Output, Interest Rate & Exchange Rate (Mundell–Fleming)

Mundell–Fleming — Fixed vs Floating Exchange Rates

coreExam · highTA · PS5-Q1, PS5-Q2

The Mundell–Fleming model extends IS–LM to the open economy. Open IS includes net exports NX(Y,ε): appreciation (↑ε) reduces NX and shifts IS left. LM remains flat at i = iᵀ. Under floating FX with flat LM: fiscal expansion raises Y while i and E stay unchanged (no crowding-out). Under fixed FX: i = i* is forced by interest parity — monetary policy is impossible (the impossible trinity).

Derivation

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flat LM: i = iᵀ, E adjusts

Floating FX with flat LM: fiscal raises Y without changing E. Monetary easing depreciates E, shifts IS further right via NX.

Shocks

G (fiscal)200

iᵀ (monetary)4.0%

ΔY*0

Δi0.0 pp

ΔEunchanged

Floating: fiscal → ΔY only. Monetary → ΔY amplified by NX.

Fixed: fiscal → full multiplier. Monetary → impossible.

Impossible trinity: pegged E + free capital → no independent i.

The Open-Economy IS Curve

Adding net exports $NX(Y, \varepsilon)$ to the IS relation:

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

Appreciation ( $\uparrow \varepsilon$ ) makes exports expensive → $NX$ falls → IS shifts left.

Interest Parity

Arbitrage links domestic and foreign interest rates:

i = i^* + \frac{E^e - E}{E}

With fixed exchange-rate expectations: higher domestic $i$ → appreciation.

Policy Under Floating FX (Flat LM)

Since $i = i^T$ is fixed by the central bank, a fiscal expansion does not trigger appreciation:

| Policy | $i$ | $E$ | $NX$ | $Y^*$ | |--------|-----|-----|-------|-------| | $\uparrow G$ (fiscal) | unchanged | unchanged | unchanged | $\uparrow$ full multiplier | | $\downarrow i^T$ (monetary) | $\downarrow$ | depreciates | $\uparrow$ | $\uparrow\uparrow$ amplified |

Policy Under Fixed FX

$E = \bar{E}$ + interest parity $\Rightarrow$ $i = i^*$ at all times:

| Policy | Effective? | |--------|-----------| | $\uparrow G$ (fiscal) | Yes — IS right, $Y^*$ rises at forced $i = i^*$ | | $\downarrow i^T$ (monetary) | No — reserve outflows immediately reverse it |

The Impossible Trinity

A country cannot simultaneously maintain all three:

Fixed exchange rate
Perfect capital mobility
Independent monetary policy

The euro area chose 1 + 2, surrendering national monetary policy to the ECB.

Worked Example

Country A has floating FX, c₁=0.6, d₁=500, iᵀ=i*=3%. (a) Government raises G by 50. What happens to Y*, i, and E? (b) Central bank instead lowers iᵀ to 1%. What happens?

(a) IS shifts right by ΔG/(1−c₁)=50/0.4=125. iᵀ unchanged → E unchanged via interest parity. ΔY*=125.
(b) LM shifts down to i=1%. Lower i → interest parity → E depreciates → NX rises → IS also shifts right. Y* rises by more than 125.
Under fixed FX: (a) same — fiscal works. (b) impossible — reserve outflows reverse operation immediately.

Floating: (a) ΔY*=125, i unchanged, E unchanged. (b) Y* rises further — depreciation amplifies monetary easing. Fixed: fiscal works; monetary does not.

Common Mistakes

—Assuming fiscal expansion appreciates the exchange rate under flat LM — it doesn't (i is unchanged).
—Saying monetary policy always works — under fixed FX it is neutralised by reserve flows.
—Forgetting that under fixed FX, fiscal policy IS effective.
—Confusing the impossible trinity: naming only two of the three properties.

Exam Cues

→Exam pattern: 'fixed exchange rate, ↑G' → Y rises, i stays at i*, no crowding-out. Full multiplier.
→Exam pattern: 'floating FX, ↓iᵀ' → Y rises, E depreciates, NX rises — amplified effect.
→Impossible trinity: name all three (fixed E, perfect capital mobility, independent i). Euro area chose 1+2.
→German reunification: Bundesbank raised i → EMS members forced to match → other countries' Y fell.