Exchange rates

• Calculate the price of a good in another currency, and the percentage change in the value of a currency from data.
• Draw an exchange rate diagram and explain how a floating rate is determined and why it appreciates or depreciates.
• Explain how each of the ten factors shifts the demand for or the supply of a currency.
• Discuss, using an AD/AS diagram, what a depreciation or an appreciation does to five macroeconomic indicators.
• Explain, with a diagram, how a central bank maintains a fixed exchange rate, and distinguish devaluation and revaluation from depreciation and appreciation.
• Explain how a managed exchange rate works and what follows from an overvalued or an undervalued currency.

An exchange rate is the price of one currency expressed in terms of another. Every exchange rate therefore involves two currencies: the one being priced, and the one in which the price is stated. Written as 1 A = r B, the rate says that one unit of currency A costs r units of currency B. A is the currency being priced and B is the unit of price.

The same rate can be quoted the other way round by taking its reciprocal. If 1 A = 4 B, then 1 B = 1 ÷ 4 = 0.25 A. The two quotations describe one market price, so a rise in the first is always a fall in the second.

Exchange rates matter because buyers pay in their own currency while sellers want to be paid in theirs. An importer in country B who buys a good priced in currency A must first buy currency A, so the price the importer really pays depends on the exchange rate as well as on the seller's price. Converting a price from one currency to another is the calculation behind every later argument about exports, imports and competitiveness.

• To convert a price in currency A into currency B, multiply by r, the number of units of B per 1 A: price in B = price in A × r.
• To convert a price in currency B back into currency A, divide by the same rate: price in A = price in B ÷ r. Multiplying by the reciprocal rate (1 ÷ r) gives the same answer.
• Check the direction by sense. If one unit of A buys more than one unit of B, the number in B must be larger than the number in A; if it buys less than one unit of B, the number in B must be smaller.
• Give money answers with the currency name and to two decimal places unless they are whole numbers. Do not round the reciprocal rate before using it: divide by the original rate instead.

A change in the exchange rate changes these converted prices even when no seller changes a price list. The second example keeps the two goods and lets the Zentian dollar fall in value.

Currencies are bought and sold in the foreign exchange market. Under a floating exchange rate system the value of a currency is determined only by the demand for and the supply of that currency in this market: the government and the central bank do not intervene to influence it. The pound sterling, priced in US dollars, is the example used below.

The demand for pounds comes from holders of other currencies who need pounds. They do not want the currency for its own sake: they want something that is priced in it, so the demand for a currency is derived from the demand for the country's goods, services and assets.

• Foreign buyers of UK exports of goods and services, including tourists who visit the UK, buy pounds to pay UK sellers.
• Foreign firms and investors buy pounds to invest in the UK: to build or buy businesses, to buy shares and bonds, or to hold bank deposits.
• People abroad who send money to the UK, such as UK nationals working overseas who send part of their pay home, have that money converted into pounds.
• Speculators buy pounds when they expect the pound to rise in value.

The supply of pounds comes from holders of pounds who want another currency. To obtain it they sell pounds, so every item on the supply side is the mirror image of an item on the demand side.

• UK residents who buy imports of goods and services, including UK tourists travelling abroad, sell pounds to obtain the sellers' currencies.
• UK firms and investors sell pounds to invest in other countries.
• Foreign workers in the UK who send money to their home countries sell pounds.
• Speculators sell pounds when they expect the pound to fall in value.

The demand curve for pounds slopes downward. At a lower dollar price of the pound, UK goods, services and assets are cheaper for holders of dollars, so more of them are bought and a larger quantity of pounds is demanded. The supply curve is drawn sloping upward. At a higher dollar price of the pound each pound buys more dollars, so foreign goods and assets are cheaper for UK residents; they buy more of them and, on the assumption that they then spend more pounds in total, a larger quantity of pounds is supplied.

