Understanding Aggregate Demand and Exchange Rates in an Open Economy

Posted on Sep 5, 2024 in Economy

Demand in an Open Economy

Aggregate demand represents the total demand for goods and services within a country, originating from households, firms, and governments globally.

In the short run, aggregate output hinges on aggregate demand.
Conversely, long-run output necessitates the full employment of all factors of production.

Aggregate demand comprises Consumption (C), Investments (I), Government Spending (G), and Net Exports (NX).

Determinants of the Current Account

The current account reflects the balance between a country’s exports and imports. It’s primarily influenced by the real exchange rate (q), relative price levels between countries, and domestic disposable income (Y^d).

The real exchange rate influences relative prices, impacting net exports.
Disposable income affects both consumption expenditure and import expenditure.

We can express this as: CA = CA (EP*/P, Y^d) where CA = EX – IM

An increase in the price of foreign goods, measured in domestic goods, signifies an overall rise in the relative price of foreign products. Consequently, an increase in the real exchange rate (q = EP*/P) makes foreign goods more expensive compared to domestic goods. This encourages foreign consumers to substitute imported goods with domestically produced ones, leading to an increase in domestic exports and, consequently, an improvement in the domestic current account.

Conversely, as imports become relatively more expensive, substitution towards domestic goods occurs, and the value (price) of each imported unit rises. However, the substitution effect outweighs the price effect.

A real depreciation typically improves the current account, while an appreciation tends to worsen it.

The second effect stems from disposable income (Y^d).

An increase in disposable income boosts aggregate demand for consumption goods, including imported goods.
Exports remain unaffected as they depend on the foreign country’s import demand.

Output in the Short Run: Goods Market Equilibrium

Goods markets achieve equilibrium when real output (Y) matches the aggregate demand (D) for domestic goods from both domestic and foreign sources. This can be represented as: Y = D (NX (EP* /P); Y – T; I ;G )

We assume fixed money prices for goods and services in the short run. Changes in output under fixed prices create price pressures, gradually pushing the economy towards long-run equilibrium.

In the long run, the availability of production factors and the level of technology determine the output level.
Prices and the real exchange rate work to balance demand and supply.

Aggregate demand is a function of income:

Investments, government purchases, and taxes are considered exogenous.
The real exchange rate is also taken as given.
Aggregate demand equals output (D = Y) on the 45º line, denoted as point 1.
At production point Y2, firms can sell more at the given prices, leading them to increase output to meet the excess demand.
Conversely, at production point Y3, firms produce partially for storage, prompting them to reduce production to address the excess supply.
Short-run equilibrium is achieved at D = Y1, where consumers satisfy their needs, and firms sell their entire output.

The DD Schedule: Goods Market Equilibria in the Short Run

Simultaneous equilibrium in the goods market, money market, and foreign exchange market signifies general equilibrium. The DD schedule illustrates the relationship between the exchange rate and output at equilibrium.

This represents a short-run relationship due to the assumption of fixed prices.
At every point on the DD schedule, D = Y holds true.

Factors such as government demand, taxes, investments, domestic and foreign price levels, consumption functions, and foreign demand all influence the position of the DD schedule in the output-exchange rate space.

Any factor that boosts aggregate demand for domestic output shifts the DD schedule to the right, while factors that lower aggregate demand shift it to the left.

The AA Schedule: The Asset Market in the Short Run

The AA schedule represents all exchange rate-output combinations that result in simultaneous equilibria in the money market and the foreign exchange market.

The equilibrium in the foreign exchange market is determined by the interest rate parity condition: R = R* + (E^e – E)/E, where R* and E^e are fixed.

The interest rate (R) is determined in the money market, and money market equilibrium is achieved when money supply equals money demand: M^s/P = L(R;Y). Real money demand decreases with a rise in R and increases with a rise in Y.

Nominal money supply (M^s), domestic price level (P), foreign interest rate (R*), and expected future exchange rate (E^e) are considered exogenous.

