Fetching primary parquet sources and computing exhibits.
Tariff Lab · interactive
What does a tariff do?
A partial-equilibrium Armington model with one import-demand price elasticity ε (negative by convention). Move the sliders: watch imports shrink, the consumer pay more, the government collect revenue, and a deadweight triangle open up.
import value$85.0M
Δ imports-15.0%
tariff revenue$8.5M
dwl$417K
cs loss$4.6M
Controls
5.0%
10.0%
-3.5
$100.0M
presets:
Figure 1
Import quantity as a function of the new tariff rate
The curve traces imports Q(t) for every tariff between 0 and 50 percent, holding the baseline t₀ = 5.0% fixed. At the current new tariff t₁ = 10.0%, imports change to $85.0M, a change of -15.0%. The curvature steepens with |ε|: a more elastic import demand means the same tariff bites harder.
Method: Q₁ = Q₀·((1+t₁)/(1+t₀))^ε, where ε is the price elasticity of import demand (negative). In CES Armington, ε ≈ −σ with σ the elasticity of substitution (positive).Figure 1b
Implied import-demand curves for a family of substitution elasticities
The family of curves sweeps the new tariff t₁ ∈ [0, 50%] for five elasticities ε ∈ {−1, −2, −3, −5, −8} (equivalently σ ∈ {1, 2, 3, 5, 8}), each passing through the baseline (t₀ = 5.0%, Q₀ = $100.0M). The slope dQ/dt₁ steepens with |ε|: raw-commodity lines (ε ≈ −1) barely bend, while differentiated manufactures (ε ≈ −8) collapse by roughly half at a 20-percent wall. The median HS-10 US import sits near ε = −3 per Broda & Weinstein (2006, QJE121(2): 541-585); Kee, Nicita & Olarreaga (2008, ReStat90(4): 666-682) show a cross-product spread from near zero for raw commodities to below −10 for differentiated manufactures, the full family drawn here. Read horizontally: the same tariff t₁ delivers very different import reductions depending on which ε column the HS line falls in.
Method: Q(t1; ε) = Q0 · ((1+t1)/(1+t0))^ε under CES Armington demand, ε = −σ. Baseline t0 and Q0 read from the sliders above. References: Armington (1969, IMF Staff Papers 16(1)); Broda & Weinstein (2006, QJE 121(2)); Kee, Nicita & Olarreaga (2008, ReStat 90(4)).Figure 2
Four outcomes, before and after the tariff change
Final tariff revenue: $8.5M, compared with $5.0M at baseline. Approximate consumer-surplus loss: $4.6M. The local adjustment triangle is $417K. It is a nonnegative local-slope approximation around t₀, not the change in total welfare from an existing tariff. The foreign exporter price is fixed in this model.
Method: Harberger (1964, AER Papers & Proceedings 54(3): 58-76) triangles. ΔCS is the trapezoidal approximation P₀(t₁−t₀)(Q₀+Q₁)/2 (exact for linear demand, approximate for CES); DWL = ½·(t₁−t₀)²·|ε|·P₀Q₀/(1+t₀) is the marginal deadweight triangle under the small-country assumption.Figure 2b
Fiscal and consumer changes from the baseline tariff
At t₀ = 5.0% and t₁ = 10.0%, tariff revenue changes by $3.5M and consumer surplus changes by -$4.6M using the demand-chord approximation. Positive bars are gains; negative bars are losses. Foreign producer surplus is fixed at zero. These bars compare separate outcomes; they are not an additive decomposition of consumer loss. The local adjustment triangle is shown separately above.
Method: small-country Armington PE comparison of changes. Tariff revenue change = t₁P₀Q₁ - t₀P₀Q₀; consumer-surplus change = -ΔCS. ΔCS ≈ P₀(t₁−t₀)(Q₀+Q₁)/2 (trapezoidal). Revenue = t₁·P₀·Q₁. DWL = ½·(t₁−t₀)²·|ε|·P₀Q₀/(1+t₀). Producer surplus abroad is held at zero under the small-country price-taker assumption. References: Harberger (1964, AER P&P 54(3)); Broda, Limão & Weinstein (2008, AER 98(5)) on the terms-of-trade margin that this figure suppresses.Figure 3
Welfare surface, marginal deadweight loss over the tariff × elasticity grid
The 2D field sweeps the new tariff t₁ from 0 to 50% and the import-demand elasticity ε from −1 to −10, holding the baseline t₀ = 5.0% and import value = $100.0Mfixed. Each cell is the Harberger triangle ½ (t₁ − t₀)² |ε| P₀Q₀ / (1 + t₀); the intensity grows quadratically with the tariff gap and linearly with |ε|. The open ring marks the current slider point, and the dashed line marks t₀ (where DWL is zero by construction). This is a partial-equilibrium CGE-style scan: a full general-equilibrium welfare surface under Arkolakis, Costinot & Rodríguez-Clare (2012) would additionally fold in the home expenditure share λi and a single trade elasticity θ, collapsing to Ŵi = λi−1/θ. The shape of the isoquants above carries over; the level scales up once re-sorting across origins is allowed (Costinot & Rodríguez-Clare 2014, Handbook of International Economics vol. 4, ch. 4).
