How Do We Calculate the Costs of Trade Protection?
Let P be dollars per unit, Qd domestic demand and Qs domestic supply in thousands of units per month. Use Qd = 120 − 2P and Qs = 2P. The coefficient 2 means a one-dollar price change changes quantity by two thousand units. Pw is world price. Multiplying price by these quantities gives thousand dollars per month.
Builds on: How Do Administrative Barriers Affect Trade?
What you will learn
- Define quantities and prices first, then calculate the correct payment base and surplus changes.
- Separate transfers from efficiency losses
Essential definitions
- Deadweight loss
- Lost total surplus not received as a benefit by another group in the model.
- Government tariff revenue
- Tariff per unit multiplied by imports remaining after the tariff.
Define the common market
Let P be dollars per unit, Qd domestic demand and Qs domestic supply in thousands of units per month. Use Qd = 120 − 2P and Qs = 2P. The coefficient 2 means a one-dollar price change changes quantity by two thousand units. Pw is world price. Multiplying price by these quantities gives thousand dollars per month.
At Pw = 20, Qd = 80 and Qs = 40, so imports are 40. A tariff of 5 raises price to 25 while imports remain: demand is 70, supply 50 and imports 20. Consumer expenditure rises from 1,600 to 1,750, domestic producer revenue from 800 to 1,250, and tariff revenue is 5 × 20 = 100. Revenue differs from producer surplus because costs still have to be covered.
Calculate surplus before adding welfare
Price is vertical and quantity horizontal in each diagram. Consumer surplus lies below demand and above price; producer surplus lies above supply and below price. A triangle's area is ½ × base × height. A quantity base in thousands per month times a dollar-price height gives thousand dollars per month.
Demand reaches zero at price 60; supply begins at zero. Under the tariff, consumer surplus falls by 375 and producer surplus rises by 225. Add government revenue of 100: national change = −375 + 225 + 100 = −50. The two loss triangles are each ½ × 5 × 10 = 25. This cross-check distinguishes lost resources or consumption from transfers.
Change the payment base when the instrument changes
A quota of 20 gives the same quantities here. Rent is (25 − 20) × 20 = 100. It remains domestic surplus only if domestic parties capture it; foreign capture adds to the national loss. Government does not automatically receive it.
For a 5-dollar subsidy on all domestic production, consumers still pay 20 and buy 80. Producers receive 25 and supply 50; imports are 30. Public cost is 5 × 50 = 250. Producer surplus gains 225, leaving a net loss of 25 with no lost-consumption triangle.
Check the exporting case separately
At Pw = 40, supply is 80 and demand 40, giving exports of 40. An export subsidy of 5 raises domestic price to 45, supply to 90 and reduces demand to 30. Exports become 60 and public cost is 5 × 60 = 300.
Consumer surplus falls from 400 to 225, a loss of 175. Producer surplus rises from 1,600 to 2,025, a gain of 425. National change is −175 + 425 − 300 = −50 thousand dollars per month. Paying only on exports produces a different consumer-price effect and payment base from the domestic production subsidy.
Tariff welfare, step by step
- Consumer surplus before = ½ × (60 − 20) × 80 = 1,600; after = ½ × (60 − 25) × 70 = 1,225.
- Producer surplus before = ½ × 20 × 40 = 400; after = ½ × 25 × 50 = 625.
- Net change = −375 + 225 + 100 = −50 thousand dollars.
- Check: production loss = ½ × 5 × 10 = 25; consumption loss = ½ × 5 × 10 = 25.
Transfers cancel within national surplus; the two triangles total 50 thousand dollars.
Import tariff: transfers and welfare loss
A tariff raises the domestic price, increases domestic output and reduces consumption and imports. The rectangle is government revenue; the two triangles are production and consumption losses.
How to read this diagram
- Put price vertically and quantity per month horizontally. Draw D and S; mark E1 where D meets the world-price line.
- Add Pw + tariff above it and mark E2 where it meets D.
- Mark old and new quantities. Shade tariff × remaining imports, then the two loss triangles.
Blue: policy revenue, rent or fiscal cost. Orange: efficiency loss. D: Qd = 120 − 2P. S: Qs = 2P. Values are illustrative; calculations are HL.
