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 and 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 6 percent in Home,
the money supply grows at 9 percent in Foreign,
real GDP grows at 4 percent in Home, and
real GDP grows at 3 percent in Foreign.

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 and 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 6 percent in Home,
the money supply grows at 9 percent in Foreign,
real GDP grows at 4 percent in Home, and
real GDP grows at 3 percent in Foreign.

BlackTom AI · Accepted Answer

First, we restate the problem in our own words to anchor the calculation: we are to find the long-run percentage change in the exchange rate E between Home and Foreign using the quantity theory of money with V assumed constant, and given money growth rates and real GDP growth rates for both countries.

We rely on the quantity theory in the form M_t V_t = P_t Y_t. With V_t constant, the growth rate form gives inflation as the difference between money growth and real GDP growth: π ≈ ΔM − ΔY.

Now compute the inflation in each country:
- Home: ΔM_H = 6%, ΔY_H = 4%, so π_H ≈ 6% − 4% = 2%.
- Foreign: ΔM_F = 9%, ΔY_F = 3%, so π_F ≈ 9% − 3% = 6%.

The long-run exchange rate, in this framework, moves to reflect the relative price levels, i.e., E ≈ P_H / P_F. Therefore the proportional change in E over the long run is governed by the inflation differential: Δπ_E ≈ π_H − π_F.

Compute the inflation differential:
π_H − π_F = 2% − 6% = −4%.

A negative differential means the Home price level grows more slowly than the Foreign price level, which implies that the Home currency depreciates relative to Foreign. Equivalently, the percentage change in the exchange rate E (the amount of Home currency per unit of Foreign currency) is a positive 4%: E rises by 4% in the long run.

Now map this to the provided answer formats:
- If you see a value of 4, this represents 4 percentage points, i.e., a 4% change. This aligns with the computed depreciation of 4% in the exchange rate.
- If you see a value of 0.04, this is the decimal form of 4%, i.e., 4 percent. It conveys the same magnitude as 4.

Both representations, 4 and 0.04, describe the same 4% long-run depreciation of Home’s currency relative to Foreign.

So, the underlying reasoning shows that the difference in inflation rates (2% vs. 6%) drives a 4 percentage point depreciation in E, consistent with either 4 or 0.04 depending on whether you express the result as a percentage or a decimal. Any phrasing that communicates a 4% change in E would be correct in this context.

FA25 ECON 302 002 Final Exam (Chapters 7-9, 11-13, 19-20): Sample Questions

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