2.1 — Tariffs

# 2.1 — Tariffs

## ECON 324 • International Trade • Spring 2023

### Ryan Safner Associate Professor of Economics <a href="mailto:safner@hood.edu">safner@hood.edu</a> <a href="https://github.com/ryansafner/tradeS23">ryansafner/tradeS23</a> <a href="https://tradeS23.classes.ryansafner.com"> tradeS23.classes.ryansafner.com</a>

---
class: inverse

# Outline

### [Tariffs](#3)

### [Effects of an Import Tariff in a Small Country](#14)

### [Effects of an Import Tariff in a Large Country](#14)

### [Optimal Tariff Theory](#14)

### [The Effective Rate of Protection](#14)

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# Tariffs

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# Tariffs, According to POTUS 45

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# But It's Not Just a Trump Thing...

]

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# ...Or Just A Recent Thing

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# Tariffs, According to Professional Economists

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# International Trade Policies

- Yet free trade is rare in the world

- Two questions:
    1. Why is free trade rare? Or, why are trade restrictions common?
    2. What are the consequences of restricting trade?

]

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# International Trade Policies

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# Tariffs

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# Tariffs

.pull-left[
.smallest[
- Most common way to restrict trade is through a .hi[tariff] (historically called a .hi[“duty”]), a tax specifically targeted towards internationally-traded goods

- .hi[Import tariff]: tax on imported goods
	- This is by far the most common type of trade restriction

- .hi[Export tariff]: tax on exported goods
  - Rare in developed countries but sometimes occurs in developing countries as a way to generate government revenue

]
]

---

# Types of Tariffs

.pull-left[
.smallest[
- .hi-purple[Ad valorem tariff] taxes a fixed percentage of the value of a good
  - e.g. 25% U.S. tariff on (prices of) imported trucks

- .hi-purple[Specific tariff] taxes a fixed sum per unit of a good
  - e.g. $3/barrel of oil

- .hi-purple[Compound tariff] combines ad valorem and specific tariffs
  - Rare in developed countries but sometimes occurs in developing countries as a way to generate government revenue
]
]

---

# Tariff Schedule

.center[
![:scale 40%](../images/tariffscheduleflax.png)
.smallest[
U.S. tariff schedule on imported woven flax fabrics, [Harmonized Tariff Schedule](https://hts.usitc.gov/current), United States International Trade Commission Chapter 53, p. 53-4
]]
---

# Tariff History

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# Tariff History

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# Effects of an Import Tariff in a Small Country

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# Import Tariff Effects in a Small Country

1. Effect of a tariff in a .hi[“small” country]
  - “Small” `$\implies$` its domestic market is too small to affect world prices
  - Effectively, it is a .hi-purple[price-taker]: it can import as much as it wants and not drive up the price

2. Effect of a tariff in a .hi[“large” nation]
  - “Large” `$\implies$` changes in the country’s domestic market *can* affect world prices

]
]
.pull-right[
.center[
![](../images/bigvssmallcountry.jpg)
]
]

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# Import Tariff Effects in a Small Country

]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-1-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Small Country

- .hi-blue[Domestic Demand] for sugar in Belgium
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-2-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Small Country

- .hi-blue[Domestic Demand] for sugar in Belgium

- .hi-red[Domestic Supply] of sugar in Belgium

]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-3-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Small Country

- .hi-blue[Domestic Demand] for sugar in Belgium

- .hi-red[Domestic Supply] of sugar in Belgium

- Autarky price: 10¢/lb, 10 billion lbs exchanged within Belgium
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-4-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Small Country

- .hi-blue[Domestic Demand] for sugar in Belgium
  - .blue[Consumer surplus] = WTP - p*

- .hi-red[Domestic Supply] of sugar in Belgium

- Autarky price: 10¢/lb, 10 billion lbs exchanged within Belgium
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-5-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Small Country

- .hi-blue[Domestic Demand] for sugar in Belgium
  - .blue[Consumer surplus] = WTP - p*
  - = 0.5(10-0)($0.20-$0.10) = $0.5 billion

- .hi-red[Domestic Supply] of sugar in Belgium

- Autarky price: 10¢/lb, 10 billion lbs exchanged within Belgium
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-6-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Small Country

- .hi-blue[Domestic Demand] for sugar in Belgium
  - .blue[Consumer surplus] = WTP - p*
  - = 0.5(10-0)($0.20-$0.10) = $0.5 billion

