When there is a permanent fall in the domestic money supply, the exchange rate:

Question

BlackTom AI · Accepted Answer

A permanent fall in the money supply raises the domestic nominal interest rate initially, so the domestic currency appreciates (the exchange rate, defined here as units of domestic currency per unit of foreign currency, falls) — this is the key insight from Dornbusch’s overshooting model.

1) Relevant knowledge points and concepts
- Money supply contraction → short-run decrease in real money balances (with sticky prices) → nominal interest rate rises.
- Higher domestic interest rate → capital inflows and immediate currency appreciation.
- Prices are sticky in the short run but flexible in the long run; in the long run money is neutral, and the exchange rate is tied to relative price levels (PPP).
- Dornbusch overshooting: the exchange rate adjusts more in the short run than its long-run change because asset markets move faster than goods prices.

2) Step-by-step reasoning
- Step 1 (short run): Money supply falls permanently. With sticky prices, real money balances fall, so the nominal interest rate must rise to equilibrate money demand and supply.
- Step 2 (asset market response): The higher domestic interest rate attracts capital, causing the domestic currency to appreciate immediately. Since exchange rate is domestic currency per foreign unit, appreciation means the exchange rate falls.
- Step 3 (long run adjustment): Goods prices gradually fall in response to the lower nominal money supply. Lower domestic price level implies a stronger real exchange rate, but because prices adjust, the required long-run appreciation is smaller in magnitude than the initial short-run jump.
- Step 4 (overshooting): As prices fall, the interest rate declines toward its new long-run level, and the exchange rate partially depreciates from its initially strong (low) level toward the long-run equilibrium. Thus the exchange rate "rises slightly" from the short-run trough.

3) Calculations: qualitative no-arithmetic; the sequence of interest-rate ↑ → E ↓ (short run) then prices ↓ → E ↑ slightly (toward long-run).

4) Why the correct answer is correct
Because of sticky prices and fast-moving asset markets, the initial appreciation (fall in E) overshoots the new long-run appreciation. Over time E rises a bit from that overshoot as prices adjust.

5) Why other options are incorrect
- (a) Incorrect: it predicts rise (depreciation) in the short run; but interest-rate mechanics yield immediate appreciation, not depreciation.
- (c) Incorrect: it predicts further fall over the long run, but overshooting implies the short-run fall is larger than the long-run change, so E must rise back somewhat.
- (d) Incorrect: it predicts short-run depreciation (rise) then slight long-run fall; this contradicts the effect of a contractionary money shock on interest rates and the overshooting result.

Conclusion: The exchange rate falls in the short run and rises slightly over the long run; this matches answer b.

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When there is a permanent fall in the domestic money supply, the exchange rate:单项选择题

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