ch 6 Output and the Exchange Rate in the Short Run

Determinants of Aggregate Demand in the Open Economy

• Definition of Aggregate Demand: Aggregate demand is the total amount of goods and services that individuals and institutions are willing to buy. It is composed of four components:    

• Consumption Expenditure ($C$): Purchases by private households.     

• Investment Expenditure ($I$): Purchases by firms for capital equipment or inventories.    

• Government Purchases ($G$): Purchases by federal, state, or local governments.    

• Net Expenditure by Foreigners (Current Account, $CA$): The value of exports minus the value of imports.

• Consumption Expenditure Determinants: Disposable Income ($Y_d$): Defined as total income from production ($Y$) minus taxes ($T$). Formula: $Y_d = Y - T$.     

• There is a positive relationship: higher disposable income leads to higher consumption, though consumption typically increases by less than the full increase in disposable income.     

• Factors assumed to be relatively unimportant in this specific short-run model include real interest rates (affecting saving/spending) and wealth.

• Current Account Determinants: Real Exchange Rate ($q$): Defined as the prices of foreign products relative to domestic products, expressed in domestic currency: $q = \frac{EP^<em>}{P}$.          As $q$ rises (real depreciation of domestic currency), domestic products become cheaper relative to foreign products. This leads to increased expenditure on domestic products and decreased expenditure on foreign products.    

• Disposable Income ($Y_d$): Higher disposable income leads to more spending on imports, which worsens the current account.

• Value Effect vs. Volume Effect: The current account is approximated as: $CA \approx EX - IM$.    

• When the real exchange rate ($q$) rises: Volume Effect: The quantity of exports bought by foreigners increases; the quantity of imports bought by domestic residents decreases.

• Value Effect: The value/price of imports in terms of domestic products rises because foreign goods are more expensive.     *

• If volumes do not change significantly (e.g., due to contract obligations), the value effect can dominate, initially worsening the CA. However, evidence shows the volume effect typically dominates within one year or less for most countries. This model assumes the volume effect dominates (real depreciation improves the CA).

• Aggregate Demand Function: The full expression is: $D = C(Y - T) + I + G + CA(\frac{EP^<em>}{P}, Y - T)$.      Simplified form: $D = D(\frac{EP^<em>}{P}, Y - T, I, G)$.      Determinants and effects on AD:  Real exchange rate ($q$) \uparrow \rightarrow $CA$ \uparrow \rightarrow $D$ \uparrow.       

• Disposable income ($Y_d$) \uparrow \rightarrow $C$ \uparrow (increases AD) and $CA$ \downarrow (decreases AD).

• Since consumption expenditure on domestic goods is usually larger than on foreign imports, the consumption effect dominates. Thus, $Y_d$ \uparrow \rightarrow $D$ \uparrow, but by less than the increase in income.

Short-Run Output Market Equilibrium: The DD Schedule

• Equilibrium Condition: Output market equilibrium occurs when the value of output/income from production ($Y$) equals aggregate demand ($D$): $Y = D(\frac{EP^*}{P}, Y - T, I, G)$.

• The DD Schedule Definition: The DD schedule shows all combinations of output ($Y$) and the exchange rate ($E$) where the output market is in short-run equilibrium ($D = Y$).

• Slope: The DD curve slopes upward because a rise in the exchange rate ($E$, a depreciation) increases aggregate demand, necessitating a rise in output ($Y$) to maintain equilibrium.

• Factors Shifting the DD Curve:    

• Government Purchases ($G$): An increase in $G$ raises aggregate demand; the DD curve shifts right.    

• Taxes ($T$): A decrease in $T$ increases consumption; the DD curve shifts right.    

• Investment ($I$): An increase in investment shifts the DD curve right.     

• Domestic Prices ($P$): Higher $P$ makes domestic goods more expensive, reducing export demand; the DD curve shifts left.    

• Foreign Prices ($P^<em>$): Higher $P^</em>$ makes domestic goods relatively cheaper; the DD curve shifts right.    

• Consumption ($C$): Increased willingness to consume and save less shifts the DD curve right.   

• Demand Shift: A shift in preference toward domestic goods over foreign goods shifts the DD curve right.

Asset Market Equilibrium: The AA Schedule

• Foreign Exchange Market Equilibrium: Represented by the Interest Parity Condition: $R = R^* + \frac{E^e - E}{E}$.

• Money Market Equilibrium: Defined by the equality of real money supply and demand: $\frac{M^s}{P} = L(R, Y)$.

• Relationship Between Output and the Exchange Rate:  When income ($Y$) increases, the demand for real monetary assets ($L(R, Y)$) increases ($\uparrow$).    

• This leads to an increase in the domestic interest rate ($R \uparrow$).    

• Higher interest rates lead to an appreciation of the domestic currency ($E \downarrow$).     

• Conversely, a decrease in $Y$ leads to a depreciation ($E \uparrow$).

• The AA Schedule Definition: The AA curve summarizes the inverse relationship between output and exchange rates needed to keep foreign exchange and money markets in equilibrium.

• Slope: The AA curve slopes downward.

• Factors Shifting the AA Curve:

• Money Supply ($M^s$): An increase in $M^s$ reduces interest rates, causing depreciation ($E \uparrow$); the AA curve shifts up (right).     

• Domestic Prices ($P$): An increase in $P$ decreases the real money supply, raising interest rates and causing appreciation ($E \downarrow$); the AA curve shifts down (left).     

• Expected Exchange Rate ($E^e$): If market participants expect future depreciation ($E^e \uparrow$), the domestic currency depreciates today; the AA curve shifts up (right).    