- .hi-red[Domestic Supply] of sugar in Belgium
  - .red[Producer surplus] = p* - WTA

- Autarky price: 10¢/lb, 10 billion lbs exchanged within Belgium
]

]
.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-7-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Import Tariff Effects in a Small Country

- .hi-blue[Domestic Demand] for sugar in Belgium
  - .blue[Consumer surplus] = WTP - p*
  - = 0.5(10-0)($0.20-$0.10) = $0.5 billion

- .hi-red[Domestic Supply] of sugar in Belgium
  - .red[Producer surplus] = p* - WTA
  - = 0.5(10-0)($0.10-$0.00) = $0.5 billion
  
- Autarky price: 10¢/lb, 10 billion lbs exchanged within Belgium
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-8-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Small Country

- .hi-blue[Domestic Demand] for sugar in Belgium

- .hi-red[Domestic Supply] of sugar in Belgium

- Suppose Belgium opens up to international trade

- .hi-orange[World Supply] of sugar at 4¢/lb
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-9-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Small Country

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-10-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Small Country

.smaller[
- At 4¢/lb:
  - .blue[Belgian consumers] want to consume 16 bn lbs
  - .red[Belgian producers] will produce 4 bn lbs
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-11-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Small Country

.pull-left[
.smaller[
- At 4¢/lb:
  - .blue[Belgian consumers] want to consume 16 bn lbs
  - .red[Belgian producers] will produce 4 bn lbs
  - Belgium will .orange[import] 12 bn lbs from the .orange[rest of the world]
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-12-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Import Tariff Effects in a Small Country

- .blue[Consumer surplus] = WTP - p*
  - = 0.5(16-0)($0.20-$0.04) = $1.280 billion

]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-13-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Import Tariff Effects in a Small Country

- .blue[Consumer surplus] = WTP - p*
  - = 0.5(16-0)($0.20-$0.04) = $1.280 billion

- .red[Producer surplus] = p* - WTA
  - = 0.5(4-0)($0.04-$0.00) = $0.080 billion

]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-14-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Small Country

- .blue[Consumer surplus] = WTP - p*
  - = 0.5(16-0)($0.20-$0.04) = $1.280 billion

- .red[Producer surplus] = p* - WTA
  - = 0.5(4-0)($0.04-$0.00) = $0.080 billion

- Trade benefits .blue[Belgian consumers] at expense of .red[Belgian sugar producers]
 - But gain is much bigger than loss!
]
]
.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-15-1.png" width="504" style="display: block; margin: auto;" />
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# Import Tariff Effects in a Small Country

.pull-left[
<img src="2.1-slides_files/figure-html/unnamed-chunk-16-1.png" width="504" style="display: block; margin: auto;" />

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.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-17-1.png" width="504" style="display: block; margin: auto;" />

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- Note at a price of ¢10 there is no import demand, all sugar can be produced in Belgium

]

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# Import Tariff Effects in a Small Country

.pull-left[
<img src="2.1-slides_files/figure-html/unnamed-chunk-18-1.png" width="504" style="display: block; margin: auto;" />

]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-19-1.png" width="504" style="display: block; margin: auto;" />

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- Note at a price of ¢10 there is no import demand, all sugar can be produced in Belgium

- We have been assuming the world supply of sugar is perfectly elastic at 4¢

- Sets equilibrium amount of imports in Belgium, 12 bn lbs imported

]

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# Import Tariff Effects in a Small Country

.pull-left[
.smaller[
- Suppose the government levies a 4¢/lb .hi-purple[tariff] on sugar imports
]
]
.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-20-1.png" width="504" style="display: block; margin: auto;" />
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# Import Tariff Effects in a Small Country

- At new domestic sugar price of 8¢/lb
]
]
.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-21-1.png" width="504" style="display: block; margin: auto;" />
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# Import Tariff Effects in a Small Country

- At new domestic sugar price of 8¢/lb
 - .blue[Belgian consumers] want to consume 12 bn lbs (less than before)
]
]
.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-22-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Import Tariff Effects in a Small Country

- At new domestic sugar price of 8¢/lb
 - .blue[Belgian consumers] want to consume 12 bn lbs (less than before)
 - .red[Belgian producers] will produce 8 bn lbs (more than before)
]
]
.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-23-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Small Country

