Exchange Rates, Net Exports, and Aggregate Demand

Why Exchange Rates Matter for Trade

A change in interest rates can affect the exchange rate as well as borrowing and saving decisions. If the domestic currency depreciates, domestic goods may become cheaper to foreign buyers while imported goods become more expensive to domestic buyers. But this does not by itself guarantee an improvement in net exports. The result depends on how strongly buyers adjust quantities, how much exchange-rate changes pass through to prices, and the initial values of exports and imports.

This tutorial follows that chain from exchange rates to trade values and aggregate demand. To keep the direction clear, it uses one exchange-rate convention throughout. Let $E$ be the number of units of domestic currency needed to buy one unit of foreign currency. An increase in $E$ is a domestic-currency depreciation; a decrease is an appreciation. For example, if $E$ rises from 1.20 to 1.32 domestic currency units per foreign currency unit, the domestic currency has depreciated.

Definition: Net exports, denoted $NX$, equal the value of exports $X$ minus the value of imports $M$: $NX=X-M$. A trade surplus means $NX>0$; a trade deficit means $NX<0$. In the expenditure identity for aggregate demand, $AD=C+I+G+NX$, consumption $C$, investment $I$, government purchases $G$, and net exports are measured for the same period and in consistent units.

A depreciation can raise export demand when it lowers the foreign-currency price of domestic goods. It can reduce import demand when it raises the domestic-currency price of foreign goods. These directions assume that foreign-currency prices of exports and foreign-currency prices of imports are otherwise fixed, and that the exchange-rate change passes through to buyers’ prices. In practice, firms may adjust markups or set prices in the buyer’s currency, so pass-through may be incomplete or delayed.

An interest-rate differential can be one influence on the exchange rate: for example, a fall in the domestic interest rate relative to foreign rates may put downward pressure on the domestic currency, all else equal. It is not a mechanical rule that a particular rate change produces a particular exchange-rate movement. In the examples below, any exchange-rate movement is specified as an assumption, so the trade calculations can be isolated.

From a Currency Movement to Trade Values

It is important to distinguish quantities from values. If an import price rises but its quantity falls, import expenditure depends on the product of the new price and new quantity. Likewise, export value depends on both the export price and the quantity sold. The following examples use full pass-through where stated and calculate the new values directly rather than treating every finite percentage change as an exact elasticity.

Worked Example: Depreciation with Exact Quantity Changes

A hypothetical economy initially exports goods worth $100 million and imports goods worth $100 million in a year, so its initial net exports are zero. The domestic interest rate falls from 4% to 3% per year while the foreign rate is unchanged. Suppose the domestic currency then depreciates by 10%, with full pass-through to import prices. Export quantities rise by 6%, while import quantities fall by 8%. Export prices in domestic currency and foreign import prices are held fixed. Find the new net exports and compare them with a first-order estimate.

Method. Calculate the new export value and the new import expenditure separately. A depreciation raises the domestic-currency price of each imported unit by 10%, so the import price factor is 1.10.

New export value:

X_1=100(1+0.06)=106\text{ million dollars}.

New import expenditure includes both the 10% price increase and the 8% quantity decrease:

M_1=100(1+0.10)(1-0.08)=100(1.10)(0.92)=101.2\text{ million dollars}.

Therefore,

NX_1=106-101.2=4.8\text{ million dollars}.

Initially, $NX_0=100-100=0$, so net exports improve by $4.8 million. The first-order elasticity estimate is different from the exact finite-change calculation. Treating the observed quantity changes as approximate responses to a 10% depreciation gives approximate elasticities $0.06/0.10=0.6$ for exports and $0.08/0.10=0.8$ for imports. With initially equal export and import values of $100 million, the estimate is

100\left(\frac{0.06}{0.10}+\frac{0.08}{0.10}-1\right)(0.10) =100(0.6+0.8-1)(0.10)=4.0\text{ million dollars}.

The exact change is $4.8 million, not $4.0 million. The estimate is first-order: it omits the interaction between the 10% import-price increase and the 8% quantity decrease. Indeed, import expenditure rises by only 1.2%, since $1.10\times0.92=1.012$, rather than the 2% change obtained by simply adding the two separate first-order effects.

