Enter Values

Qd = a - bP; quantity when P = 0
Units decrease per $1 price increase
Qs = c + dP; quantity when P = 0
Units increase per $1 price increase
$
Price of imports before tariff
$
Dollar amount of tariff per unit imported
Curve Equations
Demand: Qd = a - bP
Supply: Qs = c + dP
Domestic Price: Pd = Pw + t
Imports: Qd - Qs
Model Assumptions
  • Small-country assumption: world price is exogenous
  • Linear supply and demand curves
  • Per-unit (specific) tariff, not ad valorem
  • Partial equilibrium (ignores cross-market effects)
  • No retaliation or terms-of-trade effects
  • No exchange-rate pass-through

Most reliable for small tariff changes. Large tariff scenarios are approximations. For educational purposes only.

Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Tariff Analysis Results

Free Trade (at Pw)
Price $80.00
Demand 600.00
Supply 340.00
Imports Before Tariff 260.00
Post-Tariff (at Pw + t)
Domestic Price $100.00
Demand 500.00
Supply 400.00
Imports After 100.00
Import Change -160.00
Welfare Effects
Government Revenue $2,000.00
Total Deadweight Loss $1,600.00
Production DWL $600.00
Consumption DWL $1,000.00
Surplus Changes
Consumer Surplus (ΔCS) -$11,000.00
Producer Surplus (ΔPS) +$7,400.00
Welfare Identity Check
|ΔCS| = ΔPS + Gov Rev + DWL ✓

Interpretation

A $20 per-unit tariff raises the domestic price to $100, reducing demand by 100 units and expanding domestic production by 60 units. Imports fall from 260 to 100 units. The government collects $2,000 in revenue while the economy loses $1,600 in deadweight loss.

Supply & Demand Diagram

Supply and demand diagram with tariff welfare visualization
Demand (D) Supply (S) Pw Pw + t Revenue DWL

Formula Breakdown

DWL = ½ × t × (ΔQs + ΔQd)
Gov Revenue = t × Importsafter

Understanding Tariff Welfare Effects

What Is a Tariff and How Does It Affect Welfare?

A tariff is a tax on imported goods. When a small country imposes a per-unit tariff, the domestic price rises by the full amount of the tariff (since the country cannot affect world prices). This price increase has four welfare effects: consumers lose surplus, domestic producers gain surplus, the government collects tariff revenue, and the economy suffers deadweight loss from inefficient production and reduced consumption.

Tariff Welfare Formulas
Domestic Price = Pw + t
Gov Revenue = t × Importsafter
Prod DWL = ½ × t × (Qs,after - Qs,before)
Cons DWL = ½ × t × (Qd,before - Qd,after)

The Four Welfare Regions

The tariff welfare diagram shows four distinct areas:

  • Region a (Producer Transfer): The increase in domestic producer surplus. Not a net loss, just a transfer from consumers.
  • Region b (Production DWL): Resources used to produce domestically at costs above the world price. Pure efficiency loss.
  • Region c (Government Revenue): Tariff times import quantity. A transfer from consumers to the government, not a net loss.
  • Region d (Consumption DWL): Lost consumer benefit from reduced purchases. Pure efficiency loss.

The Welfare Identity

Consumer surplus loss equals the sum of all four regions: producer gain (a) + production DWL (b) + government revenue (c) + consumption DWL (d). This identity verifies that all welfare changes are accounted for. The net welfare loss to the economy is the total deadweight loss (b + d), since the other changes are transfers.

Verification Example: Qd = 1000 - 5P, Qs = 100 + 3P, Pw = $80, t = $20.
Free trade: Qd = 600, Qs = 340, Imports = 260.
Post-tariff: Pdom = $100, Qd = 500, Qs = 400, Imports = 100.
Revenue = $2,000, Total DWL = $1,600, |ΔCS| = $11,000 = ΔPS + Rev + DWL ✓
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Frequently Asked Questions

An import tariff is a tax that a government applies to goods purchased from abroad. In the small-country model used here, the country is too small to affect the world price, so the tariff fully passes through to domestic consumers. The new domestic price equals the world price plus the per-unit tariff. Domestic producers benefit because they receive the higher domestic price for their output, while domestic consumers pay more and import less.

A tariff creates two deadweight loss triangles. The production DWL equals half times the tariff times the increase in domestic production (Qs,after minus Qs,before). The consumption DWL equals half times the tariff times the decrease in domestic consumption (Qd,before minus Qd,after). The total deadweight loss is the sum of these two triangles and represents the welfare lost because the country produces inefficiently and consumes too little.

Both arise from the wedge that the tariff drives between the world price and the domestic price. Production DWL captures the inefficiency of expanding domestic production: the country pulls resources into making goods at a marginal cost above the world price. Consumption DWL captures forgone gains from trade on the consumer side: some consumers who would have bought at the world price choose not to buy at the higher domestic price.

No. Government revenue equals the per-unit tariff times the volume of imports under the tariff. If the tariff is so large that domestic supply rises to meet domestic demand entirely, imports fall to zero and revenue is zero. This is called a prohibitive tariff. In that case the deadweight loss is even larger because the country is essentially in autarky.

The small-country assumption keeps the world price exogenous (constant) regardless of how much the country imports. This simplifies welfare accounting because there are no terms-of-trade effects. Large countries can sometimes improve their welfare with an optimal tariff by lowering the world price they pay, but that requires a different model. For most countries facing world markets, the small-country approximation is reasonable for moderate tariff changes.

With an import tariff, consumers lose surplus equal to a trapezoid (the price increase times the average quantity demanded before and after). That loss is split four ways: (1) part transfers to domestic producers as additional producer surplus; (2) part transfers to the government as tariff revenue; (3) part is lost to production deadweight loss; (4) part is lost to consumption deadweight loss. The calculator verifies this: |ΔCS| should equal ΔPS plus Government Revenue plus Total DWL.

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Sources

Krugman, P., Obstfeld, M., & Melitz, M. (2022). International Economics: Theory and Policy (12th ed.). Pearson.

Disclaimer

This calculator is for educational purposes only. Results are based on a small-country, partial-equilibrium model with linear supply and demand curves. Real-world trade involves nonlinear curves, large-country effects, exchange rate changes, retaliation, and legal considerations not captured here. This tool should not be used for policy, legal, or investment decisions.