- At new domestic sugar price of 8¢/lb
 - .blue[Belgian consumers] want to consume 12 bn lbs (less than before)
 - .red[Belgian producers] will produce 8 bn lbs (more than before)
 - Belgium will .orange[import] 4 bn lbs from the .orange[rest of the world] (less than before)
]
]
.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-24-1.png" width="504" style="display: block; margin: auto;" />

]
---

# Import Tariff Effects in a Small Country

- Tariff is a tax, so government earns revenue:
 - 4 bn lbs $\times $ 0.04/lb = $0.160 bn
]
]
.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-25-1.png" width="504" style="display: block; margin: auto;" />

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# Import Tariff Effects in a Small Country

- .blue[Consumer surplus] = WTP - p*
  - = 0.5(12-0)($0.20-$0.08) = $0.720 billion
  - Less than before (free trade)
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-26-1.png" width="504" style="display: block; margin: auto;" />

]

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# Import Tariff Effects in a Small Country

- .blue[Consumer surplus] = WTP - p*
  - = 0.5(12-0)($0.20-$0.08) = $0.720 billion
  - Less than before (free trade)

- .red[Producer surplus] = p* - WTA
  - = 0.5(8-0)($0.08-$0.00) = $0.320 billion
  - More than before (free trade)
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-27-1.png" width="504" style="display: block; margin: auto;" />

]

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# Import Tariff Effects in a Small Country

- Two new sources of market inefficiency created, .b[“deadweight loss (DWL)”]

]
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.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-28-1.png" width="504" style="display: block; margin: auto;" />

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# Import Tariff Effects in a Small Country

]
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.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-29-1.png" width="504" style="display: block; margin: auto;" />

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# Import Tariff Effects in a Small Country

- Two new sources of market inefficiency created, .b[“deadweight loss (DWL)”]
 1. Inefficient domestic production (cheaper for foreigners to produce sugar)
 - 0.5(8-4)($0.08-$0.04) = $0.080 Billion
 2. Lost gains from exchange (consumers wanted to buy more from world)
 - 0.5(16-12)($0.08-$0.04) = $0.080 Billion
]
]
.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-30-1.png" width="504" style="display: block; margin: auto;" />

]

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# Import Tariff Effects in a Small Country

.pull-left[
<img src="2.1-slides_files/figure-html/unnamed-chunk-31-1.png" width="504" style="display: block; margin: auto;" />

]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-32-1.png" width="504" style="display: block; margin: auto;" />

]

- Decline of imports at higher price in Belgium

- Size of DWL in import market = sum of both DWL triangles in Belgian market ($0.160 bn)
]

---

# Import Tariff Effects in a Small Country

1. .blue[Decrease in consumer surplus]:
  - $0.720 bn-$1.280 bn = .blue[-$0.460 bn]
  
2. .red[Increase in producer surplus]:
  - $0.320 bn-$0.080 bn = .red[$0.240 bn]

3. .green[Government tax revenue]:
  - .green[$0.160 bn]

4. .b[Deadweight losses]
  - $-0.080 bn - $0.080 bn = .b[-$0.160 bn]
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-33-1.png" width="504" style="display: block; margin: auto;" />

]

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# Import Tariff Effects in a Small Country

- A $240m gain to a small group of domestic sugar producers at a $460m expense to consumers

- Concentrated benefit, dispersed cost each consumer pays $0.04/lb more for sugar

- Harm to foreigners: hurts exporters and consumers in other countries from lost trade
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-34-1.png" width="504" style="display: block; margin: auto;" />

]

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# Tariff Effects in a Large Country

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# Large Countries in International Trade

.pull-left[
.smallest[
- A .hi-purple[“large country”] has a sufficiently large domestic demand to affect international prices

- The decrease in domestic demand from an import tariff (from higher import price) is sufficiently large to .hi-purple[lower the world price of the good]

- This is called the .hi[“terms of trade effect”] of a tariff
  - can provide a *benefit* to domestic country
  - harms foreign exporters due to lower world price
]

]

---

# Import Tariff Effects in a Large Country

- Autarky price: 10¢/lb, 10 billion lbs exchanged within U.S.
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-35-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Large Country

- .hi-orange[World Supply] of sugar at 4¢/lb:
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-36-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Import Tariff Effects in a Large Country

- .hi-orange[World Supply] of sugar at 4¢/lb:
  - .blue[U.S. consumers] want to consume 16 bn lbs
  - .red[U.S. producers] will produce 4 bn lbs
  - U.S. will .orange[import] 12 bn lbs from the .orange[rest of the world]
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-37-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Large Country

.pull-left[
<img src="2.1-slides_files/figure-html/unnamed-chunk-38-1.png" width="504" style="display: block; margin: auto;" />

]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-39-1.png" width="504" style="display: block; margin: auto;" />

]

- Because U.S. is a large country, the world supply curve (exports from other countries) to U.S. is *upward* sloping
  - sufficiently high demand from U.S. stimulates production abroad for export to U.S.

