Lecture 09

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

---

``` r
if (!require("pacman")) install.packages("pacman")
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")
  ),
  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):]
- Phasing in 2023-2026, full implementation 2026
- Covers cement, iron/steel, aluminum, fertilizers, electricity, hydrogen
- Importers must purchase certificates matching EU ETS price

---

# Understanding border carbon adjustments

---

# 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

---

# Tariffs are taxes on imports

A tariff is a .hi[tax on imports]

In this lecture we study the .hi[small-country] case:
- country `$i$` is too small to affect the world price
- imports are available at the exogenous world price `$P_W$`
- this is the benchmark that makes leakage especially transparent later on

---

# 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

---

# Supply and demand refresher

In this market:

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

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

- If `$P_W$` is below the autarky 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-tariff-1.png" width="100%" style="display: block; margin: auto;" />
]

With free trade at price `$P_W$`:
- Domestic production is `$q_i^S$`
- Domestic consumption is `$q_i^D$`
- Imports are `$q_i^D - q_i^S$`

]

---
count: false
# The tariff wedge

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-tariff-stage2-1.png" width="100%" style="display: block; margin: auto;" />
]

Suppose we implement an import tariff `$\tau$`:
- The domestic price rises from `$P_W$` to `$P_W + \tau$`
- Imported units now enter at the tariff-inclusive price
- Domestic suppliers can charge that same higher price

]

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

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-tariff-stage2.1-1.png" width="100%" style="display: block; margin: auto;" />
]

A tariff `$\tau$` raises the domestic price to `$P_W + \tau$`:
- Domestic production rises to `$q_{i\tau}^S$`
- Domestic consumption falls to `$q_{i\tau}^D$`
- Imports shrink to `$q_{i\tau}^D - q_{i\tau}^S$`

]

---
count: false
# Consumer surplus refresher

.pull-left[
<img src="09-slides-carbon-tariffs_files/figure-html/fig1-consumer-surplus-1.png" 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" 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
# Welfare accounting under a tariff

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

- `$a$`: producer gain on the original domestic output
- `$b$`: producer gain on the extra domestic output
- `$c$`: production deadweight loss
- `$d$`: tariff revenue on remaining imports
- `$e$`: consumption deadweight loss

]

---
count: false
# Consumer loss and redistribution

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

- `$\Delta PS = a + b$`
- `$\Delta CS = -(a + b + c + d + e)$`
- `$R = d$`
- `$\Delta W_i = \Delta PS + R - \Delta CS$`
- 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" width="100%" style="display: block; margin: auto;" />
]

Triangle `$c$` is a production distortion:
- The tariff shifts production from lower-cost foreign supply to higher-cost domestic production
- For those extra domestic units, MC (`$S[i]$`) exceeds MB (`$P_W$`)

]

---
count: false
# Consumption distortion

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

Triangle `$e$` is a consumption distortion:
- The tariff eliminates units consumers value above the world price but below the tariff-inclusive price
- For those lost units, MB (`$D[i]$`) exceeds MC (`$P_W$`)

]

---

# 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" 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 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" 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 `$SMC$`

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" 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 `$CO_2$`:

- 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)

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

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

- You can think of a tax `$t = e \times d$` as shifting `$S[i]$` up to `$SMC[i]$`, so firms produce until `$S[i] + t = P_W$`
- Equivalently, firms keep the same supply curve `$S[i]$` but face the net-of-tax price `$P_W - t$`

]