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
)
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$echo <- FALSE
  }
knitr::opts_chunk$set(echo = TRUE, fig.align="center")
  options
})
```

```
## 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
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```
## 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?

---

# Understanding border carbon adjustments

---

# Carbon tariffs

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):]
- Phasing in 2023-2026, full implementation 2026
- Covers cement, iron/steel, aluminum, fertilizers, electricity, hydrogen
- Importers must purchase certificates matching EU ETS price

---

# This lecture

We will use a simple partial equilibrium 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

---

# A simple trade model

Consider a small open economy (country `$i$`) that:
- Takes world prices 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

---

# Free trade equilibrium

With free trade at price `$P_W$`:
- Domestic production: `$q_i^S$`
- Domestic consumption and imports: `$q_i^D$` and `$q_i^D - q_i^S$`

---
count: false
# Adding a tariff

Suppose we implement an import tariff `$\tau$`:
- Price of imports increases to `$P_W + \tau$`
- Domestic suppliers can now charge `$P_W + \tau$`

---
count: false
# Adding a tariff

A tariff `$\tau$` raises the equilibrium domestic price to `$P_W + \tau$`:
- Production rises to `$q_{i\tau}^S$` and consumption falls to `$q_{i\tau}^D$`
- Imports fall to `$q_{i\tau}^D - q_{i\tau}^S$`

---
count: false
# Tariff revenue

The tariff creates:
- Revenue: `$R(\tau) = \tau (q_{i\tau}^D - q_{i\tau}^S)$`
- Deadweight loss: triangles `$a + b$`

---
count: false
# Deadweight loss

Triangle `$a$` is a production distortion:
- The tariff shifts production from lower-cost foreign supply to higher-cost domestic production: MC (`$S[i]$`) is higher than the MB (`$P_W$`)

---
count: false
# Deadweight loss

Triangle `$b$` is a consumption distortion:
- The tariff eliminates units consumers value above the world price but below the tariff-inclusive price: MB (`$D[i]$`) is higher than the MC (`$P_W$`)

---

# 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[marginal social cost (MSC)] of production is: `$MSC = S + e \times d$`

MSC 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" 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" width="100%" style="display: block; margin: auto;" />
]

Country `$i$`'s MSC 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" width="100%" style="display: block; margin: auto;" />
]

The green region is the domestic deadweight loss from producing beyond the efficient output level

]

---
count: false
# Free trade with pollution

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig2a-pollution-stage4-1.png" 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 `$MSC$`

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" width="100%" style="display: block; margin: auto;" />
]

From a global perspective:
- Free-trade output is where `$D = S$`
- Efficient output is where `$D = MSC$`
- 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 `$CO_2$`:

- Damages occur regardless of where emissions happen
- No country has incentive to fully internalize the externality
- Free trade leads to .hi[too much production] globally

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)

---

# Effects of unilateral carbon tax

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

Before the tax, the domestic market is at the free-trade benchmark with price `$P_W$`

]