The equilibrium exchange rate is the rate at which the quantity of pounds demanded equals the quantity supplied. Above it there is excess supply of pounds: sellers who cannot find buyers accept fewer dollars per pound, and the rate falls. Below it there is excess demand: buyers who cannot obtain pounds offer more dollars, and the rate rises. In a floating system this adjustment needs no action by the authorities.

A rise in the value of a currency in a floating system is an appreciation: one unit buys more of the other currency. A fall in its value is a depreciation. Both result from a shift of the demand curve or the supply curve of the currency, never from a decision to set a new rate.

Every transaction in this market has two sides. Selling pounds to buy dollars is the same act as demanding dollars with pounds, so an increase in the supply of pounds is an increase in the demand for dollars. It follows that a depreciation of the pound against the dollar is an appreciation of the dollar against the pound.

Data questions give exchange rates at two or more dates and ask by how much a currency has changed in value. The size of an appreciation or a depreciation is a percentage change in the currency's price: percentage change in the value of currency A = (new price of A − old price of A) ÷ old price of A × 100, where both prices are stated in currency B. A positive answer is an appreciation of A and a negative answer is a depreciation of A.

• Use the rate that prices the currency the question asks about. If the data give 1 A = r B and the question asks about B, turn each rate round first (1 ÷ r) and then apply the formula.
• Divide by the old rate, never by the new one, and by the rate at the start of the period in question when the table covers several periods.
• Read the direction before calculating. If more of currency B is needed to buy one unit of A than before, A has appreciated; if less is needed, A has depreciated.
• State the currency, the direction and the percentage in the answer ('the Zentian dollar depreciated by 20%'), rounding to two decimal places where the figure does not terminate.

The two currencies in a rate never change by the same percentage. If currency A falls by 20% against B, each unit of A is worth 0.8 of what it was, so each unit of B is worth 1 ÷ 0.8 = 1.25 times what it was: B has risen by 25% against A. The two changes are measured from different starting values, so a 20% depreciation of one currency is a 25% appreciation of the other.

A floating exchange rate changes whenever the demand curve or the supply curve of the currency shifts. Each factor below is analysed in the same three steps. First, does it change how much of the currency foreigners need to buy (demand) or how much residents sell (supply)? Second, in which direction does that curve shift? Third, what happens to the equilibrium rate? The currency of the country being discussed is called the home currency.

Foreign demand for exports. When foreign demand for the country's exports rises, because incomes abroad rise, tastes move towards the country's goods or its goods become more competitive, foreign buyers need more of the home currency to pay the exporters. The demand for the currency shifts right and it appreciates. A fall in export demand shifts the demand for the currency left and it depreciates.

Domestic demand for imports. When residents buy more imports, because their incomes rise or their tastes move towards foreign goods, they sell more of the home currency to obtain foreign currency. The supply of the currency shifts right and it depreciates. The change is on the supply side: foreigners' demand for the currency is unaffected. A fall in import demand shifts supply left and the currency appreciates.

Foreign direct investment (FDI) is long-term investment by a firm that sets up or takes control of productive assets in another country, such as building a factory or buying a controlling share of a company. Inward FDI requires the foreign firm to buy the home currency to pay for land, construction and wages, so the demand for the currency shifts right and it appreciates. Outward FDI requires domestic firms to sell the home currency for foreign currency, so supply shifts right and it depreciates.

Portfolio investment is the purchase of financial assets in another country, such as shares and bonds, for the financial return and without control of a business. When foreigners buy more of the country's shares and bonds they must buy its currency, so demand shifts right and the currency appreciates; when residents buy more foreign shares and bonds they sell the home currency, so supply shifts right and it depreciates. Portfolio investment and bank deposits can be moved within seconds and respond quickly to changes in expected returns, so these flows can reverse quickly. FDI is slower to arrive and slower to leave.

Remittances are money sent by people working abroad to family or others in their home country. A country whose nationals work abroad receives remittances in foreign currency, which is converted into the home currency: the demand for the currency shifts right and it appreciates. A country that hosts many foreign workers sees the opposite flow: the workers sell the host country's currency to send money home, so its supply shifts right and it depreciates.