- Consumer price / producer receipts
- 25 / 25 dollars per unit
- Domestic output / consumption
- 50 / 70 thousand units
- Imports
- 20 thousand units
- Government net revenue (negative = cost)
- 100 thousand dollars
- Efficiency loss
- 50 thousand dollars
On a small screen, scroll the graph horizontally to read all labels.
Assumptions and limits: Small price-taking country; tariff passed fully into price; imports remain positive. Numerical welfare calculations are HL.
Binding import quota and quota rents
A quota limits imports, raising the price until domestic excess demand equals the quota. The rectangle is quota rent, not automatically government revenue.
How to read this diagram
- Put price vertically and quantity per month horizontally. Mark E1 where D meets Pw. Set permitted imports below free-trade imports.
- Add the quota horizontally to domestic supply; mark E2 where S + quota meets D.
- Mark domestic supply and demand at that price; their gap equals the quota.
Blue: policy revenue, rent or fiscal cost. Orange: efficiency loss. D: Qd = 120 − 2P. S: Qs = 2P. Values are illustrative; calculations are HL.
- Consumer price / producer receipts
- 25 / 25 dollars per unit
- Domestic output / consumption
- 50 / 70 thousand units
- Imports
- 20 thousand units
- Quota rent
- 100 thousand dollars
- Efficiency loss
- 50 thousand dollars plus rent if captured abroad
On a small screen, scroll the graph horizontally to read all labels.
Assumptions and limits: Competitive allocation; same D and S as the tariff example. Rents may go to government, domestic importers or foreign exporters. Calculations are HL.
Domestic production subsidy in an importing economy
The subsidy shifts effective supply down. Consumers still pay Pw while producers receive Pw + subsidy. Output rises and imports fall. Government pays the shaded rectangle; the extra-production triangle is the net loss.
How to read this diagram
- Put price vertically and quantity per month horizontally. Draw D, S and Pw; the consumer-market equilibrium E is where D meets Pw.
- Shift S down by the unit subsidy.
- At Pw read subsidized output; at that quantity mark producer receipts Pw + subsidy on original S.
Blue: policy revenue, rent or fiscal cost. Orange: efficiency loss. D: Qd = 120 − 2P. S: Qs = 2P. Values are illustrative; calculations are HL.
- Consumer price / producer receipts
- 20 / 25 dollars per unit
- Domestic output / consumption
- 50 / 80 thousand units
- Imports
- 30 thousand units
- Government net revenue (negative = cost)
- -250 thousand dollars
- Efficiency loss
- 25 thousand dollars
On a small screen, scroll the graph horizontally to read all labels.
Assumptions and limits: Subsidy paid on all domestic output; positive imports; fixed world price. Numerical welfare calculations are HL.
Export subsidy and domestic consumers
Producers can receive Pw + subsidy on exports. With free redirection of sales, domestic price rises to that level. Production rises and domestic consumption falls. The rectangle is the export subsidy bill; both triangles are losses.
How to read this diagram
- Put price vertically and quantity per month horizontally. Start with Pw above the no-trade price; mark E1 where D meets Pw.
- Add Pw + export subsidy and mark the new domestic price and E2 where the new line meets D.
- Shade the subsidy over new exports; identify extra-production and lost-consumption triangles.
Blue: policy revenue, rent or fiscal cost. Orange: efficiency loss. D: Qd = 120 − 2P. S: Qs = 2P. Values are illustrative; calculations are HL.
- Consumer price / producer receipts
- 45 / 45 dollars per unit
- Domestic output / consumption
- 90 / 30 thousand units
- Exports
- 60 thousand units
- Government net revenue (negative = cost)
- -300 thousand dollars
- Efficiency loss
- 50 thousand dollars
On a small screen, scroll the graph horizontally to read all labels.
Assumptions and limits: Small exporter with unchanged world price; eligible exports only; no externalities. Numerical calculations are HL.
Apply and evaluate
- These totals exclude externalities, retaliation and adjustment costs.
- A prohibitive tariff has no remaining imports and therefore no tariff revenue.
Common misconceptions
- Use post-policy imports for revenue.
- Consumer expenditure can rise while consumption falls; price and quantity both matter.
Knowledge check
At a subsidy of 5 and eligible domestic output of 50, what is the budget cost?
What to remember
Define quantities and prices first, then calculate the correct payment base and surplus changes. Transfers cancel within national welfare; real efficiency losses remain.
Completion records your reflection, not a test score.
Lessons in this section
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