Exchange rates — practice questions

1. Initial Current Account Balance:

• Exports (X) = £200 billion
• Imports (M) = £250 billion
• Initial Balance = X - M = £200bn - £250bn = -£50 billion (Deficit)

2. Check Marshall-Lerner Condition: The condition states that for a depreciation to improve the current account, the sum of the price elasticities of demand for exports and imports must be greater than one.

• Formula: $PED_x + PED_m > 1$
• Calculation: $0.6 + 0.7 = 1.3$
• Result: Since $1.3 > 1$, the condition is met. The current account balance is expected to improve.

3. Calculate New Export Revenue: A 10% depreciation makes UK exports 10% cheaper for foreign buyers (a -10% price change).

• Percentage change in quantity of exports demanded = $PED_x \times (\text{absolute \% price change}) = 0.6 \times 10\% = +6\%$.
• New export revenue (assuming UK producers receive the same price in £) = Initial Revenue $\times$ (1 + % change in quantity)
• New Export Revenue = £200bn $\times 1.06 = £212 billion$.

4. Calculate New Import Expenditure: The 10% depreciation makes imports 10% more expensive for UK buyers (a +10% price change).

• Percentage change in quantity of imports demanded = $-PED_m \times (\%\text{ price change}) = -0.7 \times 10\% = -7\%$.
• New import expenditure = Initial Expenditure $\times$ (1 + % price change) $\times$ (1 + % quantity change)
• New Import Expenditure = £250bn $\times (1 + 0.10) \times (1 - 0.07)$
• New Import Expenditure = £250bn $\times 1.10 \times 0.93 = £255.75 billion$.
• Note: Import expenditure rises because the demand for imports is price inelastic ($PED_m < 1$). The 10% price rise is not fully offset by the 7% fall in quantity.

5. Calculate New Current Account Balance:

• New Balance = New Export Revenue - New Import Expenditure
• New Balance = £212bn - £255.75bn = -£43.75 billion (Deficit)

6. Conclusion: The current account deficit has fallen from £50 billion to £43.75 billion, an improvement of £6.25 billion. This confirms the prediction from the Marshall-Lerner condition.

Exchange rate effect:

• Higher interest rates → foreign investors seek higher returns → capital inflows.
• Demand for domestic currency rises → appreciation (or reduced depreciation).

Current account effects:

• Appreciation → exports more expensive abroad → X likely falls.
• Imports cheaper → M likely rises.
• Current account may worsen — conflicts with anti-inflation policy if deficit already exists.

Domestic growth effects:

• Higher rates → ↓ C and I → AD falls → growth slows (intended to reduce inflation).
• Stronger currency further reduces net exports → additional AD contraction.
• Combined: significant growth slowdown — unemployment may rise (Phillips trade-off accepted to cut inflation).

Impossible trinity context:

• With free capital mobility and floating rate, the country retains monetary independence — rate rise is effective domestically.
• If the rate were fixed, raising rates would attract inflows but require intervention or domestic contraction to maintain peg — trilemma binds.

Judgement: Policy likely reduces inflation but at cost of slower growth, higher unemployment, and possible BOP deterioration via appreciation — illustrates conflict between macro objectives.