Exchange Rates and Import-Export Prices

From an Exchange-Rate Quote to a Product Price

An exchange-rate movement matters to buyers and sellers because it changes the currency cost of a transaction. The key is to keep the quotation convention straight. In this tutorial, let $E$ denote the number of units of domestic currency required to buy one unit of foreign currency. A rise in $E$ is a depreciation of the domestic currency: foreign currency has become more expensive in domestic currency. A fall in $E$ is an appreciation of the domestic currency.

Assume initially that a foreign supplier keeps its price fixed in foreign currency and that the exchange-rate change is passed through fully. The domestic-currency price of an imported good then changes in direct proportion to $E$. For an export priced by a domestic seller in domestic currency, the foreign-currency price moves in the opposite direction if the seller keeps that domestic price fixed.

Definition: Let $P_M^*$ be an import's foreign-currency price, $P_M$ its domestic-currency price, $P_X$ an export's domestic-currency price, and $P_X^*$ its price in foreign currency. With $E$ measured in domestic currency per unit of foreign currency, the full-pass-through, fixed-price relationships are $$ P_M = E P_M^*, \qquad P_X^* = \frac{P_X}{E}. $$ These relationships assume that the relevant foreign-currency import price or domestic-currency export price stays fixed. If a seller changes its price or absorbs some of the exchange-rate movement in its margin, the price response differs.

For imports, a domestic-currency depreciation raises the converted price if the foreign-currency price is unchanged. For exports priced in domestic currency, that same depreciation lowers the price faced by foreign buyers. An appreciation reverses these directions. These are price effects; whether quantities sold change, and by how much, depends on buyers' responses and on how quickly contracts and purchasing decisions adjust.

Worked Example: A Depreciation and the Cost of an Import

A domestic retailer imports a component priced at 400 foreign-currency units. The exchange rate rises from $E=1.50$ to $E=1.65$ domestic-currency units per foreign-currency unit. Assume the supplier keeps its foreign-currency price fixed and exchange-rate pass-through to the import price is complete. Calculate the import's domestic-currency price before and after the change, then find the percentage change.

Method. Convert the foreign-currency price at each exchange rate using $P_M=EP_M^*$. The foreign price is $P_M^*=400$ at both dates.

Before the depreciation, $$ P_M = 1.50 \times 400 = 600 $$ domestic-currency units.

After the depreciation, $$ P_M = 1.65 \times 400 = 660 $$ domestic-currency units. The increase is $660-600=60$, so the percentage increase is $$ \frac{60}{600}\times 100\% = 10\%. $$ The exchange rate also rose by $(1.65-1.50)/1.50=10\%$, as full pass-through and a fixed foreign price imply.

Check and common mistake. The new price is higher, consistent with foreign currency costing more domestic currency. Multiplying the old price of 600 by 1.65 would be wrong: 1.65 is already a conversion rate, not a percentage factor. The correct calculation converts the original foreign-currency price of 400.

Exchange-Rate Pass-Through

The full-pass-through calculation is a useful benchmark, not a universal outcome. A foreign supplier might lower its foreign-currency price when the domestic currency depreciates, or an importer might absorb some of the increased cost in its margin rather than changing the price charged to local buyers. Prices may also be set in advance under contracts. Consequently, a given exchange-rate movement need not produce an equal percentage change in the observed import price.

Definition: Exchange-rate pass-through to an import price is the percentage response of that price, measured in domestic currency, to a percentage change in the exchange rate. For a finite change, a commonly used approximation is $$ \text{pass-through} \approx \frac{\%\Delta P_M}{\%\Delta E}. $$ A value of 1 (or 100%) represents full pass-through: the import price changes by the same percentage as the exchange rate. A value between 0 and 1 represents incomplete pass-through. A value of 0 means the observed import price does not change over the period being measured. This ratio is an empirical description, not a rule that every product or period must follow.

The distinction can also be seen by writing the import price as $P_M=E P_M^*$. Taking percentage changes approximately gives $\%\Delta P_M \approx \%\Delta E+\%\Delta P_M^*$. If the foreign-currency price changes in response to the exchange rate, the change in $P_M^*$ offsets or reinforces the direct conversion effect. Incomplete pass-through may reflect that offset, a change in the importer’s margin, or the fact that a price has not yet been reset.