Elasticities and the Net-Export Effect

An elasticity measures a percentage response in one variable to a percentage change in another. For this application, define the export-demand elasticity $\varepsilon_X$ as the percentage increase in export quantity associated with a 1% depreciation, under the stated price assumptions. Define the import-demand elasticity $\varepsilon_M$ as the percentage decrease in import quantity associated with a 1% depreciation. These are nonnegative response magnitudes. In a small-change calculation, the export quantity changes by approximately $\varepsilon_X\delta$ and the import quantity by approximately $-\varepsilon_M\delta$, where $\delta$ is the proportional depreciation. This approximation is not an exact rule for large changes.

Assume full pass-through, a fixed domestic-currency price for exports, a fixed foreign-currency price for imports, and a small depreciation $\delta>0$. To first order, export value rises by approximately $X\varepsilon_X\delta$. The domestic-currency cost per imported unit rises by approximately $\delta$, while import quantity falls by approximately $\varepsilon_M\delta$. Thus import expenditure rises by approximately $M(1-\varepsilon_M)\delta$. Subtracting this change in imports from the change in exports gives the approximate net-export effect.

First-order result: Under the assumptions just stated, a small depreciation has approximate effect $$ \Delta NX \approx \left[X\varepsilon_X-M(1-\varepsilon_M)\right]\delta. $$ Here $X$ and $M$ are initial export and import values. The approximation is for small changes; exact finite changes should be calculated using the changed prices and quantities.

The result follows from multiplying price and quantity changes and dropping products of small changes. For exports, the domestic-currency unit price is held fixed, so the percentage change in export value is approximately the percentage increase in export quantity, $\varepsilon_X\delta$. For imports, the new expenditure is approximately $M(1+\delta)(1-\varepsilon_M\delta)$. Expanding gives $M(1+\delta-\varepsilon_M\delta-\varepsilon_M\delta^2)$. For a small $\delta$, the second-order term $\varepsilon_M\delta^2$ is omitted, leaving an approximate import-expenditure change of $M(1-\varepsilon_M)\delta$. The difference of the two changes gives the stated formula.

If the initial trade values are equal, $X=M$, the formula simplifies to

\Delta NX\approx X(\varepsilon_X+\varepsilon_M-1)\delta.

In this balanced-trade case, the depreciation improves net exports to first order when $\varepsilon_X+\varepsilon_M>1$. This familiar condition is not a universal test independent of initial values. With a trade surplus or deficit, the more general weighted expression $X\varepsilon_X-M(1-\varepsilon_M)$ determines the direction under the model’s assumptions. Partial pass-through, changing export prices, or other price responses can also alter the result.

Worked Example: A Depreciation That Worsens the Trade Balance

A hypothetical economy initially exports $80 million and imports $100 million per quarter. Its domestic interest rate falls from 5% to 4% per year, and the domestic currency depreciates by 5%. Assume full pass-through, unchanged domestic-currency export prices, unchanged foreign-currency import prices, a 2% rise in export quantity, and a 3% fall in import quantity. Calculate the new net exports and explain why they worsen.

Method. The initial trade balance is $80-100=-20$ million dollars. Calculate each new trade value, including the exchange-rate effect on the domestic price of imports.

The new export value is

X_1=80(1.02)=81.6\text{ million dollars}.

The domestic-currency import price factor is 1.05, and the import quantity factor is 0.97. Thus,

M_1=100(1.05)(0.97)=101.85\text{ million dollars}.

New net exports are

NX_1=81.6-101.85=-20.25\text{ million dollars}.

Net exports fell from $-20.00$ million to $-20.25$ million, a deterioration of $0.25 million. The 5% rise in import prices more than offsets the 3% quantity decline: import expenditure rises by 1.85%. The example shows why “depreciation makes imports fall” is an incomplete statement. Import quantity falls here, but import expenditure rises.

Connecting Net Exports to Aggregate Demand

In the expenditure identity $AD=C+I+G+NX$, a change in net exports changes aggregate demand if the other components are held fixed. Thus, if the depreciation in the first example raises net exports by $4.8 million and consumption, investment, and government purchases do not change, aggregate demand rises by $4.8 million in the same currency units. This is an accounting comparison, not a claim that the exchange-rate effect is always large or that other components must remain unchanged.

An appreciation reverses the price incentives under the same assumptions: domestic goods become more expensive to foreign buyers, while imported goods become cheaper in domestic currency. Export quantity may fall and import quantity may rise. The resulting change in net exports depends on the initial trade values and how responsive quantities are. It is not necessarily the exact opposite of a past depreciation, because prices, quantities, and elasticities may differ across the two situations.