Changes in output lead to changes in interest rates, which, in turn, induce changes in the exchange rate.

An increase in output leads to an interest rate increase, resulting in an appreciation of the domestic currency.
Conversely, decreases in output lead to an interest rate decrease and a depreciation of the domestic currency.

An increase in output from Y¹ to Y² raises aggregate money demand, creating excess money demand. With money supply (M^s) and price level (P) unchanged, the interest rate rises as individuals demand more liquidity to conduct additional transactions. Higher interest rates make domestic deposits more attractive, increasing the demand for domestic currency. As a result, the domestic currency appreciates at constant P* and E^e.

To maintain equilibrium in asset markets, a rise in domestic output must be accompanied by an appreciation of the domestic currency, assuming all else remains equal.

Asset Market Schedule

The AA schedule consists of all combinations of exchange rates and output levels that equalize the money and foreign exchange markets. For each output level (Y), there exists a unique exchange rate (E) that satisfies this condition.

Higher output levels necessitate lower exchange rates, resulting in a downward-sloping AA schedule in the Y-E space, and vice versa.

This relationship assumes constant money supply (M^s), price level (P), exchange rate expectations (E^e), foreign interest rate (R*), and the function describing real money demand (L).

DD Schedule versus AA Schedule

The DD schedule represents all income-interest rate combinations that establish goods market equilibrium, where the expected demand for goods from all economic actors equals the supply from firms. The real exchange rate influences net exports, leading to a positive slope for the DD schedule in the income-interest rate space.

On the other hand, the AA schedule represents all income-interest rate combinations that establish asset market equilibrium, where the asset demand from all actors matches the supply. Output affects the exchange rate through cross-border asset flows, resulting in a negative slope for the AA schedule in the income-interest rate space.

Short-Run Equilibrium for an Open Economy

DD schedule: Represents goods market equilibrium.
AA schedule: Represents asset market equilibrium.

Both schedules illustrate combinations of output (Y) and exchange rate (E). Economic equilibrium requires equilibrium in both markets.

Consider a point above both the AA and DD schedules. At a given output level, if the exchange rate is too high, interest rate parity doesn’t hold, leading to excess demand for domestic currency. This higher exchange rate makes domestic goods relatively cheaper abroad, causing excess demand in the goods market.

Excess demand in the currency market immediately lowers the exchange rate: The exchange rate adjusts to balance the expected returns on deposits in different currencies (interest rate parity).
Excess demand for domestic goods increases output: The economy moves along the AA schedule, reflecting changes in assets due to changes in output.
Output rises, and the exchange rate falls: Increasing output leads to higher money demand, raising the interest rate. This appreciation maintains interest rate parity.

Temporary Changes in Monetary and Fiscal Policy

While many variables influencing short-run equilibrium output are exogenous, we focus on varying money supply (M^s) and government expenditure (G), with some qualifications:

We consider a one-time policy change.
The expected exchange rate is assumed to equal the long-run exchange rate.
Domestic prices, foreign prices, and foreign interest rates are assumed to be unaffected.

Effects

Ø Monetary Policy:

A one-time increase in money supply shifts the AA schedule to the right. This lowers the interest rate (R) without affecting E^e, leading to an increase in the exchange rate.

The goods market remains unaffected at unchanged prices, keeping the DD schedule unchanged. However, there’s movement along the DD schedule: depreciation lowers the relative price of domestic goods, increasing foreign demand.

The new short-run equilibrium reflects higher output (Y²) – indicating increased output and employment – and a higher exchange rate (E²) – indicating depreciation.

Ø Fiscal Policy:

A one-time expansion in government spending shifts the DD schedule to the right. This additional demand for goods prompts firms to increase production. The asset market remains unaffected, leaving the AA schedule unchanged. However, there’s movement along the AA schedule: higher output at constant real money demand increases the interest rate (R). With the expected exchange rate (E^e) and foreign interest rate remaining unchanged, the domestic currency appreciates.