Speculation is buying or selling a currency in the expectation of profiting from a future change in its value. Traders who expect the currency to rise buy it now, so demand shifts right, and existing holders delay selling, so supply shifts left: the currency appreciates today. Traders who expect it to fall sell it now, so supply shifts right and demand shifts left: it depreciates today. Speculation therefore moves the rate in whichever direction traders expect, and the expectation can fulfil itself, because selling in anticipation of a fall causes the fall.

Relative inflation rates. If the country's inflation rate is higher than its trading partners', its goods become dearer relative to foreign goods at the existing exchange rate. Foreigners buy fewer of its exports, so the demand for the currency shifts left; residents switch towards relatively cheaper imports, so the supply of the currency shifts right. Both shifts lower the rate, so the currency depreciates. A country with lower inflation than its partners sees its currency appreciate for the opposite reasons.

Relative interest rates. If the country's interest rates rise relative to rates elsewhere, deposits and bonds in its currency pay a higher return than similar assets abroad. Foreign savers and investors move funds in, which requires them to buy the currency, so demand shifts right; residents keep more of their savings at home, so supply shifts left. The currency appreciates. The chain assumes that investors regard the country as safe and do not expect the currency to fall by more than the extra interest they earn. If interest rates are high because inflation or the risk of default is high, the inflow may not occur. A fall in relative interest rates works in reverse and the currency depreciates. This link is part of how monetary policy works in an open economy: a higher interest rate appreciates the currency, which lowers net exports.

Relative growth rates. If the country's economy grows faster than its trading partners', its households and firms have higher incomes and buy more imports, so the supply of the currency shifts right and it depreciates. If the trading partners grow faster, they buy more of the country's exports, the demand for the currency shifts right and it appreciates. This is the effect through trade. It can be offset, because strong growth may also attract foreign investment and lead markets to expect higher interest rates, both of which raise the demand for the currency. The trade effect is the one to state first; the investment effect is the qualification.

Central bank intervention is the buying or selling of its own currency by a central bank in order to influence the exchange rate. When the central bank buys its own currency it pays with foreign-currency reserves, the foreign currencies and gold it holds: the demand for the currency shifts right and it appreciates, or a fall is prevented. When the central bank sells its own currency for foreign currency, supply shifts right and the currency depreciates, or a rise is prevented, and reserves increase. In a floating system intervention is at most occasional; when it is regular or continuous the system is a managed or a fixed one, covered in later sections. Changing interest rates is the central bank's second way of influencing the rate.

The factors differ in speed. Financial flows can be moved at once, so expectations and interest rates tend to dominate movements from day to day and month to month. Trade flows, relative inflation and relative growth change more slowly and matter more over periods of years.

A change in the exchange rate works through two sets of prices. After a depreciation the country's exports are cheaper in foreign currency, although exporters' prices in the home currency have not changed, and imports are dearer in the home currency, although foreign sellers' prices have not changed. An appreciation does the reverse. Every consequence below follows from these two price changes. The depreciation is set out in full and the appreciation as its mirror image.

The first route runs through aggregate demand. Because exports are cheaper abroad, foreign buyers purchase a larger volume of them; because imports are dearer at home, residents buy a smaller volume and switch to domestic substitutes. The value of net exports (X − M) rises, provided demand for exports and imports is price elastic enough for the changes in volume to outweigh the changes in price. Net exports are a component of aggregate demand, so AD shifts right. Volumes respond more as time passes, because contracts run their term and buyers need time to find new suppliers.

The second route runs through costs. Imported raw materials, components and energy cost more in the home currency, so firms' costs of production rise at every level of output and short-run aggregate supply shifts left. The two routes act on the price level in the same direction and on real output in opposite directions.