Worked Example: Appreciation and Aggregate Demand

A hypothetical economy exports $120 million and imports $100 million per quarter. Its domestic interest rate rises from 3% to 4% per year while the foreign rate is unchanged. Suppose the domestic currency appreciates by 4%, so $E$ falls by 4%. With full pass-through, export quantities fall by 3%, import quantities rise by 5%, domestic-currency export prices remain fixed, and foreign-currency import prices remain fixed. Find the change in net exports and the change in aggregate demand if $C$, $I$, and $G$ are unchanged.

Method. An appreciation lowers the domestic-currency price factor for imports to 0.96. Apply the stipulated quantity changes to both trade flows.

New export value:

X_1=120(1-0.03)=116.4\text{ million dollars}.

New import expenditure:

M_1=100(0.96)(1+0.05)=100.8\text{ million dollars}.

Initial net exports are $120-100=20$ million dollars. New net exports are

NX_1=116.4-100.8=15.6\text{ million dollars}, \qquad \Delta NX=15.6-20=-4.4\text{ million dollars}.

Because the other aggregate-demand components are unchanged, $\Delta AD=\Delta NX=-4.4$ million dollars. The result is consistent with the assumed price and quantity responses; it is not inferred from the interest-rate change alone.

Common Mistakes and What the Result Depends On

Reversing the quotation. With $E$ defined as domestic currency per foreign currency, a rise in $E$ is a domestic depreciation. Always check the stated convention before describing an exchange-rate movement.
Equating quantity and expenditure. A fall in import quantity does not ensure a fall in import spending. Calculate price times quantity, as in $1.10\times0.92=1.012$.
Treating a finite percentage change as an exact elasticity. A 6% observed quantity increase after a 10% depreciation implies an approximate elasticity of $0.06/0.10=0.6$, not 0.06. Even then, the elasticity formula is a first-order estimate, not an exact calculation for finite changes.
Applying the balanced-trade condition to every economy. The condition $\varepsilon_X+\varepsilon_M>1$ is the simplified first-order test when initial exports and imports have equal values. Otherwise use the weighted expression.
Assuming the exchange rate is the only determinant of trade. Income, preferences, production capacity, contracts, pricing decisions, and other influences can also affect trade flows. The calculations here hold these influences fixed.

For aggregate demand, the accounting link is direct: holding $C$, $I$, and $G$ constant, a one-dollar increase in net exports raises $AD$ by one dollar. The uncertain part is the behavioral chain leading from interest rates to the exchange rate and from the exchange rate to prices and quantities. This is why a careful answer states the quotation convention, the pass-through assumption, the initial trade values, and the response of quantities before claiming a net-export effect.

Check Your Understanding

For each question, use the stated exchange-rate convention and assumptions. Treat exact price and quantity changes multiplicatively unless the question specifically asks for a first-order estimate.

A hypothetical economy initially exports $60 million and imports $60 million. A 5% depreciation, with full pass-through, raises export quantity by 4% and lowers import quantity by 2%. Export prices in domestic currency and foreign import prices are fixed. What is the exact change in net exports? (Answer: an increase of $0.66 million)
Initially, exports are $150 million and imports are $120 million. A 4% appreciation lowers export quantity by 3% and raises import quantity by 2%. Assume full pass-through and the same fixed-price assumptions as above. Find the change in net exports. (Answer: a decrease of $2.004 million)
Initial exports are $90 million and imports are $110 million. A 8% depreciation raises export quantity by 4% and lowers import quantity by 7%, with full pass-through. Calculate the new net exports and the change from the initial balance. (Answer: new net exports are $-$16.884$ million; an improvement of $3.116 million)
Initial export and import values are each $200 million. For a small 3% depreciation, estimated elasticities are $\varepsilon_X=0.7$ and $\varepsilon_M=0.5$. Use the first-order formula to estimate the change in net exports. (Answer: an increase of $1.2 million)
Initial exports are $80 million and imports are $100 million. For a small 2% depreciation, estimated elasticities are $\varepsilon_X=0.8$ and $\varepsilon_M=0.5$. Under full pass-through and the first-order model, estimate the change in net exports and state its direction. (Answer: an increase of $0.28 million)

What You'll Learn