The new equilibrium is reached at a higher output level and an appreciated exchange rate.

Ø Full Employment Policy:

Temporary monetary and fiscal policies can stabilize output and employment during cyclical recessions. While both policies can achieve stabilization, the exchange rate reacts differently:

Fiscal policy leads to an appreciation.
Monetary policy, in contrast, leads to a depreciation.

The most suitable policy depends on the specific disturbance affecting the equilibrium.

If only fiscal policy is available for stabilization, consider:

Large time lags
The government’s intertemporal budget constraint

If individuals anticipate misuse, pricing might be biased towards higher levels, leading to self-fulfilling inflation expectations. A possible response to this could be central bank independence.

Permanent Effects of Monetary and Fiscal Policy

Permanent economic policy changes affect not only current output and exchange rates but also long-run exchange rate expectations. Let’s consider an economy initially in equilibrium:

Full employment of resources
Exchange rate equals the long-run exchange rate
Interest rates in the domestic and foreign countries are the same

A Permanent Increase in Money Supply:

Short-Run Effects:

Higher money supply lowers the interest rate. For any output level, asset market equilibrium is achieved at a lower interest rate only with a higher exchange rate, shifting the AA schedule outward. Since the increase in M^s is permanent, individuals adjust their exchange rate expectations. This increase in M^s leads to a proportional increase in the expected exchange rate (E^e), further shifting the AA schedule outward.

The new equilibrium point reflects higher E and Y compared to a temporary money expansion.

Adjustment to the Long Run:

The short-run equilibrium production point is above full employment, leading to an increase in the price level over time due to:

The competitive environment allowing for price increases
Rising costs of labor and materials

In the long run, prices increase proportionally to the money supply, resulting in no real effects. Inflation restores full employment. The increase in domestic prices shifts the DD schedule inward.

Exports become relatively more expensive, while imports become relatively cheaper, leading to a decline in net exports.

After a real appreciation, the goods market clears at any nominal exchange rate at a lower output level. The higher price level reduces real money supply, increasing the interest rate (R). This higher interest rate shifts the AA schedule inward, as only a lower exchange rate (appreciation) can now maintain interest rate parity.

Both schedules shift gradually with rising prices until full employment is reached. At this point, there’s no further upward pressure on prices. The exchange rate and price level have risen proportionally to the money supply.

A Permanent Fiscal Expansion:

A permanent fiscal expansion immediately impacts the goods market, leading to a permanent appreciation of the currency.

A one-time increase in government spending shifts the DD schedule to the right, as additional demand for goods encourages firms to increase production. The asset market remains unaffected, leaving the AA schedule unchanged. However, there’s movement along the AA schedule: higher output at constant real money demand increases the interest rate (R). With the expected exchange rate (E^e) and foreign interest rate remaining unchanged, the domestic currency appreciates.

Now, we factor in the inward shift of the AA schedule: expectations of a lower exchange rate in the future increase the demand for domestic assets. The asset market reaches equilibrium at any output level (Y) at a lower exchange rate (E).

The new short-run equilibrium shows an appreciated currency and unchanged production. In an economy starting at long-run equilibrium, a permanent fiscal policy change has no net effect on output. Instead, it causes an immediate and permanent exchange rate jump that fully offsets the fiscal policy’s direct effect on aggregate demand.

Macroeconomic Policy and the Current Account

Having examined the effects on output, let’s analyze the impact on the current account using a new tool: the XX Schedule.

The XX schedule represents different Y-E combinations that result in the same current account balance (X).
It has a positive slope in the Y-E space, as higher output/income (leading to higher imports) is associated with a higher exchange rate (depreciation, leading to stronger exports) to maintain a constant current account balance.
The XX schedule’s slope is flatter than the DD schedule’s because higher exports (induced by depreciation) must offset not only higher imports but also higher savings to keep aggregate demand equal to output.

