In November 2020, the price level in the U.S. was
𝑃
𝑈
𝑆
=
120
. At the same date, the price level in the Eurozone was
𝑃
𝐸
𝑈
=
105
. One year later, the price levels were
𝑃
𝑈
𝑆
=
125
and
𝑃
𝐸
𝑈
=
108
. During this 12-month period, the real exchange rate was constant. The nominal exchange rate (E) is reported in euros per dollar (i.e., how many euros do we need to purchase one dollar). Using the information above, calculate the rate of change of E during this time (in percent).

Round your answer to the nearest tenth of a percent.

Question

In November 2020, the price level in the U.S. was 
𝑃
𝑈
𝑆
=
120
. At the same date, the price level in the Eurozone was 
𝑃
𝐸
𝑈
=
105
. One year later, the price levels were 
𝑃
𝑈
𝑆
=
125
 and 
𝑃
𝐸
𝑈
=
108
. During this 12-month period, the real exchange rate was constant. The nominal exchange rate (E) is reported in euros per dollar (i.e., how many euros do we need to purchase one dollar). Using the information above, calculate the rate of change of E during this time (in percent).

Round your answer to the nearest tenth of a percent.

BlackTom AI · Accepted Answer

First, restate the problem in my own words to ensure understanding: we are told that the price level in the U.S. (P_US) was 120 initially and rose to 125 after one year, while the price level in the Eurozone (P_EU) was 105 initially and rose to 108 after one year. The nominal exchange rate E is euros per dollar, and the real exchange rate is assumed constant over the year. We must find the percentage change in E over the year.

To analyze, recall the real exchange rate definition: R = E × (P_US / P_EU). If R is constant, then the ratio E2 / E1 must equal (P_EU2 / P_US2) ÷ (P_EU1 / P_US1), which simplifies to E2 = E1 × (P_EU2 × P_US1) / (P_US2 × P_EU1).

Plug in the given numbers: P_US1 = 120, P_EU1 = 105, P_US2 = 125, P_EU2 = 108.

Compute the multiplier: (P_EU2 × P_US1) / (P_US2 × P_EU1) = (108 × 120) / (125 × 105) = 12,960 / 13,125 ≈ 0.987.

Thus E2 ≈ E1 × 0.987, meaning the nominal exchange rate fell slightly over the year.

The rate of change in E is (E2 − E1) / E1 × 100% = (0.987 − 1) × 100% ≈ −1.3% (rounded to the nearest tenth).

Key point: the negative sign indicates that the dollar appreciated slightly in terms of euros (fewer euros needed per dollar) over the period, even though the eurozone price level also rose, due to the requirement that the real exchange rate stayed constant.

Note on the provided answer format: the result should be reported with its sign, so the rate of change of E is approximately −1.3%. If a positive value is presented without a sign, it would misstate the direction of the change.

FA25 ECON 302 002 Final Exam

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