Coffee Bean Trade Policy

ACT 1

Free Trade Equilibrium Establish the baseline before any policy intervention

Market Setup — Home Country Coffee Bean Market

Home is a small country: it cannot affect the world price of coffee beans.

Q^S = −20 + 4P | P = 5 + Q/4 Q^D = 300 − 4P | P = 75 − Q/4 P^World = $20/bag

P is in $/bag · Q is in million bags per year

Calculate the free trade equilibrium — enter your answers below:

Step 1 of 5

What is the autarky equilibrium price and quantity?
Set Q^S = Q^D and solve.

P* = $ , Q* =

Step 2 of 5

At the world price P^W = $20, find domestic quantity supplied and demanded.

Q^S = , Q^D =

Step 3 of 5

How many bags does Home import under free trade?

Imports =

Step 4 of 5

Calculate Consumer Surplus and Producer Surplus under free trade.
Hint: CS = ½ × (P_max − P^W) × Q^D | PS = ½ × (P^W − P_min) × Q^S
P_max is the demand intercept. P_min is the supply intercept (what P gives Q^S=0?).

CS = $ , PS = $

Step 5 of 5

What is total Home welfare under free trade?

TW = $

ACT 2

Specific vs. Ad Valorem Tariff Identify the correct policy before we calculate

⚠ Breaking News

The Coffee Farmers Association Is Lobbying!

Domestic coffee farmers are suffering from cheap imports. They have successfully lobbied Congress for a tariff. The government announces an ad valorem tariff of t = 25%.

Recall from Class

In class, we analyzed a specific tariff: the domestic price rises by a fixed dollar amount, so P_domestic = P^W + t (parallel upward shift of export supply curve).

Today's policy is an ad valorem tariff: the domestic price is a percentage of the world price, so P_domestic = P^W × (1 + t).

The four graphs below each show a horizontal export supply curve at P^W = $20 and a potential new supply curve after the tariff. Which graph correctly illustrates the effect of a 25% ad valorem tariff?

Graph A

New price = $20 × 1.25 = $25

Graph B

New price = $20 + $10 = $30

Graph C

Export supply slopes down after tariff

Graph D

Export supply rotates from horizontal

ACT 2

What if Home Were a Large Country? How does the export supply curve change under ad valorem tariff?

Recall: Large vs. Small Country

For a small country, the foreign export supply curve is horizontal — the world price is fixed no matter how much Home imports. That's why an ad valorem tariff just shifts the horizontal curve up by a fixed amount (P^W×t).

For a large country, foreign exporters must be offered a higher price to supply more — so the export supply curve is upward sloping. Now the ad valorem tariff (×(1+t)) multiplies every point on the curve by (1+t), so higher-priced points shift up more in absolute terms. The new curve is therefore steeper than a parallel shift.

Which graph correctly shows the effect of an ad valorem tariff when Home is a large country?
Each graph shows the original export supply curve (solid) and the post-tariff curve (dashed).

Graph A

Horizontal → horizontal parallel shift

Graph B

Horizontal becomes upward sloping

Graph C

Upward sloping → parallel shift up

Graph D

Upward sloping → steeper (rotation up)

ACT 3

Ad Valorem Tariff Analysis t = 25% · New domestic price = P^W × 1.25 = $25

Policy in Effect

We are working under the small country assumption. Home cannot affect the world price, so the export supply curve is horizontal at P^W = $20.

The government imposes a 25% ad valorem tariff. The new domestic price is:

P_t = P^W × (1 + t) = $20 × 1.25 = $25

Q^S = −20 + 4P | P = 5 + Q/4 Q^D = 300 − 4P | P = 75 − Q/4

Calculate the new equilibrium and welfare effects:

Step 1 of 5

At the new domestic price P_t = $25, find the new Q^S and Q^D.

Q^S = , Q^D =

Step 2 of 5

How many bags does Home import now? How has this changed from free trade?

Imports =

Step 3 of 5

Calculate the new CS and PS at P_t = $25.

CS = $ , PS = $

Step 4 of 5

What is the government's tariff revenue?
TR = tariff per unit × volume of imports

Tariff Revenue = $

Step 5 of 5

What is the total deadweight loss (DWL) from the tariff?
There are two triangles of lost welfare — one from over-production, one from under-consumption. Each = ½ × (P_t − P^W) × change in quantity.

DWL = $

Welfare Comparison: Free Trade vs. Tariff

Welfare Component	Free Trade	Tariff (t=25%)	Change
Consumer Surplus (CS)	$6,050	$5,000	−$1,050
Producer Surplus (PS)	$450	$800	+$350
Tariff Revenue	$0	$600	+$600
Total Home Welfare	$6,500	$6,400	−$100

Key Insight: The tariff creates a net welfare loss of $100 (= DWL = $50 + $50). Consumers lose $1,050, but this is only partially offset by producer gains ($350) and government revenue ($600). The small country cannot improve welfare with a tariff.