Effects of Macro Policies on the Current Account:

The current account can deviate from the target value (X), implying that the short-run equilibrium might not lie on the XX schedule.
If NX > X, the DD schedule lies above the XX schedule.
If NX
Expansionary monetary policy shifts the short-run equilibrium, leading to a positive change in the current account as the new equilibrium lies above the XX schedule.
Expansionary fiscal policy (temporary) shifts the short-run equilibrium, leading to a negative change in the current account as the new equilibrium lies below the XX schedule.

Part 4: Stabilization with Fixed Exchange Rates

Fixed exchange rates are common and crucial for understanding stabilization policy, especially in the context of the European Union, where EMU countries have fixed exchange rates among themselves.

Under a fixed exchange rate system, the central bank commits to buying and selling domestic currency at the fixed rate in the market. This requires holding foreign reserves to sell when necessary. These transactions influence the money supply.

The central bank’s balance sheet records these transactions, reflecting the principle of double-entry bookkeeping.

Assets:

Foreign assets: Bonds denominated in foreign currencies and gold
Foreign reserves: Change with interventions in the foreign exchange market
Domestic assets: Primarily domestic bonds

Liabilities:

Deposits by private banks: Subject to legally mandated minimum reserve requirements
Currency in circulation

Foreign Exchange Interventions:

These interventions alter both assets and liabilities on the central bank’s balance sheet.

For example:

Asset purchase: Increases liabilities to private banks (if paid by check) or increases currency in circulation (if paid in cash)
Asset sale: Decreases liabilities to private banks (if paid by check) or decreases currency in circulation (if paid in cash)

Central bank asset purchases increase domestic money supply, while asset sales decrease it.

Foreign Exchange Interventions and Money Supply:

Interventions in the foreign exchange market aim to maintain the fixed exchange rate, consequently influencing domestic money supply.

Selling foreign assets strengthens the domestic currency, reduces the central bank’s foreign asset holdings, and decreases currency in circulation and/or private bank deposits.

Purchasing foreign assets using domestic currency weakens the domestic currency, increases liabilities to foreigners, and increases currency in circulation and/or private bank deposits.

Interventions to strengthen the domestic currency reduce domestic money supply, effectively shrinking the central bank’s balance sheet.

Central Bank Balance Sheet and Money Supply:

The central bank’s balance sheet reflects a surplus or deficit resulting from net purchases of foreign assets by the domestic central bank minus net purchases of domestic assets by foreign central banks. This is equivalent to the sum of the current account surplus/deficit and the surplus/deficit from the (private) capital account.

Central bank deficit: Net liabilities in foreign currency have increased.
Central bank surplus: Net liabilities in foreign currency have decreased.

Market Equilibrium Under a Fixed Exchange Rate

Maintaining a fixed exchange rate requires central bank intervention in the foreign exchange market to stabilize the equilibrium at the announced rate.

Equilibrium in the foreign exchange market necessitates interest rate parity. With fixed exchange rates, expected depreciation is zero, requiring equal interest rates domestically and abroad (R = R*). Therefore, exchange rate intervention must ensure interest rate equalization, with interest rates determined in the money market.

Money Market Equilibrium Under a Fixed Exchange Rate:

Foreign interest rates are exogenous to the domestic central bank but influence the domestic money market equilibrium: M^S/P = L(R;Y). The price level (P) and output (Y) are fixed.

Money supply becomes the endogenous variable that clears the money market.

Adjustment After an Increase in Output:

An increase in output/income raises money demand, putting upward pressure on domestic interest rates. This attracts capital inflows, necessitating central bank intervention in the foreign exchange market to prevent currency appreciation. The central bank buys foreign currency, increasing domestic money supply and mitigating upward pressure on interest rates.

