`
- same producer price: `$P_p = 50$`
- same domestic demand: `$Q_D = 50$`
- same domestic supply: `$Q_S = 30$`
- same imports: `$M = 20$`
- same net government revenue: 200

---

# World carbon tax

---

# World carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig6-world-tax-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Suppose the rest of the world already prices carbon so `$P_W$` reflects the carbon cost *abroad*:
- Country `$i$` still produces `$q_i^S$` without its own carbon tax
- The efficient output for country `$i$` is `$q_{it}^S$`, where SMC = `$P_W$`

]

---

# World carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig6-world-tax.1-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

- At `$q_i^S$`, SMC exceeds the revenue from selling the good at `$P_W$`
- `$q_i^S - q_{it}^S$` is leakage *into* the country from carbon taxation abroad 
- `$a$` is the resulting deadweight loss from overproduction domestically

]

---

# World carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig6-world-tax.2-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

If country `$i$` also imposes the carbon tax `$t$`:
- Producers receive net of tax price `$P_W - t$`
- Supply falls from `$q_i^S$` to `$q_{it}^S$`
- Imports rise to `$q_i^D-q_{it}^S$`
- Consumers still face the world price `$P_W$`

]

---
count: false

# World carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig6-world-tax-stage2-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

Why are those extra imports not leakage?
- Foreign producers already face the same carbon price
- The earlier distortion was leakage from the rest of the world to country `$i$`
- Those imports reverse that leakage
- The DWL `$a$` disappears

]

---
count: false

# World carbon tax

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig6-world-tax-stage3-1.png" alt="" width="100%" style="display: block; margin: auto;" />
]

At that point the allocation is efficient:
- Every country has internalized the externality
- Global SMC equals the marginal benefit of the last unit consumed
- Production is cost effective across countries
- A carbon tariff is unnecessary

]

---

# Complications

---

# Real world complications

Several factors complicate carbon tariff design:

1. .hi[Resource shuffling:] clean production exported, dirty production consumed domestically

2. .hi[Non price policies:] regulations vs. carbon prices

3. .hi[Export rebates:] should exports get carbon tax rebates?

4. .hi[Retaliation:] trading partners may impose counter tariffs

---

# Retaliation risk

Trading partners may retaliate

<video width="900" controls preload="metadata" style="display:block;margin:auto;" onplay="document.querySelectorAll('video').forEach(v => { if (v !== this) v.pause(); });"><source src="videos/09-carbon-tariffs-retaliation-trade-war.mp4" type="video/mp4"><track kind="captions" src="videos/09-carbon-tariffs-retaliation-trade-war.en.vtt" srclang="en" label="English" default></video>

---

# Resource shuffling

Suppose country `$j$` has both clean and dirty production

With a carbon tariff based on average intensity:
- Export the clean stuff to country `$i$`
- Consume the dirty stuff domestically

No change in country `$j$`'s total emissions!

This is .hi[another form of leakage]

---

# Non price policies

Many countries use regulations rather than carbon prices:
- Fuel economy standards
- Renewable portfolio standards
- Building codes

How do you calculate the "equivalent carbon price"?

Very difficult: may require complex modeling

---

# Export rebates

Should country `$i$` rebate carbon taxes on exports?

Arguments for:
- Maintains competitiveness
- Symmetric with import tariffs

Arguments against:
- Reduces domestic incentive to decarbonize
- May look like an export subsidy (WTO issues)

---

# WTO compatibility

Carbon tariffs face WTO scrutiny:

1. .hi[National treatment:] can't discriminate against foreign goods

2. .hi[Most favored nation:] can't discriminate among trading partners

3. .hi[GATT Article XX:] exceptions for environmental protection

EU CBAM designed carefully to fit within WTO rules

---
class: inverse, center, middle
name: takeaways

# Key takeaways

---

# Summary

1. .hi[Carbon tariffs] aim to address leakage and competitiveness concerns

2. .hi[Carbon tax + tariff] is equivalent to a consumption tax
   - Reduces consumption of carbon intensive goods
   - Can improve welfare if environmental benefit exceeds distortion costs

3. .hi[Carbon tariff alone] = consumption tax + production subsidy
   - May increase domestic emissions
   - Less effective than tax + tariff

---

# Summary (continued)

4. .hi[World carbon tax] is first best
   - Carbon tariffs are second best when global coordination fails

5. .hi[Many complications] in practice
   - Resource shuffling, non price policies, export rebates, WTO rules

---

# The bottom line

Carbon tariffs are a .hi[complement] to carbon pricing, not a substitute

They work best when:
- Combined with a domestic carbon tax
- Set based on actual carbon content
- Part of broader international coordination

Alone, they are an imperfect tool that may create new distortions