Open Economy and Exchange Rates

I. International Flows of Capital and Goods

• National Income Identity: $Y = C + I + G + NX$, where:

  • Y = GDP (Gross Domestic Product): Total value of all goods and services produced within a country's borders during a specific period. GDP is a primary indicator of a country's economic health and growth rate, often measured quarterly or annually.

  • C = Consumption: Household spending on goods and services. This includes durable goods (e.g., cars, appliances), non-durable goods (e.g., food, clothing), and services (e.g., healthcare, education).

  • I = Investment: Spending on capital equipment (e.g., machinery, tools), inventories, and structures (e.g., factories, residential buildings). Investment is crucial for long-term economic growth.

  • G = Government Spending: Expenditures by the government on goods and services. Examples include infrastructure projects, defense spending, and public education.

  • NX = Net Exports (Trade Balance): Difference between a country's exports and imports, indicating whether a country is a net exporter or importer.

• Trade Balance (NX): $NX = EX - IM$, where:

  • EX = Exports: Goods and services sold to foreign countries. Exporting boosts a country's GDP and can create jobs.

  • IM = Imports: Goods and services purchased from foreign countries. Importing allows a country to access goods and services it may not produce efficiently.

• Trade Balance and Domestic Spending: $NX = Y – (C + I + G)$

  • Goods and services market: Trade balance equals output minus domestic spending. This relationship highlights how domestic economic activity influences the trade balance.

  • NX > 0: Trade surplus (net seller). A trade surplus indicates that a country exports more than it imports.

  • NX 0: Net capital inflow. When national saving is less than investment, a country must borrow from abroad, resulting in a net capital inflow.

• Private saving: $(Y – T – C)$: Disposable income less consumption. Private saving is the portion of household income that is not used for consumption or taxes.

• Public saving: $(T – G)$: Government tax revenue less government spending. Public saving can be positive (budget surplus) or negative (budget deficit).

• National saving: Private saving + Public saving = $(Y – C – G) = I + NX$

• Open economy: $S = I + NX$

• Closed economy: $S = I$

• U.S. Trade Balance and Saving/Investment Trends: The U.S. experienced a trade deficit. Saving and investment are also shown as percentages of GDP. Saving has generally exceeded investment. Figures are detailed from 1960 to 2015.

• Major Foreign Holders of United States Treasury Securities (December 2024): Largest holders include Japan ($1,591.3 billion), China Mainland ($1,059.8 billion), United Kingdom ($759 billion) and Luxembourg ($722.7 billion). These holdings indicate the financial interdependence between countries and the U.S.

• Largest Importers of Goods (2023):

  1. U.S. ($3.17T, 13.1% global share)

  2. China ($2.56T, 10.6%)

  3. Germany ($1.46T, 6.0%)

  4. Netherlands ($842B, 3.5%)

  5. UK ($791B, 3.3%)

  6. France ($786B, 3.2%)

  7. Japan ($786B, 3.2%)

  8. India ($673B, 2.8%)

  9. Hong Kong ($654B, 2.7%)

  10. South Korea ($643B, 2.7%)

  • World total: $24.2T

• Largest Exporters of Services: Transportation, tourism, education, telecommunications, financial and insurance services, computer and information services. The export of services contributes significantly to the economy.

• EU Digital Services Taxes: Digital enterprises (online advertising, digital marketplaces, and data transmission) pay taxes in countries where they generate significant revenue, even without a physical presence. This addresses the challenges of taxing digital businesses in the global economy.

• FRED Data: Ratio of All Employees in Manufacturing to All Employees in Total Nonfarm (multiplied by 100). In March 2025, the approximate value is 8%.

II. Nominal and Real Exchange Rates

1. Nominal Exchange Rates:

• Definition: Relative price of the currencies of two countries.

• Examples (as of a certain date):

  • $1 = 0.87 \text{ Euro (€)}

  • $1 = 0.75 \text{ British Pound (£)}

  • $1 = 1.38 \text{ C$}

  • $1 = 19.58 \text{ Pesos ($)}

  • $1 = 140.73 \text{ Japanese Yen (¥)}

  • $1 = 7.30 \text{ CNY (¥)}

• e: Foreign currency/domestic currency ($1).