Stabilization Policy Under Fixed Exchange Rates

With money supply being endogenous, it cannot be used as a policy tool while maintaining a fixed exchange rate.

Consider an economy in short-run equilibrium under a fixed exchange rate (E₀). The domestic interest rate equals the foreign interest rate, clearing the money market and determining M^S.

If the central bank attempts to expand the money supply to increase output (Y), it would put downward pressure on the interest rate and create depreciation pressure (due to interest rate parity). Under flexible exchange rates, the AA schedule would shift to the right.

Maintaining the Fixed Exchange Rate:

To maintain the fixed exchange rate, the central bank must sell foreign assets. The domestic currency used for this intervention reduces domestic money supply, returning the asset market equilibrium to its initial state. Therefore, under a fixed exchange rate, the central bank’s monetary policy tools are ineffective in influencing the money supply or output.

Fiscal Policy Under Fixed Exchange Rates

Consider an economy in short-run equilibrium under a fixed exchange rate (E₀).
A fiscal expansion (ΔG) shifts the goods market equilibrium schedule (DD) to the right. For any given exchange rate, expenditure is higher by ΔG compared to the scenario without expansion.
Without intervention in the foreign exchange market, the exchange rate would depreciate.
However, the central bank guarantees the fixed exchange rate by purchasing foreign assets and expanding domestic money supply.
The exchange rate remains constant at E₀.
Higher money supply shifts the AA schedule to the right.
A new equilibrium is reached at a higher output level (Y₃).

Discretionary Currency Devaluation

While the central bank maintains a fixed exchange rate, it can decide to change it.
For instance, in an administrative devaluation, the central bank announces a higher price for domestic currency in terms of foreign currency.
Increasing the exchange rate from E₀ to E₁ reduces the relative price of domestic goods, leading to additional demand and increased output.
This creates excess demand for money.
Upward pressure on interest rates necessitates central bank intervention in the foreign exchange market.
The central bank purchases foreign assets to maintain the exchange rate at E₁.
Money supply expands until the AA schedule intersects at the new equilibrium point, reflecting the higher exchange rate and increased output.

Effects of a Currency Devaluation:

Improvement in the current account
Output expansion and reduction of the output gap
Accumulation of foreign reserves

For these reasons, currency devaluation can be an effective stabilization policy tool for an economy operating under a fixed exchange rate regime.

The European Monetary Union

The European Monetary Union (EMU) is a currency union within the European Union, where member countries share a single currency (the euro).
Some non-EMU countries have pegged their currencies to the euro, while others have floating exchange rates.
The EMU has expanded to 19 member countries.
The EMU faces challenges, as institutions are still developing to ensure a completely smooth functioning monetary union.
While monetary policy is centralized, fiscal and other economic policies remain under national control.

Reasons for European Cooperation in Monetary Policy

The transition from a fixed exchange rate mechanism to a currency union:

Increases European influence in international currency markets, reducing the dominance of the US dollar, creating a second global reserve currency, and enabling European firms to invoice in euros for international trade.
Completes the creation of a single European market, removing cross-border restrictions and promoting the four freedoms of movement (goods, services, capital, and labor).

European Monetary Union (EMU) Requirements

EU members joining the EMU must:

Achieve exchange rate stability as defined by the exchange rate mechanism before adopting the euro.
Achieve price stability, with a maximum inflation rate of 1.5% above the average of the three member states with the lowest inflation rates.
Maintain a restrictive fiscal policy, with a maximum deficit ratio of 3% of GDP and a debt ratio of 60% of GDP.

Members must be willing to replace their national currencies with the euro and maintain restrictive fiscal policies to remain in the EMU.

Four main reasons for creating the EMU:

Complete market integration by reducing barriers to trade and financial flows.
Coordinate political interests.
Moderate German influence through the European System of Central Banks.
Make currency speculation more difficult with a single currency.