Method: marginal Harberger triangle DWL(t₀→t₁, ε) = ½·(t₁−t₀)²·|ε|·P₀Q₀/(1+t₀) evaluated on a 50×40 grid of (t₁, ε). Level scaling via ACR (2012, AER 102(1)) is qualitative; this is a partial-equilibrium scan, not a quantitative-trade-model welfare surface. References: Harberger (1964, AER P&P 54(3)); Arkolakis, Costinot & Rodríguez-Clare (2012, AER 102(1)).Figure 4
Tariff-revenue Laffer curve (static, t₀ = 0)
Revenue per dollar of baseline import value as a function of the tariff rate t₁, holding t₀ = 0 and import value normalised to $1, for three substitution elasticities. Each curve has an interior maximum at the revenue-maximising tariff t* = 1 / (σ − 1) = −1 / (1 + ε), the closed-form Laffer point under CES Armington demand: ε = −4 (σ = 4) peaks at t* = 33.3%; ε = −8 (σ = 8) at 14.3%; ε = −2 (σ = 2) at 100%, off this chart. Higher elasticity sectors (differentiated manufactures) have lower revenue-maximising rates because imports collapse faster than the rate rises. Crucially the revenue-maximising tariff is not the welfare-optimal tariff: under the small-country assumption the welfare-optimal tariff is zero (Armington 1969, Harberger 1964); only with terms-of-trade power does the revenue peak coincide with a positive optimum (Johnson 1953-54 RES; Broda, Limão & Weinstein 2008 AER 98(5): 2032-2065). This figure is precomputed and does not move with the sliders above.
Method: R(t1; ε) = t1 · (1+t1)^ε per unit baseline import value, with t0 = 0 (clean Laffer benchmark). Revenue-maximising tariff in closed form: t* = -1/(1+ε) = 1/(σ-1). References: Armington (1969, IMF Staff Papers 16(1): 159-178) on CES import demand; Johnson (1953-54, Review of Economic Studies 21(2): 142-153) on optimal tariffs and the Laffer point; Broda, Limão & Weinstein (2008, AER 98(5): 2032-2065) 'Optimal Tariffs and Market Power' on empirical estimates of revenue-max rates by HS line.
Why it works this way
In the Armington (1969) framework, domestic and imported varieties are imperfect substitutes. An ad-valorem tariff raises the tax-inclusive price by a factor of (1+t), and quantity demanded slides along a CES demand curve whose elasticity of substitution σ is strictly positive; the implied price-elasticity of import demand is ε = −σ (negative). In the small-country case, the exporter's price is pinned by the world market, so the entire price wedge is paid by the importing country's consumer: producer surplus abroad is unchanged, consumer surplus at home falls, and part of the loss is recycled as tariff revenue.
What is notrecycled is the deadweight triangle: units that would have been traded at the lower price are now not traded at all. The magnitude scales as (t₁−t₀)², which is why small tariffs are nearly free and prohibitive tariffs are extraordinarily costly. Broda & Weinstein (2006) estimate a median σ of roughly 3 across HS-10 US imports, implying ε ≈ −3; Kee, Nicita & Olarreaga (2008, Review of Economics and Statistics 90(4): 666-682) document a wide cross-product distribution of import-demand elasticities, running from near zero for some raw commodities to below −10 for differentiated manufactures.
The three presets span that territory: a typical MFN bound renegotiation (5→10%), the US Section-301 schedule on Chinese imports (3→25%), and a prohibitive wall (5→50%). Try them and notice how the DWL-to-revenue ratio rises sharply with t₁.
From partial equilibrium to economy-wide welfare
Arkolakis, Costinot & Rodríguez-Clare (2012, American Economic Review 102(1): 94–130) derive a welfare relationship under stated trade-model restrictions. With positive trade elasticity θ, the welfare ratio between the current equilibrium and autarky is λii−1/θ, where λii is the domestic expenditure share. For a change between two qualifying equilibria, the percentage change is 100 × [(λiinew / λiiold)−1/θ − 1]. This page's single-product import-demand elasticity ε does not by itself establish the economy-wide trade elasticity or the new domestic expenditure share.
The authors explicitly note in footnote 33 that tariff changes require modifying their welfare formula to account for tariff revenue. It is not an upper bound on the cost of a tariff schedule. This Lab does not compute a general-equilibrium welfare estimate or an official policy score.
Reading the scenario
The displayed revenue is the final tariff-revenue level. To compare it with the change in consumer surplus, subtract baseline revenue t₀ × P₀ × Q₀ first. The consumer-surplus trapezoid and local-slope deadweight triangle are approximations for finite tariff changes. The triangle is not an additional loss to subtract from consumer surplus plus the revenue change. Results for one product cannot be scaled into economy-wide welfare without accounting for other markets, domestic production, tariff revenue and income responses.
References: Armington (1969) IMF Staff Papers16(1): 159-178; Arkolakis, Costinot & Rodríguez-Clare (2012) AER102(1): 94-130; Costinot & Rodríguez-Clare (2014) Handbook of International Economics vol. 4, ch. 4; Harberger (1964) 'The Measurement of Waste' American Economic Review Papers & Proceedings54(3): 58-76; Broda & Weinstein (2006) QJE 121(2): 541-585; Feenstra (2015) Advanced International Trade(Princeton, 2nd ed.), ch. 7; Kee, Nicita & Olarreaga (2008) Review of Economics and Statistics 90(4): 666-682.