\%\Delta P_M \approx \%\Delta E + \%\Delta P_M^*

Worked Example: Measuring Incomplete Import-Price Pass-Through

An exchange rate rises from $E=1.25$ to $E=1.35$ domestic-currency units per foreign-currency unit. Over the same interval, an import's domestic-currency price rises from 200 to 210. Calculate the approximate pass-through and infer the foreign-currency price at each date, assuming the price identity $P_M=EP_M^*$ applies.

Step 1: Calculate the exchange-rate change. The increase is $1.35-1.25=0.10$. Relative to the initial rate, the percentage increase is $$ \frac{0.10}{1.25}\times 100\% = 8\%. $$

Step 2: Calculate the import-price change. The price rises by $210-200=10$, so its percentage increase is $$ \frac{10}{200}\times 100\% = 5\%. $$

Step 3: Calculate pass-through. Using the finite-change approximation, $$ \text{pass-through} \approx \frac{5\%}{8\%}=0.625, $$ or 62.5%. The import price rose, but by less than the exchange rate.

Step 4: Recover the foreign-currency prices. Initially, $P_M^*=200/1.25=160$. At the later date, $$ P_M^*=\frac{210}{1.35}=155.555\ldots $$ foreign-currency units. The foreign-currency price fell, partly offsetting the more expensive conversion into domestic currency.

Check and common mistake. The pass-through denominator is the 8% exchange-rate change, not the 0.10 change in the quoted rate. Using $5/8$ gives 0.625. Treating 0.10 as a 10% change would incorrectly produce a different pass-through estimate.

Export Prices and the Response of Trade Flows

If a domestic exporter keeps its domestic-currency price fixed, the price paid by a foreign buyer is $P_X^*=P_X/E$. A domestic-currency depreciation therefore lowers that foreign-currency price; an appreciation raises it. This conversion effect can affect export demand, but the quantity response depends on foreign buyers’ price sensitivity. It also depends on whether the exporter keeps its domestic price fixed or changes it.

For a simple quantity calculation, suppose the foreign demand for an export follows a constant-elasticity demand function $Q=A(P_X^*)^{-\epsilon}$, where $A$ is a positive constant, $Q$ is the quantity demanded, and $\epsilon>0$ is the absolute value of the price elasticity of demand. The function implies that a lower foreign-currency price raises quantity demanded. The exact quantity ratio is

\frac{Q_1}{Q_0} = \left(\frac{P_{X,1}^*}{P_{X,0}^*}\right)^{-\epsilon}.

This model assumes that the demand relationship and its elasticity remain stable over the comparison. In practice, an exchange-rate movement does not instantly change all quantities: contracts, inventories, production capacity, and the time needed to find alternative suppliers can delay responses. A price conversion alone therefore does not establish the eventual quantity or trade-balance effect.

Worked Example: Export Prices, Quantity, and Receipts

A domestic exporter sells a product for 100 domestic-currency units per unit. Initially $E=1.00$ domestic-currency unit per foreign-currency unit. The domestic currency then depreciates, and $E$ rises to 1.25. Assume the exporter keeps its domestic price fixed and foreign demand is $Q=50{,}000/P_X^*$, where $P_X^*$ is the foreign-currency price. Initially, 500 units are sold. Calculate the foreign-currency price and quantity at each exchange rate, then compare foreign-currency revenue and domestic-currency receipts.

Step 1: Convert the export price. Initially, $$ P_{X,0}^*=\frac{100}{1.00}=100 $$ foreign-currency units per product. After the depreciation, $$ P_{X,1}^*=\frac{100}{1.25}=80. $$ The price to foreign buyers falls by $(80-100)/100=-20\%$.

Step 2: Calculate demand at the new price. The specified demand function gives $$ Q_1=\frac{50{,}000}{80}=625 $$ units. Initially it gives $Q_0=50{,}000/100=500$ units, consistent with the stated initial quantity. Sales therefore rise by $625-500=125$ units, or $125/500=25\%$.

Step 3: Compare receipts. Initial foreign-currency revenue is $100\times500=50{,}000$ foreign-currency units. New foreign-currency revenue is $80\times625=50{,}000$, unchanged under this unit-elastic demand function. Domestic-currency receipts are $100\times500=50{,}000$ initially and $100\times625=62{,}500$ after the depreciation, a 25% increase.

Check and common mistake. The price paid by foreign buyers falls because the domestic-currency export price is divided by a larger $E$. It would be incorrect to multiply 100 by 1.25 to obtain the foreign price. The quantity calculation uses the stated demand function, not an assumed percentage rule.

