The Goods Market in Open Economy

Open-Economy Goods Market & Marshall–Lerner

coreExam · high

The open-economy goods market adds net exports NX(Y, Y*, ε) = X(Y*, ε) − IM(Y, ε)/ε to aggregate demand. Exports depend on foreign income Y* (↑) and ε (↓). Imports depend on home income Y (↑) and ε (↑). A real depreciation improves NX iff the Marshall–Lerner condition holds (export + import demand elasticities sum to >1).

Derivation

Step 1 / 7

1Press Space or click Reveal next
(hidden)
2Press Space or click Reveal next
(hidden)
3Press Space or click Reveal next
(hidden)
4Press Space or click Reveal next
(hidden)
5Press Space or click Reveal next
(hidden)
6Press Space or click Reveal next
(hidden)
7Press Space or click Reveal next
(hidden)

Aggregate Demand in the Open Economy

Z = C(Y-T) + I(Y, i) + G + NX(Y, Y^*, \varepsilon)

Net exports have three distinct arguments:

$Y$ : home income → affects imports (more income, more spending including on foreign goods)
$Y^*$ : foreign income → affects exports (foreigners' spending on our goods)
$\varepsilon$ : real exchange rate → relative-price effect on both X and IM

The NX Function

NX(Y, Y^*, \varepsilon) = X(Y^*, \varepsilon) - \frac{IM(Y, \varepsilon)}{\varepsilon}

The $1/\varepsilon$ converts imports (measured in foreign-good units) into domestic-good units so $NX$ is in the same units as $Y$ .

Why the Multiplier Shrinks

A fiscal expansion raises $Y$ → imports rise → some demand leaks abroad instead of feeding back through the multiplier loop. With marginal propensity to import $m$ :

\text{Open multiplier} = \frac{1}{1 - c_1 + m} < \frac{1}{1 - c_1} = \text{Closed multiplier}

Marshall–Lerner Condition

A real depreciation affects $NX$ through three channels:

Volume of exports rises (exports cheaper abroad).
Volume of imports falls (foreign goods more expensive at home).
Price of imports rises (relative-price effect works against $NX$ ).

ML condition: $|\eta_X| + |\eta_{IM}| > 1$ means volume effects dominate, so $\partial NX / \partial \varepsilon < 0$ .

The J-curve

Even when ML holds in the long run, it typically fails in the first 3–6 months after a depreciation:

Pre-signed contracts mean volumes are slow to adjust.
Import prices rise immediately.
Short-run effect: $NX$ worsens.
Long-run effect: $NX$ improves.

The empirical J-shape of $NX$ after major currency movements.

Worked Example

Closed multiplier = 1/(1−c₁) = 1/(1−0.6) = 2.5. Open marginal propensity to import m = 0.2. Find the open-economy multiplier for ΔG = 50.

Open multiplier = 1/(1 − c₁ + m) = 1/(1 − 0.6 + 0.2) = 1/0.6 ≈ 1.67.
ΔY = 1.67 × 50 ≈ 83 (vs 125 in closed economy).
Leakage: (2.5 − 1.67) × 50 ≈ 42 flows out via imports.

Open multiplier ≈ 1.67 < 2.5 closed. Imports leak stimulus. ΔY ≈ 83 instead of 125.

Common Mistakes

—Confusing the two effects of Y on NX: domestic Y enters IM; foreign Y* enters X (separately).
—Getting the sign of ε wrong: ↑ε means real appreciation (domestic goods expensive), which hurts NX.
—Forgetting to divide IM by ε when converting to domestic-good units.
—Assuming Marshall–Lerner always holds — it fails in the very short run (J-curve).

Exam Cues

→Open multiplier < closed multiplier because imports leak.
→Fiscal expansion in open economy: Y rises less, NX falls (↑Y → ↑IM).
→Real depreciation: works on NX only if ML holds. J-curve in the short run.
→Policy combination (Ch 20): fiscal expansion + fixed FX → full multiplier but NX deterioration.