EXCHANGE RATES: EC1001

Overview of the Foreign Exchange Market

• Foreign Exchange (FX) Market: The global marketplace where currencies are traded.
• Trade and Investment: International trade and cross-border investment necessitate the exchange of currencies to facilitate transactions.
• The Eurozone Exception: The Eurozone is a notable exception to the requirement for exchange, as its member countries share a common currency (the Euro).
• Foreign Exchange Transaction: Defined as the specific act of exchanging one currency for another.

Definitions and Mechanics of the Exchange Rate

• Standard Definition (E): The exchange rate is defined as the amount of foreign currency (FC) per unit of domestic currency (DC).
• Mathematical Formula: $E = \frac{\text{FC}}{\text{DC}}$
• UK Contextual Example: If the UK is the domestic country, an exchange rate of $E = 1.2\,US\$/\pounds$ indicates that the price of $\pounds 1$ is $US\$1.2$.
• Appreciation of Domestic Currency: An increase in the external value of the domestic currency.   - One unit of domestic currency buys more foreign currency.   - Corresponds to a rise in the exchange rate variable ($E$).
• Depreciation of Domestic Currency: A decrease in the external value of the domestic currency.   - One unit of domestic currency buys less foreign currency.   - Corresponds to a decrease in the exchange rate variable ($E$).

Numerical Examples of Appreciation and Depreciation

• Base Case: Domestic currency = $\pounds$, Foreign currency = $\$$. Initial state: $\pounds 1 = \$1.20$, so $E = 1.20$.
• Appreciation (Domestic Currency Strengthens):   - The price of $\pounds 1$ moves from $\$1.20$ to $\$1.35$.   - New exchange rate: $E = 1.35$.   - Because $E$ rises, the currency has appreciated.
• Depreciation (Domestic Currency Weakens):   - The price of $\pounds 1$ moves from $\$1.20$ to $\$0.95$.   - New exchange rate: $E = 0.95$.   - Because $E$ falls, the currency has depreciated.

Alternative Exchange Rate Definition

• Definition: The exchange rate can also be expressed as the number of units of domestic currency needed to buy one unit of foreign currency.
• Mathematical Formula: $E = \frac{\text{DC}}{\text{FC}}$
• UK Context: $E = \pounds/\text{FC}$.
• Mechanical Differences:   - Appreciation: Fewer domestic currency units are needed per unit of foreign currency, causing $E$ to fall.   - Depreciation: More domestic currency units are needed per unit of foreign currency, causing $E$ to rise.
• Module Convention: For consistency, this course utilizes the first definition ($E = \frac{\text{FC}}{\text{DC}}$) throughout all materials.

Market Determination of Exchange Rates

• Relative Price Nature: Because the exchange rate is a relative price, movements are reciprocal:   - If the domestic currency appreciates, the foreign currency must depreciate.   - If the domestic currency depreciates, the foreign currency must appreciate.
• Currency Interdependence:   - An increase in the Demand for foreign currency ($\text{FC}$) implies an increase in the Supply of domestic currency ($\text{DC}$).   - An increase in the Supply of foreign currency ($\text{FC}$) implies an increase in the Demand for domestic currency ($\text{DC}$).

Demand for the British Pound (Domestic Currency)

Factors contributing to the demand for the pound include:

• UK Exports: Increased volume of exports leads to higher demand for pounds by foreign buyers, creating upward pressure on the currency value.
• Income Payments and Transfers: When more income flows into the UK (e.g., dividends, interest, or migrant remittances), the demand for pounds increases.
• Capital Inflows: Greater investment into UK assets (stocks, bonds, real estate) raises the demand for pounds.
• Reserve Currency: Requirement for foreign central banks to hold pounds as a reserve asset.