Why the Price Change Does Not Settle the Trade-Flow Question

A depreciation can make imports more expensive in domestic currency and exports cheaper in foreign currency under the fixed-price, full-pass-through benchmark. These price movements create incentives to reduce import purchases and increase export purchases, but they do not guarantee that those quantity changes will occur immediately or be large enough to offset the price effects on spending.

For example, if import quantity barely changes in the short run, the higher domestic-currency price can raise the amount paid for imports. If buyers have time to adjust and respond strongly to prices, import quantities may fall substantially. Similarly, lower foreign-currency export prices can attract more foreign buyers, but exporters may face capacity limits or may adjust their domestic prices instead of holding them fixed. The resulting change in trade spending depends on both prices and quantities.

A useful way to organize an analysis is to separate the steps rather than jumping from “depreciation” to “exports rise” or “imports fall.” First identify which currency price changes under the stated pricing assumption. Next determine the degree of pass-through. Then apply the demand response, if the problem supplies one. Finally, calculate revenues or expenditures using the resulting price and quantity. Without information about pass-through and demand, the direction of a price effect can often be established, while the size or even the direction of a total spending effect may remain uncertain.

Read the quotation.
With $E$ in domestic currency per foreign-currency unit, a rise in $E$ is domestic-currency depreciation.

Convert the relevant price.
For a fixed foreign-currency import price, use $P_M=EP_M^*$. For a fixed domestic-currency export price, use $P_X^*=P_X/E$.

Allow for pricing responses.
Use stated pass-through or price-setting information; do not assume that a seller keeps its price fixed unless the problem says so.

Calculate quantities and spending separately.
Apply the supplied demand information, then multiply the appropriate unit price by quantity. A price change alone does not determine total trade spending.

Exam trap: mixing up the quote and the percentage change. If $E$ is domestic currency per foreign unit, a rise in $E$ makes imports more expensive in domestic currency at a fixed foreign price, but makes a fixed domestic-currency export cheaper in foreign currency. Reversing either conclusion usually means the quote has been read as foreign currency per domestic unit. Also distinguish an absolute change in $E$ from a percentage change: a move from 1.25 to 1.35 is an increase of 0.10, but the percentage increase is $0.10/1.25=8\%$, not 10%.

These price and pass-through calculations are aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus. In applications, the stated assumptions matter: invoice currency, price-setting behavior, and the horizon over which buyers can adjust all affect how an exchange-rate movement reaches import and export prices and, ultimately, trade flows.

Check Your Understanding

For each problem, use the quotation and pricing assumptions given; distinguish the price calculation from any quantity response.

An import costs 250 foreign-currency units. The exchange rate falls from 0.80 to 0.72 domestic-currency units per foreign unit. Assume a fixed foreign price and full pass-through. Calculate the domestic import price before and after, and identify the currency movement. (Answer: 200 and 180 domestic-currency units; domestic-currency appreciation; import price falls 10%.)
An exchange rate rises from 1.20 to 1.32, while a domestic-currency import price rises from 500 to 520. Calculate approximate pass-through and the implied foreign-currency import price at the later date. (Answer: exchange rate rises 10%, import price rises 4%, pass-through is 0.40 or 40%; later foreign price is $520/1.32=393.94$ foreign-currency units, rounded to cents.)
A domestic exporter keeps its price fixed at 150 domestic-currency units per unit. The exchange rate rises from 1.50 to 1.80 domestic-currency units per foreign unit. Find the foreign-currency price at each rate and its percentage change. (Answer: 100 and 83.33 foreign-currency units per unit; the foreign-currency price falls by 16.67%, rounded to two decimals.)
An import's domestic price is initially 40 and quantity is 1,000. The exchange rate rises 5%, and import-price pass-through is 0.80. If the import-demand elasticity is $-0.50$, use percentage-change approximations to estimate the new price, quantity, and total spending. (Answer: price rises 4% to 41.60; quantity falls 2% to 980; spending rises from 40,000 to 40,768, an increase of 1.92%.)
A domestic exporter charges 120 domestic-currency units per unit. The exchange rate rises from 1.20 to 1.50 domestic-currency units per foreign unit. Foreign demand is $Q=36{,}000/P_X^*$. Find the foreign-currency prices and quantities before and after, and compare domestic-currency receipts. (Answer: foreign prices are 100 and 80; quantities are 360 and 450; domestic receipts rise from 43,200 to 54,000, a 25% increase.)

What You'll Learn