- Imagine autarky equilibrium price in exporting countries is 2¢; once they can get higher price in U.S., start exporting

- Sets equilibrium amount of imports in U.S., 12 bn lbs imported at 4¢

]

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# Import Tariff Effects in a Large Country

- Increase in costs to world sugar exporters decreases world export supply by 4¢/lb

- New equilibrium is for U.S. to import 6 bn lbs at 7¢/lb
  - But 4¢/lb of the imports are paid to U.S. government as tariffs

- Exporters to U.S. recieve *net price* (after taxes) of 3¢/lb

- Important: raise in price to U.S. consumers is less than the full 4¢/lb!
  - Tariff on the massive U.S. market has lowered the *world* price of sugar because of decreased world supply, the .hi-purple[terms of trade effect]
]

]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-40-1.png" width="504" style="display: block; margin: auto;" />

]

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# Import Tariff Effects in a Large Country

- Due to the terms of trade effect, world price of sugar will fall from less U.S. demand (to 3¢/lb)
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-41-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Large Country

- Due to the terms of trade effect, world price of sugar will fall from less U.S. demand (to 3¢/lb)

- The 4¢/lb is levied on this *new, lower* world price of sugar, raising price of sugar in U.S. to 7¢/lb
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-42-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Large Country

.smaller[
- At new domestic price of 7¢/lb:
  - .blue[U.S. consumers] want to consume 13 bn lbs (less than before)
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-43-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Import Tariff Effects in a Large Country

.pull-left[
.smaller[
- At new domestic price of 7¢/lb:
  - .blue[U.S. consumers] want to consume 13 bn lbs (less than before)
  - .red[U.S. producers] will produce 7 bn lbs (more than before)
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-44-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Import Tariff Effects in a Large Country

.pull-left[
.smaller[
- At new domestic price of 7¢/lb:
  - .blue[U.S. consumers] want to consume 13 bn lbs (less than before)
  - .red[U.S. producers] will produce 7 bn lbs (more than before)
  - U.S. will .orange[import] 6 bn lbs from .orange[rest of the world] (less than before)

- Note the changes are not as much as it was to the small country
 - U.S. “market power” forces down world price
]
]
.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-45-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Import Tariff Effects in a Large Country

- Gain to .red[U.S. producer surplus] (but less than for small country)
  - .purple[Transfer of some CS to PS]
]

]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-46-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Large Country

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-47-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Large Country

.smaller[
- Tariff will collect revenue for government
  - 4¢/lb `$\times$` 6 bn lbs = .green[$0.240 bn]

- DWLs from productive and consumption inefficiencies
  - 2 `$\times$` $-0.045 bn = .b[-$0.090 bn]
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-48-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Large Country

.pull-left[
.smaller[
- Tariff will collect revenue for government
  - 4¢/lb `$\times$` 6 bn lbs = .green[$0.240 bn]

- DWLs from productive and consumption inefficiencies
  - 2 `$\times$` $-0.045 bn = .b[-$0.090 bn]

- But: .hi-purple[gain in tariff revenue exceeds inefficiency (DWL)!]
  - .hi-purple[Tariff brings a net increase in U.S. national welfare!]
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-49-1.png" width="504" style="display: block; margin: auto;" />
]

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# Import Tariff Effects in a Large Country

.pull-left[
<img src="2.1-slides_files/figure-html/unnamed-chunk-50-1.png" width="504" style="display: block; margin: auto;" />

]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-51-1.png" width="504" style="display: block; margin: auto;" />

]

.smallest[
- Area .hi-purple[D] is the .hi-purple[Terms of trade] gain for U.S. (loss to world) due to tariff

- U.S. deadweight loss (A+B) `$<$` U.S. tariff revenue (.hi-green[C]+.hi-purple[D])