Optimal Currency Areas

Integration is beneficial if the gains outweigh the costs. This requires:

High degree of economic integration
High mobility of factors of production (capital and labor)
Synchronized business cycles
Strong political cooperation

While not all conditions are fully met in the EMU, some can emerge as a consequence of the currency union. The EMU is not yet a perfect optimal currency area.

Part 5: Intertemporal Trade

What Determines the Current Account?

We analyze the determinants of the current account using a theoretical model to clarify fundamental relationships. We’ll examine:

Consumer’s decision on intertemporal consumption allocation
Equilibrium in a small open economy
International borrowing and the current account
Temporary and permanent output changes
The role of government spending

Simplest Model – Assumptions:

Single-good economy
Endowment economy: Output is exogenously given.
Two-period model without uncertainty
Population consists of identical individuals, with size normalized to 1.
Small open economy: Interest rate is exogenous, determined in the world market.
Barter economy: No use of money
Bonds are the only type of asset.

1. Consumer’s Decision on Intertemporal Consumption Allocation

The intertemporal utility function of the representative consumer (i) is: Uⁱ = u(cⁱ₁) + b u(cⁱ₂), where 0

Assumptions regarding u(.): strictly increasing, strictly concave

cⁱ_t: Consumption level of consumer i in period t = 1, 2
u: Period utility function
b: Individual discount factor

Some consumption is always desirable: lim_c→0 u'(c) = ∞

The Intertemporal Budget Constraint:

cⁱ₁ + cⁱ₂ / (1 + r) = yⁱ₁ + yⁱ₂ / (1 + r)

The present value of consumption equals the present value of endowment/output/income.

yⁱ_t: Endowment of individual i in period t = 1, 2
r: Real interest rate (world market rate) in period 1 (market discount rate)

Deriving the Intertemporal Budget Constraint:

Individuals decide on the difference between endowment and consumption, effectively determining their savings. Since bonds are the only asset, saving involves buying or selling bonds.

Budget constraint in period 1 solved for savings: bⁱ₂ = yⁱ₁ + (1 + r) bⁱ₁ – cⁱ₁
bⁱ_t+1: Net investment position abroad at the end of period t
Budget constraint in period 2: bⁱ₃ = yⁱ₂ + (1 + r) bⁱ₂ – cⁱ₂ = yⁱ₂ + (1 + r) [yⁱ₁ + (1 + r) bⁱ₁ – cⁱ₁] – cⁱ₂

Two implicit assumptions in the budget constraint (2):

No initial endowment of bonds: bⁱ₁ = 0
No assets left at the end of the final period: bⁱ₃ = 0

The Optimization Problem:

Maximize lifetime consumption (1) subject to the budget constraint.

u'(cⁱ₁) = (1 + r) b u'(cⁱ₂) b u'(cⁱ₂) / u'(cⁱ₁) = 1 / (1 + r)

Interpretation: The marginal rate of substitution of present consumption for future consumption equals the market rate of future consumption expressed in units of present consumption.
In the optimal scenario, shifting a marginal amount of consumption to the future reduces present utility and increases future utility, keeping total utility constant.

Consumption Smoothing:

The representative consumer prefers to smooth consumption over time due to the concavity of the period utility function u'(c).

Special case: If the market discount factor equals the time preference factor (1 / (1 + r) = b), marginal utility is equal in both periods (u'(cⁱ₁) = u'(cⁱ₂)), leading to equal consumption levels (cⁱ₁ = cⁱ₂) in both periods in the optimal scenario. The optimal consumption path exhibits perfect consumption smoothing, regardless of the output in each period. From (2), it follows that cⁱ_t = ((1 + r) yⁱ₁ + yⁱ₂) / (2 + r).
With b ≠ 1 / (1 + r): Consumption smoothing is not perfect but still present. The degree of consumption smoothing depends on the difference between the market discount factor and the individual discount factor. If b > 1 / (1 + r), the consumption path is increasing. If b

2. Equilibrium in a Small Open Economy

Simplifying assumptions:

Identical individuals populate the economy.
Population size is normalized to one.