• Higher 'e': Dollar appreciation (it takes more foreign currency to buy one dollar). Dollar appreciation makes U.S. goods more expensive for foreign buyers and foreign goods cheaper for U.S. buyers.

Dollar Index

• The dollar index is at 98.629. There was a 2.5% depreciation between April 2 (104.23) and April 3 (101.62) and an approximate 5% depreciation in one month. The dollar index measures the value of the U.S. dollar relative to a basket of foreign currencies.

2. Real Exchange Rates:

• Definition: Relative price of the goods of two countries.

• Example:

  • Price of a car (US): $10,000

  • Price of a similar car (China): 140,000 Yuan

  • Nominal exchange rate (e): 7 Yuan/$

  • Real exchange rate (ε) = $(10,000 * 7) / 140,000 = 0.5$

• Formula: $ε = \frac{eP}{P^*}$, where:

  • e = Nominal exchange rate

  • P = Price of domestic good

  • P* = Price of foreign good

3. Real Exchange Rate and Trade Balance

• Lower ε (cheaper domestic goods) → exports increase, imports decrease → higher NX.

• $NX = NX(ε)$: Net exports are inversely related to the real exchange rate. A lower real exchange rate makes domestic goods more competitive in international markets.

III. Exchange Rate Determination in the Long Run

1. Assumption

• Small open economy with perfect capital mobility.

• $r^*$: World interest rate.

• If $r > r^*$, capital flows in, r decreases.

• If r ##### 2. Determinants of the Real Exchange Rate (ε)

• Supply of dollars: S – I$(net capital outflow).</p><ul><li><p>$\bar{S} = Y – C – G$</p></li><li><p>$I = I(r^*) = \bar{I}$</p></li><li><p>The supply curve is vertical.</p></li></ul></li><li><p><strong>Demand for dollars:</strong> NX (foreigners need dollars to buy U.S. net exports).</p><ul><li><p>$NX = NX(ε)$</p></li><li><p>The demand curve is downward sloping.</p></li></ul></li><li><p><strong>Equilibrium:</strong>$\bar{S} – \bar{I} = NX(ε)$</p></li></ul><p>3. How Policies Influence the Real Exchange Rate</p><ul><li><p><strong>a. Fiscal policy at home (G rises or T falls):</strong></p><ul><li><p>S falls (supply curve shifts left) → ε increases → NX falls. Expansionary fiscal policy can lead to a decrease in net exports.</p></li></ul></li><li><p><strong>b. Fiscal policy abroad (foreign G rises or T falls):</strong></p><ul><li><p>World S falls →$r^*$rises → home I falls →$S – I$rises → ε decreases → NX rises. Foreign fiscal policy can affect domestic investment and net exports.</p></li></ul></li><li><p><strong>c. Shifts in investment demand (I rises, e.g., investment tax credit):</strong></p><ul><li><p>$I$rises →$S – I$falls → ε increases → NX falls. Increased investment demand tends to decrease net exports.</p></li></ul></li><li><p><strong>d. The effects of trade policies (tariff, quota):</strong></p><ul><li><p>Tariff: a tax on imported goods.</p></li><li><p>Quota: restricting the amount of imports.</p></li><li><p>tariff, quota → lower IM → higher NX (demand curve shifts upward) → higher ε (EX decrease due to higher ε, stronger dollar).</p></li><li><p>Trade balance unchanged: Protectionist trade policies do not affect the overall trade balance, but they do affect specific firms and industries. While tariffs and quotas can alter the composition of trade, they do not necessarily change the overall trade balance.</p></li></ul></li></ul><p>Word on the Street (April 13)</p><ul><li><p>Data from March 24-31, 2025, compared to April 1-8, 2025, shows:</p><ul><li><p>49$\frac{$1}{P} = \frac{e}{P^*}$</p></li><li><p>Real exchange rate =$\frac{eP}{P^*} = 1$$ (PPP)

• Nominal