- Foreign loses deadweight loss (**F**) from lost export opportunities
]

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# Import Tariff Effects in a Large Country

.pull-left[
<img src="2.1-slides_files/figure-html/unnamed-chunk-52-1.png" width="504" style="display: block; margin: auto;" />

]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-53-1.png" width="504" style="display: block; margin: auto;" />

]

- Welfare changes:
  - To US: (.hi-green[C]+.hi-purple[D])-(**A**+**B**), net gain!
  - To Rest of World: -(.hi-purple[D]+**E**), net loss
  - Whole World: .hi-green[C]-(**A**+**B**+**E**), net loss

- A “beggar thy neighbor” approach to increasing national welfare
]

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# Big vs. Small Comparisons

- With free trade:

| Country | `$p^*$` | `$q^*$` | Domestic `$q$` | .orange[Imports] | .blue[CS] | .red[PS] | .green[Tax Revenue] | .b[DWL] |
|---------|------:|------:|----:|--------:|---:|---:|---:|---:|
| Both | $0.04 | 16 bn | 4 bn | 12 bn | $1.280 bn | $0.080 bn | $0 | $0 |
]

.quitesmall[
| Country | `$p^*$` | `$q^*$` | Domestic `$q$` | .orange[Imports] | `$\Delta$` .blue[CS] | `$\Delta$` .red[PS] | .green[Tax Revenue] | .b[DWL] | `$\Delta$` Net Welfare |
|---------|------:|------:|----:|--------:|---:|---:|---:|---:|----:|
| Small (Belgium) | $0.08 | 12 bn | 8 bn | 4 bn | -$0.560 bn | $0.240 bn | $0.160 bn | -$0.160 bn | -$0.160 bn |
| Large (U.S.) | $0.07 | 13 bn | 7 bn | 6 bn | -$0.435 bn | $0.165 bn | $0.240 bn | -$0.090 bn | $0.030 bn|

]

---

# Optimal Tariff Theory

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# Optimal Tariff Theory

.pull-left[
.smallest[
- For a large country, a tariff decreases volume of trade but improves country’s terms of trade
  - Gain of tariff revenue (.hi-green[C]+.hi-purple[D])
  - Loss of deadweight loss (**A**+**B**)

- Net effect is a slight increase in (big) country’s welfare
  - Note tariffs always are a net harm to a small nation!

- Thus, there exists some .hi[optimal tariff] `$\tau > 0$` that maximizes net gains from tradeoff between terms of trade improvements against decline in trade
]

]

---

# Optimal Tariff Theory (in a Large Country)

- For low levels of `$\tau$`, terms of trade gain exceed deadweight loss
  - (.hi-green[C]+.hi-purple[D]) > (**A**+**B**)

- For high levels of `$\tau$`, deadweight loss exceeds terms of trade gain
 - (.hi-green[C]+.hi-purple[D]) < (**A**+**B**)

- Extremely high levels of `$\tau$` will close off trade completely

- Some optimal `$\tau^{\star}$` that maximizes welfare gain to importer

]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-54-1.png" width="504" style="display: block; margin: auto;" />
]

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# Optimal Tariff: Inversely Related to Supply Elasticity

- .hi-turquoise[The optimal tariff is inversely related to the price elasticity of foreign export supply]
`$$\varepsilon_{x} = \frac{\% \Delta q_s}{\% \Delta p}$$`
  - More elastic: flatter curve, lower tariff
  - Less elastic: steeper curve, higher tariff
- Note: for a small country, foreign export supply is perfectly elastic `$(\varepsilon_x = \infty)$`, so no tariff is optimal

]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-55-1.png" width="504" style="display: block; margin: auto;" />
]

---

# Optimal Tariff: Inversely Related to Supply Elasticity

.pull-left[
<img src="2.1-slides_files/figure-html/unnamed-chunk-56-1.png" width="504" style="display: block; margin: auto;" />

]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-57-1.png" width="504" style="display: block; margin: auto;" />

]

---

# Optimal Tariff Theory vs. the Real World

.pull-left[
.smaller[
- Economic theory shows the .hi-purple[theoretical possibility] of how tariffs might increase national welfare

- Regardless, tariffs harm welfare of trading partners (exporting countries)