• Foreign Interest Rate ($R^<em>$): An increase in $R^</em>$ makes foreign deposits more attractive, causing domestic depreciation ($E \uparrow$); the AA curve shifts up (right).     

• Real Money Demand Change: If residents desire to hold less real money (favoring non-monetary assets), interest rates fall, causing depreciation ($E \uparrow$); the AA curve shifts up (right).

Short-Run Equilibrium and Macroeconomic Policy

• General Equilibrium: Occurs at the intersection of the DD and AA curves. At this point, the output market, money market, and foreign exchange market are all in equilibrium simultaneously.

• Temporary vs. Permanent Policies: Temporary changes are expected to be reversed shortly and do not change long-run expectations ($E^e$ remains constant). Permanent changes modify people’s expectations about long-run exchange rates.

• Temporary Monetary Policy: An increase in $M^s$ shifts the AA curve up/right. Result: Higher output ($Y \uparrow$) and currency depreciation ($E \uparrow$).

• Temporary Fiscal Policy: An increase in $G$ or a decrease in $T$ shifts the DD curve right. Result: Higher output ($Y \uparrow$) and currency appreciation ($E \downarrow$).

• Permanent Monetary Policy Expansion:     

• Short-Run: Lower interest rates and an increase in $E^e$ (expected depreciation). This causes a larger upward shift of AA compared to the temporary case. Result: Significant depreciation and increased output.    

• Long-Run Adjustment: Employment and production rise above potential (Y > Y_f), leading to rising wages and prices ($P \uparrow$). Rising $P$ shifts the AA curve back down (left) and the DD curve left. Eventually, the economy returns to full employment ($Y_f$) at a higher exchange rate than the initial state, but lower than the short-run peak.

• Permanent Fiscal Policy Expansion: If the change is permanent, the expected appreciation of the currency ($E^e \downarrow$) shifts the AA curve down/left. This shift exactly offsets the rightward shift of the DD curve. Result: No change in output ($Y$ remains at $Y_f$), only currency appreciation ($E \downarrow$). This is known as the complete crowding out of net exports by the appreciated currency.

Trade Elasticities and the Marshall-Lerner Condition

• The Current Account Equation: Measured in domestic output units: $CA(q, Y_d) = EX(q) - q \times IM^<em>(q, Y_d)$.      $q = \frac{EP^<em>}{P}$ (real exchange rate).      $IM^<em>$ = imports measured in terms of foreign output.      $q \times IM^*$ = imports measured in domestic output units.

• Deriving the Effect of a Real Depreciation (\Delta q):     * $\frac{\Delta CA}{\Delta q} = EX_q - (q \times IM^<em>_q) - IM^</em>$.

• Marshall-Lerner Condition (MLC): States that a real depreciation improves the current account if: \eta + \eta^* > 1.     * $\eta$: Price elasticity of export demand ($\eta = |\frac{q}{EX} \times \frac{\Delta EX}{\Delta q}|$).     * $\eta^<em>$: Price elasticity of import demand ($\eta^</em> = |\frac{q}{IM^<em>} \times \frac{\Delta IM^</em>}{\Delta q}|$).     * Derivation assumed the current account is initially zero ($EX = q \times IM^*$) and disposable income is held constant.

• The J-Curve: Describes the time path of the current account following a depreciation.     1. Immediate Effect: The current account worsens (decreases) because the value of existing imports rises (Value Effect).     2. Delayed Effect: Over time (usually within a year), consumers and firms adjust quantities (Volume Effect), and the CA improves significantly.

• Exchange Rate Pass-Through: The percentage by which import prices change when the domestic currency changes by $1\%$.   

• In the standard DD-AA model, pass-through is $100\%$.    

• In reality, pass-through is often less than $100\%$ due to price discrimination, meaning the J-curve effect is dampened.

The Liquidity Trap and global Value Chains

• The Liquidity Trap: Occurs when the nominal interest rate ($R$) hits zero. People become indifferent between holding money and bonds as both yield zero returns.     Interest Parity at $R = 0$: $0 = R^* + \frac{E^e - E}{E}$.     

• The exchange rate becomes trapped at $E = \frac{E^e}{1 - R^*}$. Increasing the money supply has no effect on the exchange rate or the economy because interest rates cannot go below zero (the Zero Lower Bound, or ZLB).

• Global Value Chains (GVCs): Modern production involve complex backward linkages (imported intermediate goods used for exports) and forward linkages (exporting goods that are then used in other countries' exports).     

• These linkages dampen the effects of depreciation on trade because a cheaper currency increases the cost of imported inputs used for manufacturing exports.

Comparison with the IS-LM Model

• The IS-LM Model Overview: Generalizes the DD-AA model by including the real interest rate effect on aggregate demand ($D$).

• IS Curve: Represents combinations of interest rates ($R$) and output ($Y$) where the output and foreign exchange markets are in equilibrium.     

• Slopes downward because a fall in $R$ stimulates investment and consumption, and leads to currency depreciation (improving CA).     

• LM Curve: Represents money market equilibrium ($\frac{M^s}{P} = L(R, Y)$). Slopes upward because higher output increases money demand, necessitating higher interest rates to maintain balance.

• Policy in IS-LM:    

• Temporary Monetary Increase: Shifts LM right, decreasing $R$ and increasing $Y$.     

• Permanent Monetary Increase: Shifts both LM and IS to the right (since $E^e$ rises).     

• Permanent Fiscal Expansion: Shifts IS right and potentially LM, but in the open economy framework, output remains at $Y_f$.