ACT 4

The Equivalent Import Quota Same import quantity as the tariff — but who gets the rent?

Setup

Instead of a tariff, the government can restrict imports using a quota — a direct limit on import quantity. If we set the quota to match the tariff outcome, the domestic price stays at $25 and CS/PS are identical. The key question becomes: who captures the price gap?

Quota Rent = (P_domestic − P^W) × M = ($25 − $20) × M

Step 1 — Find the Equivalent Quota

To replicate the tariff outcome from Act 3, what import quota M (in million bags) should the government set?
Hint: Under the tariff, how many bags were imported?

M = million bags

Case A
Govt Auctions Licenses

Case B
VER — Foreign Exporters

Case C
Domestic Importers

Case A: Government Auctions Import Licenses

The government sells import licenses to domestic importers at a competitive price. The license price equals the price gap: $25 − $20 = $5 per bag. Government collects all the rent.

Case A — True or False

In a well-organized, competitive license auction, the revenue collected by the government should exactly equal the value of the quota rents ($600).

Component	Tariff	Quota (Case A)	Difference
CS	$5,000	$5,000	$0
PS	$800	$800	$0
Govt Revenue / Rent	$600	$600	$0
Total Home Welfare	$6,400	$6,400	$0

Equivalence Result: When the government auctions licenses and captures all rent, the quota is perfectly equivalent to the tariff — same prices, same quantities, same welfare distribution.

Case B: VER — Foreign Exporters Capture the Rent

If foreign exporters receive the licenses (e.g., via Voluntary Export Restraints), they sell at $25 in the Home market but only cost $20 to produce. They pocket the $5 difference. The $600 rent leaves the Home country.

Case B — Multiple Choice

Suppose the government decides to replace the VER with an auctioned import quota (Case A) of the same quantity. What happens to Home welfare?

Component	Tariff	Quota (Case B)	Difference
CS	$5,000	$5,000	$0
PS	$800	$800	$0
Govt Revenue / Home Rent	$600	$0	−$600
Foreign Rent (lost abroad)	$0	$600	↑ outflow
Total Home Welfare	$6,400	$5,800	−$600

Worse than the tariff! Home welfare is $600 lower than under the tariff. The rent that the government would have collected as tariff revenue instead flows to foreign producers. This is exactly what happens with Voluntary Export Restraints (VERs).

Case C: Domestic Importers Receive Licenses for Free

The government gives import licenses to domestic importers at no cost (e.g., first-come-first-served, or based on historical import shares). Domestic importers buy abroad at $20 and sell domestically at $25, earning the $5 rent themselves.

Case C — Multiple Choice

When licenses are given away for free, who captures the $600 quota rent?

Case C — Rent-Seeking Behavior

Because the license is worth $600 in profit, domestic importers have a strong incentive to lobby, spend time, and expend resources to obtain it. In the extreme case where competition for licenses is perfectly competitive, how much would the rent-seeking party be willing to spend in total to capture this rent?
Think: if you could earn $600 for free, how much would you spend trying to get it?

Max lobbying expenditure = $

Component	Tariff	Quota (Case C)	Difference
CS	$5,000	$5,000	$0
PS (coffee farmers)	$800	$800	$0
Govt Revenue	$600	$0	−$600
Importer Quota Rent	$0	$600	+$600
Total Home Welfare (no rent-seeking)	$6,400	$6,400	$0

Same aggregate welfare, different distribution — unless rent-seeking occurs. If importers spend resources competing for the license (lobbying, legal fees, time), those expenditures are pure social waste. In the competitive extreme, the full $600 is burned up in the contest, and Home welfare falls to $5,800 — the same as Case B.

The Full Picture: Tariff vs. Quota Comparison

Regime	CS	PS	Govt/Home Rent	Foreign Rent	Home TW
Free Trade	$6,050	$450	$0	—	$6,500
Tariff (t=25%)	$5,000	$800	$600	$0	$6,400
Quota – Case A	$5,000	$800	$600	$0	$6,400
Quota – Case B (VER)	$5,000	$800	$0	$600	$5,800
Quota – Case C	$5,000	$800	$0 (→importers)	$0	$6,400
Quota – Case C + Rent-Seeking	$5,000	$800	$0	$0	$5,800

* Case C + Rent-Seeking: the $600 importer rent is entirely consumed by lobbying and competition for licenses, yielding the same Home TW as Case B.

🎓 Key Takeaways

1. Small country result: A tariff always reduces total home welfare — the DWL is unavoidable.
2. Tariff ≡ Quota (Case A): Equivalent when government captures all quota rent via competitive auction.
3. Case B (VERs): Worse than a tariff — the $600 rent flows abroad to foreign exporters.
4. Rent-seeking: Even if rent stays home (Case C), competitive lobbying can dissipate it entirely — yielding the same outcome as Case B.
5. The real loss: The DWL triangles are unavoidable under any import restriction — rent allocation only determines who bears the additional burden.

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