International Trade: The J-Curve & Marshall-Lerner Simulator

Policy shock

Currency depreciation ε 20%

Import tariff τ 10%

Elasticities

Export elasticity η_x 0.60

Import elasticity η_m 0.60

Contract stickiness (months) 9

Time

Month 0

Trade balance

Balance now

$0.0bn

Import price shock

+0%

η_x + η_m = 1.20 — below 1.0

How it works

Depreciating the home currency and/or taxing imports both raise the home-currency price of imports immediately, before anyone has time to change how much they actually buy — contracts, shipping and habits are sticky. Volumes only catch up gradually, at a pace set by the "contract stickiness" time constant L:

adj(t) = 1 − e^(−t / L)                         (fraction of long-run adjustment reached by month t)
price shock on imports: s = (1+ε)(1+τ) − 1

Export volume:  X(t) = X₀ · (1 + η_x·ε·adj(t))
Import volume:  M(t) = M₀ · (1 − η_m·s·adj(t))
Import value:   M_val(t) = M(t) · (1 + s)
Trade balance:  TB(t) = X(t) − M_val(t)

At t = 0, adj(0) = 0: volumes haven't moved yet but the import bill already jumped by s%, so TB(0) = −M₀·s — the trade balance dips immediately. As t → ∞, adj → 1 and the long run gives the classic Marshall-Lerner condition: with balanced starting trade (X₀ = M₀), a depreciation alone (τ = 0) improves the trade balance in the long run only if

η_x + η_m > 1

Trace the dip-then-recovery on the 3D graph — that shape is the "J-curve". A low L (fast-adjusting contracts) shortens the dip; a high L (long shipping/supply contracts) stretches it out. The export flow (top lane) and import flow (bottom lane) animate at a speed proportional to their current volume, so you can watch trade physically slow down or speed up as the shock plays out.

Export flow (Home → Foreign) Import flow (Foreign → Home) Trade-balance path (J-curve)

Month 0

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