Demand and Supply Dynamics in the Forex Market

• Context: Let $\pounds$ be the domestic currency and US\ be the foreign currency, where $E = US\$/\pounds$.
• The Demand Curve (for pounds):   - Measured in terms of US dollars (the \ price of $\pounds 1$).   - Downward Sloping: As the pound value ($\pounds \downarrow, E \downarrow$) falls, UK goods become cheaper to foreigners. This increases exports, causing the quantity of pounds demanded to rise.   - Conversely, as the pound value ($\pounds \uparrow, E \uparrow$) rises, UK goods become more expensive, exports decrease, and quantity demanded falls.
• The Supply Curve (for pounds):   - Upward Sloping: As the pound value ($\pounds \downarrow, E \downarrow$) falls, foreign goods become more expensive for UK residents. Imports decrease, and the quantity of pounds supplied to the market falls.   - As the pound value ($\pounds \uparrow, E \uparrow$) rises, foreign goods become cheaper. Imports increase, leading to a higher supply of pounds to the market.
• Equilibrium: Occurs at the point where Demand equals Supply (Quantity of $\pounds$ on the x-axis, $E = US\$/\pounds$ on the y-axis).   - Excess Supply: Exists if the rate is above the equilibrium ($E_H$).   - Excess Demand: Exists if the rate is below the equilibrium ($E_L$).

Factors Influencing Equilibrium Shifts

The equilibrium exchange rate changes due to shifts in the demand or supply for the domestic currency, driven by:

• Trade and Price Competitiveness.
• Capital Flows and Interest Rates.
• Expectations and Speculation.
• Structural Competitiveness.
• Inflation Differences (Purchasing Power Parity forces).

Price Elasticity and Export/Import Effects

• Formula for Price Elasticity of Demand (PED): $PED = \frac{\%\Delta Q}{\%\Delta P}$
• Elastic Demand: \text{if } \%\Delta Q > \%\Delta P. Foreign buyers are highly responsive to price changes.
• Inelastic Demand: \text{if } \%\Delta Q < \%\Delta P. Foreign buyers are not very responsive to price changes.

Impact of a Rise in Domestic Price of Exports

Initial state: Price = $\pounds 10$, Quantity = $100\text{ units}$, Revenue = $\pounds 1,000$.

• Case A: Inelastic Demand   - Price rises $+20\%$ ($\pounds 10 \rightarrow \pounds 12$).   - Quantity falls slightly $-5\%$ ($100 \rightarrow 95$).   - New Revenue: $\pounds 12 \times 95 = \pounds 1,140$.   - Result: Revenue increases; foreign buyers need more pounds; Demand for $\pounds \uparrow$; $\pounds$ tends to appreciate.
• Case B: Elastic Demand   - Price rises $+20\%$ ($\pounds 10 \rightarrow \pounds 12$).   - Quantity falls sharply $-30\%$ ($100 \rightarrow 70$).   - New Revenue: $\pounds 12 \times 70 = \pounds 840$.   - Result: Revenue decreases; foreign buyers need fewer pounds; Demand for $\pounds \downarrow$; $\pounds$ tends to depreciate.

Impact of a Rise in Foreign Price of Imports

Initial state: Price = $\pounds 10$, Quantity = $100\text{ units}$, Spending = $\pounds 1,000$.

• Case A: Inelastic Import Demand   - Price rises $+20\%$ ($\pounds 10 \rightarrow \pounds 12$).   - Quantity falls slightly $-5\%$ ($100 \rightarrow 95$).   - New Spending: $\pounds 12 \times 95 = \pounds 1,140$.   - Result: Spending increases; more foreign currency needed; more pounds supplied to market; Supply of $\pounds \uparrow$; $\pounds$ tends to depreciate.
• Case B: Elastic Import Demand   - Price rises $+20\%$ ($\pounds 10 \rightarrow \pounds 12$).   - Quantity falls sharply $-30\%$ ($100 \rightarrow 70$).   - New Spending: $\pounds 12 \times 70 = \pounds 840$.   - Result: Spending decreases; less foreign currency needed; fewer pounds supplied to market; Supply of $\pounds \downarrow$; $\pounds$ tends to appreciate.