- Politically and practically, trading partners might .hi[retaliate] against tariffs with their own tariffs
  - Might degenerate into a .hi-purple[trade war] where potential gains from trade are lost
]
]
.pull-right[
.center[
![:scale 100%](../images/tradebarriers.jpg)
]
]

---

# The Effective Rate of Protection

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# The Effective Rate of Protection

- Seems logical to just count the percent an *ad valorem* tariff raises price over free trade price
  - This is the .hi[nominal rate of protection]: the % increase in price
  - e.g. a 50% *ad valorem* tariff raises price 50%
  - for specific tariffs, divide `$\frac{\text{price with tariff}}{\text{price without tariff}}$`
]
]
.pull-right[
.center[
![:scale 100%](../images/tradebarriers.jpg)
]
]

---

# The Effective Rate of Protection

1. If the country is “large”, part of the tariff’s effect will be to *lower foreign export prices* rather than just raise domestic prices

2. Tariffs may have different effects on different *stages* of production for a good
]
]
.pull-right[
.center[
![:scale 100%](../images/tradebarriers.jpg)
]
]

---

# The Effective Rate of Protection

.pull-left[
.smaller[
- Better to think about the .hi[effective rate of protection] as the percent change in .hi-purple[domestic value added]

- .content-box-green[
.hi-green[Example]: Suppose **cars** sell on world market for $8,000, and **car parts** sell for $6,000. If a country buys car parts and assembles them into cars, the .hi-purple[domestic value added] is:
$$\$8,000-\$6,000=\$2,000$$

]
]
]
.pull-right[
.center[
![:scale 100%](../images/car.png)

![:scale 100%](../images/carparts.jpeg)

]
]

---

# The Effective Rate of Protection: Example

.pull-left[
.quitesmall[
- Suppose .blue[Home] wants to develop a domestic **auto assembly** industry
  - .pink[Domestic value] added from .green[imports] is:
$$\$8,000-\color{green}{\$6,000}=\color{red}{\$2,000}$$

- .blue[Home] places a **25% tariff** on **imported cars**, raising the price of cars in .blue[Home] to $10,000
  - .pink[Domestic value] added from .green[imports] is:
$$\$10,000-\color{green}{\$6,000}=\color{red}{\$4,000}$$

- .hi[Domestic value added] changes by:
$$\frac{\$4,000-\$2,000}{\$2,000} \times 100 = 100\%$$
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-58-1.png" width="504" style="display: block; margin: auto;" />
]

---

# The Effective Rate of Protection: Example

.pull-left[
.quitesmall[
- Suppose .blue[Home] instead wants to develop a domestic **car parts** industry
  - .pink[Domestic value] added from .green[imports] is:
$$\$8,000-\color{green}{\$6,000}=\color{red}{\$2,000}$$

- .blue[Home] places a **25% tariff** on **imported car _parts_**, raising the price of car parts in .blue[Home] to $7,500
  - .pink[Domestic value added] for **car parts manufacturers** is:
$$\color{red}{\$7,500}$$
- Changes by:
$$\frac{\$7,500-\$6,000}{\$6,000} \times 100% = 25\%$$

]
]
.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-59-1.png" width="504" style="display: block; margin: auto;" />
]

---

# The Effective Rate of Protection: Example

- What about for **assemblers** of cars? 
  - .pink[Domestic value added] for **car assemblers** is:
$$\$8,000-\color{green}{\$7,500}=\color{red}{\$500}$$
- Changes by:
$$\frac{\$500-\$2,000}{\$2,000} \times 100% = -75\%$$
]
]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-60-1.png" width="504" style="display: block; margin: auto;" />
]

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# The Effective Rate of Protection: Example

- We can see that the .hi-purple[structure of tariffs] often impact different stages of the production process differently

- Here, a tariff on car parts gave 25% more protection to domestic car parts producers, at the expense of a 75% loss to domestic car assemblers

]

.pull-right[
<img src="2.1-slides_files/figure-html/unnamed-chunk-61-1.png" width="504" style="display: block; margin: auto;" />
]

---

# The Effective Rate of Protection

.pull-left[
.smaller[
- In general, we see that effective rate of protection `$\neq$` nominal tariff rate
  - May be higher or lower, or even negative

- Tariffs on foreign inputs generate *negative* effective rates of protection, and tariffs on final products generate *positive* eeffective rates of protection for a country’s domestic industry

]
]
.pull-right[
.center[
![:scale 100%](../images/tradebarriers.jpg)
]
]