The inflation rate. A depreciation tends to raise the rate of inflation in two ways. Dearer imported inputs raise firms' costs, and dearer imported consumer goods enter the consumer price index directly: this is imported inflation, a form of cost-push inflation. If the economy is close to full employment, the rise in net exports adds demand-pull inflation. The effect is larger the greater the share of imports in consumption and production, because more prices are affected, and the less able firms are to absorb higher costs in their profit margins. It can persist if workers obtain higher money wages to restore their real incomes, since that raises costs again.

Economic growth. Higher net exports raise aggregate demand, so real GDP rises in the short run and the rate of economic growth increases. The gain is larger when the economy has spare capacity, because firms can raise output without a large rise in costs. Growth does not rise if export and import volumes respond little to the price changes, or if production relies so heavily on imported inputs that the leftward shift of SRAS outweighs the rightward shift of AD. In the long run, dearer imported capital goods can slow investment and so the growth of productive capacity.

Unemployment. Higher output in export industries and in industries that compete with imports raises their demand for labour, so cyclical unemployment falls. The gain is not spread evenly: firms that depend on imported inputs face higher costs and may shed workers. If the economy is already at full employment there are few unemployed workers to hire, and the extra demand raises wages and prices instead of employment.

The current account balance. The current account records, among other items, the value of exports and imports of goods and services. After a depreciation, export revenue rises as more is sold abroad, and spending on imports falls if the volume bought falls by a larger percentage than the home-currency price rises. The balance therefore improves (a deficit narrows or a surplus widens), provided demand for exports and imports is price elastic enough. In the short run this condition is often not met: volumes change slowly while each unit of imports already costs more, so the balance can worsen before it improves.

Living standards. Imported goods, fuel and foreign travel cost more, so the real purchasing power of incomes falls. The loss is greatest for households that spend a large share of their income on imported necessities such as food and energy. Against that, employment and incomes rise in export and import-competing industries. Households, firms and governments that have borrowed in a foreign currency lose, because they must find more home currency to make the same repayments.

• Exporters and firms that compete with imports gain from a depreciation: their goods are more price competitive at home and abroad.
• Importers, and firms that use imported inputs, lose: their costs rise, and they must either raise prices or accept lower profit margins.
• Consumers lose purchasing power over imported goods; residents travelling abroad pay more, while the domestic tourism industry gains foreign visitors.
• Residents who hold assets abroad gain, because those assets are worth more in the home currency; borrowers with debts in a foreign currency lose.
• The government gains tax revenue if output and employment rise, and loses if it has to service foreign-currency debt or subsidise imported fuel and food.

Under a fixed exchange rate system the government or central bank sets the value of the currency against another currency, a group (basket) of currencies or, historically, gold, and then acts to keep the market rate at that value. The chosen value is often called the peg.

The value of a fixed currency changes only by official decision. A devaluation is a decision to lower the fixed value, and a revaluation is a decision to raise it. These are acts of policy in a fixed system. Depreciation and appreciation are market outcomes in a floating system, and the two pairs of terms are not interchangeable. The size of a devaluation or revaluation is calculated in the same way as any percentage change in a currency's value.

Fixing the rate does not stop the demand for and the supply of the currency from shifting. Exports, imports, investment flows and expectations change as they do under a floating rate, so the fixed rate equals the market equilibrium only by coincidence. Whenever the market rate would move away from the peg, the central bank must act. In the diagrams the fixed currency is called the peso and is priced in US dollars.

Downward pressure. Suppose that at the fixed rate the quantity of pesos supplied exceeds the quantity demanded, for example after a fall in exports or an outflow of investment. Left to the market, the rate would fall below the peg. The central bank removes the excess supply by buying pesos, paying with its foreign-currency reserves. Its purchases are an addition to the demand for pesos, so the demand curve shifts right until the market clears at the fixed rate.