Changes in Relative Price Levels

• Scenario 1: Domestic Price Level Rises (Relative to Abroad):   - Domestic goods become more expensive abroad.   - Exports $\downarrow$, Imports $\uparrow$.   - Demand for DC $\downarrow$, Supply of DC $\uparrow$.   - Domestic Currency (DC) tends to depreciate.
• Scenario 2: Foreign Price Level Rises (Relative to Domestic):   - Domestic goods become cheaper abroad.   - Exports $\uparrow$, Imports $\downarrow$.   - Demand for DC $\uparrow$, Supply of DC $\downarrow$.   - Domestic Currency (DC) tends to appreciate.

Capital Movements

• Context: Capital flows are often significantly larger than trade flows (size of capital flows > payments for exports and imports).
• Capital Outflow: Domestic investors buy foreign assets. Demand for FC $\uparrow$, which increases the Supply of DC. DC tends to depreciate.
• Capital Inflow: Foreign investors buy domestic assets. Demand for DC $\uparrow$. DC tends to appreciate.

Short-Term Capital Movements

• Interest Rate Differentials: If domestic interest rates rise relative to abroad ($i_{dom} \uparrow$), it triggers short-term capital inflows as investors seek higher returns.
• Exchange-Rate Expectations (Speculation):   - Expected Appreciation: Foreigners buy domestic assets now to profit from the higher future value, leading to capital inflows.   - Expected Depreciation: Foreigners avoid or sell domestic assets, leading to capital outflows.

Long-Term Capital Movements

• Drivers: Driven by long-run profit opportunities and expected long-run exchange rate movements.
• Investment Criteria: Foreign firms invest if expected profits are higher or if the domestic currency is expected to appreciate in the long term.
• Result: Long-term capital inflow leads to domestic currency appreciation.

Structural Changes and Competitiveness

• Variables: Technology, product quality, and comparative advantage.
• Competitiveness Deteriorates: Exports $\downarrow$, Imports $\uparrow$. Demand for DC $\downarrow$, Supply of DC $\uparrow$. DC tends to depreciate over time.
• Competitiveness Improves: Exports $\uparrow$, Imports $\downarrow$. Demand for DC $\uparrow$, Supply of DC $\downarrow$. DC tends to appreciate over time.

Graphical Shifts in Demand and Supply

• Demand for DC Rises (D0 to D1): Caused by a rise in domestic export price (if demand is inelastic) or capital inflows. Exchange rate rises from $E^<em>$ to $E^{</em>*}$.
• Demand for DC Decreases (D0 to D1): Caused by a rise in domestic export price (if demand is elastic) or capital outflows. Exchange rate falls.
• Supply for DC Rises (S0 to S1): Caused by a rise in the foreign price of imports (if demand is inelastic). Exchange rate falls from $E^<em>$ to $E^{</em>*}$.
• Supply for DC Decreases (S0 to S1): Caused by a rise in the foreign price of imports (if demand is elastic). Exchange rate rises.
• Dual Shift (Depreciation): Demand for DC decreases AND Supply for DC rises. Occurs when domestic prices rise relative to abroad or competitiveness deteriorates.
• Dual Shift (Appreciation): Demand for DC increases AND Supply for DC decreases. Occurs when foreign prices rise relative to domestic or competitiveness improves.

The Real Exchange Rate (q)

• Nominal Exchange Rate (E): The raw currency price (e.g., $E = FC/DC$).
• Definition of Real Exchange Rate: Measures the price of domestic goods relative to foreign goods after currency conversion.
• Mathematical Formula: $q = \frac{E \times P_{\text{domestic}}}{P_{\text{foreign}}}$
• Causes of Change in q: Changes in Nominal Rate ($E$), changes in relative price levels ($\frac{P_{\text{domestic}}}{P_{\text{foreign}}}$), or both.
• Competitiveness Implications:   - If q Increases: Domestic goods are more expensive; competitiveness falls; Exports $\downarrow$, Imports $\uparrow$; Pressure for currency depreciation.   - If q Decreases: Domestic goods are cheaper; competitiveness improves; Exports $\uparrow$, Imports $\downarrow$; Pressure for currency appreciation.   - Thresholds: q > 1 means domestic goods are relatively expensive/less competitive; q < 1 means domestic goods are relatively cheap/more competitive.

