Suppose exchange rates are defined as foreign currency per dollar and foreign goods per U.S. goods. According to purchasing-power parity, if the price of a basket of goods in the United States rose from $1,500 to $2,000 and the price of the same basket of goods rose from 600 units of some other country's currency to 1,000 units of that country's currency, then the

Question

Suppose exchange rates are defined as foreign currency per dollar and foreign goods per U.S. goods. According to purchasing-power parity, if the price of a basket of goods in the United States rose from $1,500 to $2,000 and the price of the same basket of goods rose from 600 units of some other country's currency to 1,000 units of that country's currency, then the

BlackTom AI · Accepted Answer

Purchasing-power parity (PPP) implies the nominal exchange rate (e, defined here as foreign currency units per US dollar) should equal the ratio of the foreign price level to the US price level: e = P_foreign / P_US. The real exchange rate (q, measured as foreign goods per US goods) can be written as q = e * (P_US / P_foreign). Under absolute PPP, q = 1 and stays unchanged if both price levels move proportionally.

Step-by-step reasoning and calculations:
1. Compute the initial nominal exchange rate using prices before the change:
   - P_US_initial = $1,500
   - P_foreign_initial = 600 (foreign currency units)
   - e_initial = P_foreign_initial / P_US_initial = 600 / 1500 = 0.4 (foreign currency per $1).
2. Compute the final nominal exchange rate after the price changes:
   - P_US_final = $2,000
   - P_foreign_final = 1,000 (foreign currency units)
   - e_final = P_foreign_final / P_US_final = 1000 / 2000 = 0.5 (foreign currency per $1).
3. Compare e_final to e_initial:
   - e increased from 0.4 to 0.5, meaning one US dollar now buys more foreign currency than before. That is a nominal appreciation of the dollar (an increase in foreign currency per dollar).

Check the real exchange rate to ensure PPP consistency:
- q_initial = e_initial * (P_US_initial / P_foreign_initial) = 0.4 * (1500 / 600) = 0.4 * 2.5 = 1.0.
- q_final = e_final * (P_US_final / P_foreign_final) = 0.5 * (2000 / 1000) = 0.5 * 2 = 1.0.
- The real exchange rate remains 1.0, so it neither appreciates nor depreciates.

Why the correct answer is correct:
- Because e rose from 0.4 to 0.5, the nominal exchange rate (foreign currency per dollar) appreciated.

Why the other options are incorrect:
- "Real exchange rate would depreciate/appreciate": incorrect because the computed real exchange rate stays constant at 1.0.
- "Nominal exchange rate would depreciate": incorrect because depreciation would mean e falls, but e actually rises.

Conclusion: The nominal exchange rate would appreciate. This matches the provided correct answer.

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