• Raising interest rates is the second tool. Higher returns attract financial inflows, which raises the demand for the currency, and discourage outflows, which lowers its supply. The cost is domestic: higher interest rates reduce consumption and investment, so output and employment fall.
• The government can borrow foreign currency from other countries or from the International Monetary Fund to rebuild its reserves. The loans must be repaid, usually with conditions attached.
• It can restrict imports, or limit the amount of foreign currency that residents may buy (exchange controls). These reduce the supply of the currency, at the cost of shortages of imports and of a parallel market in which the currency trades below its official value.
• The defence is limited by the stock of reserves, which is finite. If traders doubt that the peg can hold, speculators sell the currency, reserves drain faster and the government may be forced to devalue.

Upward pressure. Suppose instead that at the fixed rate the quantity of pesos demanded exceeds the quantity supplied, for example during an export boom. Left to the market, the rate would rise above the peg. The central bank sells pesos and buys foreign currency, which adds to the supply of pesos and to its reserves, or it lowers interest rates to deter inflows. This side of the defence has no reserve limit, because a central bank can create its own currency, so it can be sustained for longer. Its costs are that the extra domestic currency can raise the money supply and inflation, and that low interest rates may add to demand in an economy that is already growing quickly.

Governments fix exchange rates for two main reasons. A known rate removes exchange-rate risk for firms that trade and invest across borders, which encourages both. A peg to the currency of a low-inflation country also disciplines domestic inflation: firms cannot rely on a falling currency to stay competitive, so there is pressure to hold down costs and wages. The price is paid in the tools of the defence: interest rates must be set to hold the rate, and a large stock of reserves must be held idle.

A managed exchange rate, or managed float, lies between the two systems. The rate is set by the demand for and the supply of the currency, but the central bank intervenes from time to time to influence its level or to limit its swings. In practice many currencies that are described as floating are managed to some degree.

• The central bank may intervene only when the rate moves too far or too fast, to smooth sudden changes.
• It may keep the rate between an upper and a lower limit around a central value. The limits may be announced or kept private.
• It may steer the rate gradually in a chosen direction, for example allowing a slow depreciation to offset higher inflation than in its trading partners.

The tools are those used to defend a fixed rate: buying or selling the currency against reserves (central bank intervention) and changing interest rates. The difference is that they are used occasionally and at the central bank's discretion, so the rate is free to move most of the time and no single value has to be defended at any cost.

Intervention can hold a currency away from the value the market would set. An overvalued currency is one whose value is above the level that market forces would set in the long run. It may be held there by the central bank buying it with reserves, by high interest rates or by exchange controls, or pushed there by speculative inflows. An undervalued currency is one whose value is below that level, usually because the central bank sells its own currency and accumulates reserves. Overvalued and undervalued describe a level compared with the market value. They are different from appreciating and depreciating, which describe a direction of change.

Consequences of an overvalued currency. Exports are dear abroad and imports are cheap at home, so export industries and industries that compete with imports lose sales, output and jobs, and the current account moves towards deficit. The benefits are on the price side: imported food, fuel, inputs and capital goods are cheaper, which holds down inflation and the costs of firms that import, and foreign-currency debt is cheaper to service. A government may choose an overvalued rate for these reasons, to restrain inflation or to keep essential imports and machinery cheap for domestic industry.

An overvalued rate is hard to sustain. At that rate there is excess supply of the currency, so the central bank must keep selling reserves or keep interest rates high. Where it rations foreign currency instead, importers face shortages and a parallel market appears. Traders who see reserves falling expect a devaluation and sell the currency, which brings the devaluation closer.

Consequences of an undervalued currency. Exports are cheap abroad and imports are dear at home, so export and import-competing industries expand, employment in them rises, the current account moves towards surplus and reserves grow. A government may choose an undervalued rate to promote exports and industrialisation. The costs fall on residents as consumers, who pay more for imports and so have lower purchasing power, and dearer imports can add to inflation. Trading partners may regard the undervaluation as an unfair advantage and retaliate with trade barriers. The reserves that accumulate have an opportunity cost, since the same resources could have financed consumption or investment at home.

Whether a currency is overvalued or undervalued is a judgement, because the long-run market value cannot be observed directly. The usual signs are a persistent current account deficit or surplus, intervention that is always in the same direction, and reserves that fall or rise year after year.