Purchasing Power Parity (PPP)

• Absolute PPP: A long-run theory suggesting that exchange rates reflect relative purchasing power. One unit of currency should buy the same basket of goods at home and abroad after conversion. This is a long-run tendency, not a short-run predictor.
• Implied PPP Exchange Rate ($E_{PPP}$): The rate at which the same good costs the same in both countries ($P_D \times E_{PPP} = P_F$).
• Mathematical Formula: $E_{PPP} = \frac{P_F}{P_D}$

Currency Misvaluation

• Logic:   - If Domestic Goods are expensive (P_{\text{domestic}} > P_{\text{foreign}}), the currency is Overvalued. This leads to lower exports, higher imports, and an eventual depreciation.   - If Domestic Goods are cheap (P_{\text{domestic}} < P_{\text{foreign}}), the currency is Undervalued. This leads to higher exports, lower imports, and an eventual appreciation.
• Formula for % Misvaluation: $\text{\% Misvaluation} = \frac{E - E_{PPP}}{E_{PPP}} \times 100$
• Threshold Interpretations:   - E > E_{PPP}: Domestic currency is overvalued.   - E < E_{PPP}: Domestic currency is undervalued.

Absolute PPP and the Real Exchange Rate

• If Absolute PPP holds exactly:   - $E = E_{PPP} = \frac{P_{\text{foreign}}}{P_{\text{domestic}}}$   - Substituting into the Real Exchange Rate formula: $q = \left(\frac{P_{\text{foreign}}}{P_{\text{domestic}}}\right) \times \left(\frac{P_{\text{domestic}}}{P_{\text{foreign}}}\right) = 1$   - At $q = 1$, parity is achieved; purchasing power is equal with no over/undervaluation.

Comprehensive Numerical Example

• Scenario: UK (Domestic), US (Foreign).
• Nominal Exchange Rate (E): 1.50\,$/\pounds
• UK Burger Price ($P_{UK}$): $\pounds 4.80$
• US Burger Price ($P_{US}$): $\$6.00$
• Step 1: Compute Implied PPP Rate:   - E_{PPP} = \frac{P_{US}}{P_{UK}} = \frac{6}{4.8} = 1.25\,$/\pounds
• Step 2: Determine Misvaluation:   - E (1.50) > E_{PPP} (1.25), therefore the pound is overvalued.   - $\text{\% over-valuation} = \frac{1.50 - 1.25}{1.25} \times 100 = 20\%$
• Step 3: Compute Real Exchange Rate (q):   - $q = 1.50 \times \frac{4.80}{6.00} = 1.20$   - Result: q > 1, indicates UK goods are relatively expensive and less competitive.

Relative PPP and Time Horizons

• Relative PPP Formula: $\%\Delta E \approx \pi_{\text{domestic}} - \pi_{\text{foreign}}$
• Inflation Dynamics:   - Higher domestic inflation ($\pi$) leads to domestic currency depreciation.   - Lower domestic inflation ($\pi$) leads to domestic currency appreciation.
• Implication: If Relative PPP holds, the nominal exchange rate adjusts to offset inflation differences, keeping the real exchange rate stable ($q$ has no permanent trend).
• Example: If UK prices rise $20\%$ and US prices rise $5\%$, the pound loses purchasing power. To restore parity, the pound must depreciate (or dollar appreciate) by approximately $15\%$.
• Short Run vs. Long Run:   - Short Run: Prices are slow to adjust, but exchange rates move rapidly based on news, expectations, and capital flows. PPP frequently fails in the short run.   - Long Run: Evidence suggests real exchange rates tend to mean-revert toward a long-run average, indicating that PPP holds approximately in the long run.