Why a weaker currency makes the trade balance worse before it gets better, and what decides how long the dip lasts.
Warming up the engine…
The J-curve describes the trade balance after a currency depreciation: it worsens first, because import prices jump before trade volumes can adjust, then improves as exports grow and imports shrink, tracing the letter J over time.
Marshall-Lerner: a depreciation improves the balance when |e_exports| + |e_imports| > 1
On day one, contracts and habits fix quantities, so a weaker currency simply makes the existing import bill dearer. Over months, foreign buyers notice cheaper exports and households substitute away from expensive imports. Whether and when the balance recovers depends entirely on how price-responsive trade volumes are.
Always pair the J-curve with the Marshall-Lerner condition: short-run inelasticity explains the dip, long-run elasticity explains the recovery. Label the time axis, not price and quantity.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Equilibrium at t 16, NX 0.
Equilibrium: t* = 16.0, NX* = 0.0
Current equations