The interest rate (r) is the only price in the model and is exogenous due to the small-country assumption.

A small country can engage in international transactions at the given interest rate (r) without affecting it. However, the small country is constrained by its budget constraint.
The equilibrium is described by the budget constraint (C₁ + C₂ / (1 + r) = Y₁ + Y₂ / (1 + r)) and the Euler equation (u'(C₁) = (1 + r) b u'(C₂) b u'(C₂) / u'(C₁) = 1 / (1 + r)), both for the aggregate economy (cⁱ = C and yⁱ = Y).

3. International Borrowing and the Current Account

The current account equals the financial account, representing the net borrowing/lending of an economy. A current account surplus (deficit) results in an increase (decrease) in net international investment positions of the same magnitude.

We can define the current account as the change in net international investment positions: CA_t = B_t+1 – B_t, where B_t+1 represents the net international investment position at the end of period t. A current account surplus (deficit) in period t corresponds to a lender (borrower) position in period t.

Current Account in a Two-Period Model:

Assuming no investments and no government:

CAt = Bt+1 – Bt = Yt + rBt – Ct

·rBt : Income from foreign interest bearing assets

·Yt : Gross Domestic Product (GDP)

·Yt + rBt : Gross income (GNP)

·Without transfers, the current account equals the difference of GNP and consumption.

The evolution of the current account (B1 = 0):

CA1 = Y1 – C1 = B2 – B1 = B2 à CA2 = Y2 +rB2-C2 = Y2 +r (Y1-C1 )-C2 = -(Y1 – C1 ) = -B2

No foreign assets at the beginning and the end CA1 + CA2 = B3 – B1 = 0

Gains from inter-temporal trade in a small open economy:

_ No special assumption about the relationship between b and 1/(1+r) needed

_ In autarky: production and consumption in A

_ In an open economy: optimal consumption in C

_ Utility gains through inter-temporal trade – a higher indifference curve can be reached

_ Intuition: international borrowing/lending allows consumptions moothing

_ Increase in welfare is independent on the lender/borrower position of the country in period 1

4.Temporary and permanent output changes:

Effects of production changes on the current account:

Simplifying assumption b = 1/(1+r)

_ First order condition changes to u’(Y2)/u’(Y1) = 1+r/1+r^A

_ Differences in production yield the divergence of the autarky from the world interest rate

If Home expects a at production path (Y1 = Y2 ), the autarky interest rate equals the world interest rate

r = rA

·Case 1: temporary increase in output Y1 ” and Y2 unchanged

_ rA falls below r

_ Current account surplus in period 1, consumption smoothing

·Case 2: permanent increase in output Y1 ” and Y2 ” (by the same amount)

_ rA unchanged

_ No change in the current account, consumption up in both periods by the same amount

Ergo

·Permanent changes in output do not affect the current account (if b = 1 /1+r )

·Temporary changes in output (business cycle) affect the current account.

5.The role of government spending:

Additional assumptions:

_ Government spending increase the individual’s utility (utility function: u(c) + v(G))

_ Government spending is financed by lump-sum taxes

_ Budget equalization in every period (Tt = Gt )

Inter-temporal budget constraint C1 + (C2)/(1 + r)= Y1 – G1 +( Y2 – G2)/(1 + r)

Current account CAt = Bt+1 – Bt = Yt + rBt – Gt – Ct à The current account is the di_erence between the BNP and total domestic expenditure (Ct + Gt )

Part 5.2: A small open production economy

So far

_ Endowment economy, no production, no investment

_ Current account determined by consumption smoothing

_ Current account = aggregate savings = GNP-total expenditure

But: Inter-temporal trade allows to pay investments with foreign capital

Thus

_ We add investments to our analysis

_ The current account changes to: Current account = aggregate àsavings – total investments

1.Production:

Assumption:

_ Output is now endogenous, produced using capitalY = F (K ) mit F’ (K ) > 0; F’’ (K )

and lim Kà0 F’ (K ) = v

_ The representative consumer is also the representative producer

_ One unit of capital can be created from one unconsumed unit of the consumption good

_ If the capital can be retransferred into a consumption good à the relative price between consumption good and capital is 1

_ There is no depreciation on the capital

These assumptions imply:

_Saving can either increase capital or flow to a foreign country

_ Private assets at the end of period t consists of Bt+1 + Kt+1 àWhere Kt+1 capital stock at the end of period t

_ Investments It increase the capital stock

Change in the capital stockàKt+1 = Kt + It

Deriving the current account:

_ Aggregate savings (change in asset stocks of the economy) K_t+1 + B_t+1 -K_t – B_t = Y_t + rB_t – C_t – G_t

_ Plugging in and solving for the CAàCAt = Bt+1 – Bt = Yt + rBt- Ct -Gt- It = St – It

The current account is the di_erence between aggregate savings and

aggregate investments of an economy

_ Savings that exceed investment increases foreign assets

_ Savings that fall short of investments decrease foreign assets

_ Savings, investments, and the current account are endogenous and jointly determined

2.Individual’s budget constraint and optimization

The inter-temporal budget constraint: C1 + I1 + (C2 + I2)/ (1 + r) = Y1 – G1 +(Y2 – G2)/ 1 + r

The net present value of production equals the net present value of the sum of consumption and investments.

Derivation of the inter-temporal budget constraint

_ Budget constraints in period 1 (B1 = 0)àB2 = Y1 – C1 – G1 – I1

_ Budget constraint in period 2 (B3 = 0)àB3 = Y2 + (1 + r )B2 – C2 – G2 – I2

The optimization problem of the representative individual:

Individuals maximize life-time utility with respect to their Budget constraint, capital accumulation and the production function.

·K3 = 0, capital stock is completely consumed, I2 = – K2

·K1 is exogenous, “predetermined”, inherited from the previous period, outside of the model

Max_C₁_;I₁u(C1) + bu {(1 + r )[F(K1) – C1 – G1 – I1] + F(K1 + I1) – G2 + I1 + K1}

First order conditions: The marginal productivity of investing in period 1 (the marginal productivity of capital in period 2) equals the marginal income from foreign assets (i.e. the real interest rate): F0 (K2 ) = r

Results: The capital stock is unaffected from consumers’ preferences; Individuals will never miss investment opportunities that yield more than the interest rate r.

The capital stock in period 2 K2 is unaffected by government consumption à no crowding-out of private investment

Note that:

_ Perfect capital market

_ Small open economy

3.The equilibrium:

We aim at a graphic representation of the current account in an economy with investment

_ Simplification: no government spending

_ Production now endogenous, production possibility frontier must taken into account

Production possibility frontier:

_ Technology to transform period 1 consumption goods in period 2 consumption goods

C2 = F [K1 + F (K1 ) – C1 ] + K1 + F (K1 ) – C1

Characteristics:

·Horizontal constant: highest possible consumption in period 1; C1 = F (K1 ) + K1

·Vertical constant: highest possible consumption in period 2; C2 = F (K1 + F (K1 )) + K1 + F (K1)

·All other points on the production possibility frontier with positive consumption in both periods

·The production possibility frontier is strict concave, since marginal productivity of capital falls

dC2/dC1 = – [1 + F’ (K2 )] 2₁ = F’’ (K2 )

Derivation:

Period budget constraint in autarky reads

Y1 = C1 + I1

Y2 = C2 – K2 = C2 – (K1 + I1 )

Substituting I1 and solving for C2 yields

C2 = Y2 + K1 + Y1 – C1

Using the production function to derive the production possibility frontier

C2 = F [K1 + F (K1 ) – C1 ] + K1 + F [K1 ] – C