Coffee Bean Monopoly

ACT 1

No-Trade Monopoly Equilibrium The cooperative controls the domestic coffee market

Market Setup

The Home Coffee Cooperative is the sole domestic producer. It faces the same demand as before, but now sets its own price. It has constant marginal cost MC = $15/bag.

Q^D = 300 − 4P | P = 75 − Q/4 MR = 75 − Q/2 MC = $15/bag

Note: MR has the same intercept as demand but twice the slope. Under perfect competition, MR = P. Under monopoly, MR < P.

Find the no-trade monopoly equilibrium:

Step 1 of 3 — Monopoly Output

The monopolist maximizes profit by setting MR = MC. Solve for Q^M.
75 − Q/2 = 15. Solve for Q.

Q^M =

ACT 2

Free Trade — The Monopoly's Market Power Vanishes World price P^W = $20 eliminates the cooperative's pricing power

Key Insight

Under free trade at P^W = $20, foreign exporters supply any amount at that price. The cooperative cannot charge more than P^W — if it tried, consumers would simply buy from foreign suppliers. So the cooperative is forced to act like a price-taker, setting P = P^W = MC. Free trade eliminates monopoly power!

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

Calculate the free trade equilibrium:

Step 1 of 3 — Quantities

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

Q^S = , Q^D =

ACT 3

Ad Valorem Tariff — Still Competitive Behavior t = 25% · P_t = $25 · Monopolist still can't price above tariff level

Policy in Effect — Same as the Small Country Game

The government imposes a 25% ad valorem tariff. Foreign exporters must now charge P^W×(1+t) = $25 in the Home market. The cooperative can raise its price to $25 — but no higher, since imports are still available at $25. The cooperative still behaves like a competitive firm.

P_t = $20 × 1.25 = $25 Q^S = −20 + 4P | P = 5 + Q/4 Q^D = 300 − 4P | P = 75 − Q/4

Calculate the tariff equilibrium:

Step 1 of 4 — New Quantities

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

Q^S = , Q^D =

Component	Free Trade	Tariff (t=25%)	Change
Price	$20	$25	+$5
Q^S	60	80	+20
Q^D	220	200	−20
Imports	160	120	−40
CS	$6,050	$5,000	−$1,050
PS	$450	$800	+$350
Tariff Revenue	$0	$600	+$600
Total Home Welfare	$6,500	$6,400	−$100

Under a tariff, the cooperative still competes against imports at every quantity — it cannot charge above P^W+t. So tariff analysis with a monopolist gives the same result as perfect competition. The DWL = $100. This benchmark matters — the quota will be worse.

ACT 4

Equivalent Quota — The Monopoly Awakens Same import volume M₂=120 — but now the cooperative regains market power

⚠ The Critical Difference

Under a Quota, Imports Run Out

Under the tariff, imports are always available at $25 — keeping the cooperative in check. Under a quota of 120 bags, once those 120 bags are sold, no more imports can enter. The cooperative is now the only remaining seller. Its market power returns. It faces the residual demand D − M₂ and can optimize like a monopolist again.

What We Know

The government sets a quota M₂ = 120 bags — the same import volume as under the tariff. Total demand is still Q^D = 300 − 4P. Once the 120 imported bags are sold, the cooperative is the only seller left.

Q^D = 300 − 4P | P = 75 − Q/4 M₂ = 120 bags (quota) MC = $15/bag

First, derive the residual demand the cooperative faces:

Pre-Step 1 of 2 — Residual Demand (Q form)

If total demand is Q^D = 300 − 4P and 120 bags are already filled by imports, how many bags must the cooperative supply at any price P?

Q^S_coop = − 4P

Residual Demand Confirmed

With quota M₂ = 120 bags already imported, the cooperative faces:

Q^S_coop = 180 − 4P | P = 45 − Q/4 Residual MR: MR = 45 − Q/2

The P-intercept shifts down from 75 to 45: total demand intercept minus quota/slope = 75 − 120/4 = 45.

Now find the monopoly equilibrium under the quota:

Step 1 of 4 — Cooperative's Output

The cooperative maximizes profit by setting residual MR = MC. Solve for Q^S_coop.

Q^S_coop =

Component	Free Trade	Tariff	Quota (M=120)
Price	$20	$25	$30 ← higher!
Q^S	60	80	60
Q^D	220	200	180
Imports	160	120	120 (fixed)
CS	$6,050	$5,000	$4,050
PS	$450	$800	$750
Quota Rent	—	$600	$1,200
Total Home Welfare	$6,500	$6,400	$6,000 ← worse!

Key Result: The quota causes $400 more welfare loss than the tariff with identical import volume. The cooperative's restored market power lets it charge $30 instead of $25 — the quota shelters the monopolist.

ACT 5

The Verdict: Why Tariffs Beat Quotas with a Monopolist The WTO's push for tariffication explained

Regime	Price	Imports	CS	PS	Govt Rev	Home TW
No-Trade (Monopoly)	$45	0	—	—	—	—
Free Trade	$20	160	$6,050	$450	$0	$6,500
Tariff (t=25%)	$25	120	$5,000	$800	$600	$6,400
Quota (M=120)	$30	120	$4,050	$750	$1,200	$5,600*

* Welfare = CS + PS + Quota Rent = $4,050 + $750 + $1,200 = $6,000 when govt captures rent. Shown as $5,600 if foreign exporters get the quota rent (like a VER).

Conceptual Check

Why does the quota allow the cooperative to charge a higher price than the tariff, even though both restrict imports to the same 120 bags?

The Coffee Cooperative
When the Market Becomes a Monopoly