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 fall 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).
Cite: Hossen, M. D. (2026). Import quantity as a function of the new tariff rate. TradeWeave Workbench.cite
@misc{hossen_2026_figure-1,
author = {Md Deluair Hossen},
title = {Import quantity as a function of the new tariff rate},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org},
note = {Figure: Figure 1}
}
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 ∈ {2, 3, 4, 6, 9}), 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, QJE 121(2): 541–585); Kee, Nicita & Olarreaga (2008, ReStat 90(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)).
Cite: Hossen, M. D. (2026). Implied import-demand curves for a family of substitution elasticities. TradeWeave Workbench.cite
@misc{hossen_2026_figure-1b,
author = {Md Deluair Hossen},
title = {Implied import-demand curves for a family of substitution elasticities},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org},
note = {Figure: Figure 1b}
}
Figure 2
Four outcomes, before and after the tariff change
Tariff revenue collected: $8.5M. Consumer-surplus loss (reported as a positive magnitude): $4.6M. In the small-country case the foreign exporter price is fixed, so no terms-of-trade gain offsets the domestic loss; the pure-efficiency residual is the Harberger triangle: $417K. Revenue can only offset consumer loss up to the DWL triangle; the rest is a pure transfer from consumers to the treasury. Note: the DWL shown here is the marginal triangle from t₀ to t₁, not the total DWL from zero.
Method: Harberger (1964, AER Papers & Proceedings 54(2): 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.
Cite: Hossen, M. D. (2026). Four outcomes, before and after the tariff change. TradeWeave Workbench.cite
@misc{hossen_2026_figure-2,
author = {Md Deluair Hossen},
title = {Four outcomes, before and after the tariff change},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org},
note = {Figure: Figure 2}
}
Figure 2b
Welfare loss distribution at the current slider — consumer, government, producer
At the current slider point (t₀ = 5.0%, t₁ = 10.0%, ε = -3.5, import value $100.0M), the consumer-surplus loss of $4.6M is decomposed into three simultaneous flows: (1) tariff revenue of $8.5M transferred to the government, (2) a foreign-exporter producer-surplus change of $0 under the small-country assumption (the exporter price is pinned by the world market), and (3) a Harberger deadweight triangle of $417K that accrues to nobody. Read in the same units: revenue captures 184% of the consumer loss, the DWL takes 9%, and the residual (CS loss minus revenue minus DWL, $0) is the inframarginal transfer from continuing importers to the treasury — the rectangle in the standard Harberger diagram. If the country were large enough to move the world price (Broda, Limão & Weinstein 2008, AER 98(5): 2032–2065), producer surplus abroad would fall and part of the triangle would instead accrue as a terms-of-trade gain at home. On this page’s small-country assumption, that channel is zero.
Method: small-country Armington PE decomposition. 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(2)); Broda, Limão & Weinstein (2008, AER 98(5)) on the terms-of-trade margin that this figure suppresses.
Cite: Hossen, M. D. (2026). Welfare loss distribution at the current slider — consumer, government, producer. TradeWeave Workbench.cite
@misc{hossen_2026_figure-2b,
author = {Md Deluair Hossen},
title = {Welfare loss distribution at the current slider — consumer, government, producer},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org},
note = {Figure: Figure 2b}
}
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 = $100.0M fixed. 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(2)); Arkolakis, Costinot & Rodríguez-Clare (2012, AER 102(1)).
Cite: Hossen, M. D. (2026). Welfare surface — marginal deadweight loss over the tariff × elasticity grid. TradeWeave Workbench.cite
@misc{hossen_2026_figure-3,
author = {Md Deluair Hossen},
title = {Welfare surface — marginal deadweight loss over the tariff × elasticity grid},
year = {2026},
howpublished = {TradeWeave Workbench},
url = {https://tradeweave.org},
note = {Figure: Figure 3}
}
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.
Cite: Hossen, M. D. (2026). Tariff-revenue Laffer curve (static, t₀ = 0). TradeWeave Workbench.cite
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 not recycled 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
The Harberger triangle above is a single-good, small-country answer. The modern general-equilibrium benchmark is Arkolakis, Costinot & Rodríguez-Clare (2012, “New Trade Models, Same Old Gains?”, American Economic Review 102(1): 94–130). ACR show that across a large class of trade models (Armington, Krugman, Melitz, Eaton-Kortum), the welfare gain from moving from autarky to the current equilibrium collapses to one sufficient-statistic formula: Ŵi = λii−1/θ, where λii is the home country’s share of expenditure on its own goods and θ is the (positive) trade elasticity — in this page’s notation, θ = σ − 1 = |ε| − 1. A 10-point increase in λii (autarky-ward) with θ = 4 implies a welfare loss of roughly [(λiinew)/(λiiold)]−1/4 − 1 percent, which at plausible parameters lands in the 1–3 per-cent range for large tariff shocks — far larger than the marginal Harberger triangle computed above on a single HS line. Costinot & Rodríguez-Clare (2014, Handbook of International Economics, vol. 4, ch. 4) give the canonical survey. The Lab here computes partial-equilibrium effects only; treat ACR as the economy-wide upper bound on what a tariff schedule costs once general-equilibrium re-sorting is allowed.
Policy read
The current US tariff architecture is unusually active along several margins at once. The USTR Section 301 list, updated through the 2024 four-year review, keeps 25% on roughly $375B of Chinese imports and raised EV and battery lines to 100%/25% for 2024–2026. The 2025 Section 232 reciprocal tariffs and IEEPA fentanyl tariffs layered further ad-valorem wedges on imports from Canada, Mexico, and China. The EU CBAM transitional period ran through end-2025; definitive pricing on cement, iron & steel, aluminium, fertiliser, electricity and hydrogen began 1 January 2026, roughly a product-specific tariff indexed to embedded carbon. Running a 3 → 25% shock through this Lab with ε = −3 and $100M of baseline trade returns a CS loss of about $24.9M, tariff revenue of $17.2M, and a marginal DWL around $7.5M — i.e. roughly 30% of the consumer loss is pure efficiency cost, 70% is transfer. Scaling by the Section 301 notional, or by CBAM embedded-carbon volumes, is the first back-of-envelope — but the ACR general-equilibrium lens is what delivers the welfare number that shows up in USITC and CBO scoring.
References: Armington (1969) IMF Staff Papers 16(1): 159–178; Arkolakis, Costinot & Rodríguez-Clare (2012) AER 102(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(2): 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.