📊 Welfare Effects of a Tariff
The tariff diagram: A tariff raises the world price from $P_w$ to $P_w + t$. This changes domestic quantity demanded (falls), domestic quantity supplied (rises), and imports (fall).
Welfare changes
- Consumer surplus (CS) falls — consumers pay a higher price and buy less (area = large trapezoid).
- Producer surplus (PS) rises — domestic producers sell more at a higher price (area = trapezoid between old and new price, up to new domestic supply).
- Government revenue = tariff × quantity of imports = $t \times (Q_d - Q_s)$ at the tariff price (a rectangle).
- Deadweight loss (DWL) = two triangles: production inefficiency (domestic firms produce at higher cost than world) + consumption inefficiency (consumers who would buy at Pw are priced out).
Net welfare loss = loss in CS − gain in PS − government revenue = the two DWL triangles. The tariff redistributes welfare from consumers to producers and government, but creates a net loss.
🔢 Calculating Welfare Areas
Given linear demand $Q_d = a - bP$ and supply $Q_s = c + dP$ with world price $P_w$ and tariff $t$:
- At $P_w$: domestic $Q_s^1 = c + dP_w$, domestic $Q_d^1 = a - bP_w$. Imports = $Q_d^1 - Q_s^1$.
- At $P_w + t$: domestic $Q_s^2 = c + d(P_w + t)$, domestic $Q_d^2 = a - b(P_w + t)$. Imports = $Q_d^2 - Q_s^2$.
- Government revenue = $t \times (Q_d^2 - Q_s^2)$.
- Production DWL = $\frac{1}{2} \times t \times (Q_s^2 - Q_s^1)$.
- Consumption DWL = $\frac{1}{2} \times t \times (Q_d^1 - Q_d^2)$.
- Total DWL = Production DWL + Consumption DWL.
Worked example: $Q_d = 100 - 2P$, $Q_s = -20 + 3P$, $P_w = $10$, tariff $t = $5$. \n At Pw: Qd = 80, Qs = 10, Imports = 70. \n At Pw+t = $15: Qd = 70, Qs = 25, Imports = 45. \n Gov revenue = 5 × 45 = $225. \n Prod DWL = ½ × 5 × (25−10) = $37.50. \n Cons DWL = ½ × 5 × (80−70) = $25.00. \n Total DWL = $62.50.
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📋 Quota Welfare Analysis
Key difference from tariff: A quota limits the quantity of imports directly. The welfare effects are similar to a tariff, except the government does not collect revenue — that rectangle becomes 'quota rent', which typically goes to foreign exporters (or whoever holds the import licences).
- CS falls — same as with tariff (consumers face higher price).
- PS rises — same as with tariff (domestic producers gain).
- Quota rent = (price with quota − world price) × quota quantity → goes to licence holders.
- DWL = same two triangles as tariff (production + consumption inefficiency).
- BUT → no government revenue! The net welfare loss for the importing country is LARGER than with an equivalent tariff.
Tariff vs quota comparison
- Same: Both raise domestic price, reduce imports, create DWL.
- Different: Tariff generates government revenue; quota generates quota rent for licence holders.
- Economists generally prefer tariffs — at least the revenue stays with the government.
- Quotas are less transparent — the 'implicit tariff rate' is harder for consumers to see.