You know the nominal exchange rate is given by the ratio of price levels in the long run (check the lecture slides if this doesn't sound familiar).

Use this relationship, the quantity theory of the price level (
𝑀
𝑡
𝑉
=
𝑃
𝑡
𝑌
𝑡
), and the corresponding expression for inflation to calculate the long-run percentage change in the exchange rate E between Home and Foreign if:

the money supply grows at 5 percent in Home,
the money supply grows at 4 percent in Foreign,
real GDP grows at 3.5 percent in Home, and
real GDP grows at 2 percent in Foreign.

Note: Include a (-) sign if the growth rate is negative.

Question

You know the nominal exchange rate is given by the ratio of price levels in the long run (check the lecture slides if this doesn't sound familiar).

Use this relationship, the quantity theory of the price level (
𝑀
𝑡
𝑉
=
𝑃
𝑡
𝑌
𝑡
), and the corresponding expression for inflation to calculate the long-run percentage change in the exchange rate E between Home and Foreign if:

the money supply grows at 5 percent in Home,
the money supply grows at 4 percent in Foreign,
real GDP grows at 3.5 percent in Home, and
real GDP grows at 2 percent in Foreign.

Note: Include a (-) sign if the growth rate is negative.

BlackTom AI · Accepted Answer

The problem asks us to use the quantity theory of the price level, M/V = P/Y, to infer the long-run change in the exchange rate E between Home and Foreign when money supplies and real GDP grow at given rates.

First, compute the inflation rate in each country using the quantity theory approach. Under the assumption that velocity is stable, the inflation rate in a country can be approximated by the difference between money-growth and real-GDP-growth: π ≈ ΔM − ΔY.
- Home: ΔM_H = 5% and ΔY_H = 3.5%, so π_H ≈ 5% − 3.5% = 1.5%.
- Foreign: ΔM_F = 4% and ΔY_F = 2%, so π_F ≈ 4% − 2% = 2.0%.

Next, determine the inflation differential between Home and Foreign, which directly affects the long-run change in the price-level ratio and thus the exchange rate E (depending on how E is defined). The differential is π_H − π_F = 1.5% − 2.0% = −0.5 percentage points.

If we define the exchange rate E as the price level in Home relative to Foreign (i.e., E ∝ P_H / P_F), then in the long run the percentage change in E mirrors the inflation differential: ΔE/E ≈ π_H − π_F.

With the differential computed as −0.5%, the implied long-run change in E is negative, indicating a depreciation of Home’s currency relative to Foreign when expressed in the Home-denominated exchange rate, or equivalently an appreciation if E is defined as Foreign per Home. In any case, the sign is negative for the Home-to-Foreign price-level ratio interpretation, i.e., the Home–Foreign exchange rate changes by −0.5% per period under this setup.

Now consider the numeric value given in the prompt (0.5). The magnitude 0.5% matches the absolute value of the computed differential, but the sign matters for the direction of the change in E. Since the calculation yields −0.5% when using ΔE/E ≈ π_H − π_F with E ∝ P_H / P_F, the correct long-run change should be reported with a negative sign under that convention. The prompt’s note to include a negative sign for negative growth aligns with this interpretation.

In summary, the calculated inflation differential is −0.5 percentage points, and the implied long-run change in the Home-to-Foreign exchange rate (with E defined as Home price level over Foreign) is −0.5%. The magnitude 0.5% matches the number provided in the answer field, but the sign is essential to convey the direction of the change according to the chosen definition of E. If one defines E differently (e.g., Foreign price level over Home), the sign would flip accordingly.

FA25 ECON 302 002 Homework #12 (International Finance)

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