Expenditure Multipliers: Keynesian Model (Chapter 28)

Fixed Prices and Planned Expenditure

• With fixed prices for the economy as a whole:
  • The price level is fixed.
  • Aggregate demand determines real GDP.
• The Keynesian model explains fluctuations in aggregate demand at a fixed price level by identifying the forces that determine planned expenditure.
• Planned Expenditure
  • Aggregate expenditure has four components: consumption expenditure, investment, government expenditure on goods and services, and net exports (exports minus imports).
  • Aggregate planned expenditure is the sum of the planned levels of consumption expenditure, investment, government expenditure on goods and services, and exports minus imports:
    AE = C{planned} + I{planned} + G{planned} + (X{planned} - M_{planned})
• A Two-Way Link Between Aggregate Expenditure and Real GDP
  • An increase in real GDP increases aggregate expenditure.
  • An increase in aggregate expenditure increases real GDP.
  • Therefore, real GDP and aggregate expenditure are interdependent and move together in the short run when prices are fixed.

Planned Expenditure (Detailed Components)

• The components of aggregate planned expenditure are C, I, G, X, and M (net exports = X − M).
• Aggregate planned expenditure equals the sum of the planned levels of C, I, G, and NX (net exports):
  AE = C{planned} + I{planned} + G{planned} + (X{planned} - M_{planned})
• Induced vs Autonomous Expenditure
  • Induced expenditure: consumption expenditure minus imports, i.e. the portion of AE that varies with real GDP:
    ext{Induced Expenditure} = C - M
  • Autonomous expenditure: the part of AE that does not vary with real GDP, i.e. investment, government spending, and exports (and any autonomous part of consumption). In simple terms:
    ext{Autonomous Expenditure} = I + G + X
  • Therefore, aggregate planned expenditure can be viewed as:
    AE = (C - M) + (I + G + X)

Two-Way Link Between Aggregate Expenditure and Real GDP

• When real GDP (Y) rises, disposable income and other expenditure determinants move, influencing C and M and hence AE.
• When AE changes, firms adjust production, causing Y to move. The loop continues until equilibrium (see below).

Consumption and Planned Saving

• Several factors influence planned consumption expenditure and saving:
  1. Disposable income (YD)
  2. Real interest rate
  3. Wealth
  4. Expected future income
• Consumption Expenditure and Saving
  • The consumption expenditure–disposable income relationship is called the consumption function:
    C = C(Y_D)
  • The saving and disposable income relationship is called the saving function:
    S = S(Y_D)
• 45° Line
  • The 45° line represents points where consumption expenditure equals disposable income:
    C = Y_D \text{(on the 45° line)}
• Fixed Prices and Planned Expenditure
  • As disposable income increases, saving increases (income-led saving).
  • The line depicting the consumption function and saving function slope reflects how C and S respond to changes in YD.

Marginal Propensities to Consume and Save

• The slope of the consumption function is the marginal propensity to consume (MPC):
  ext{MPC} = rac{ riangle C }{ riangle Y_D }
  
• The slope of the saving function is the marginal propensity to save (MPS):
  ext{MPS} = rac{ riangle S }{ riangle Y_D }
  
• Example from the figure:
  • Change in disposable income: riangle Y_D = 2 ext{ trillion}
  • Change in consumption: riangle C = 1.5 ext{ trillion}
  • Change in saving: riangle S = 0.5 ext{ trillion}
  • MPC = rac{ riangle C }{ riangle Y_D } = rac{1.5}{2} = 0.75
  • MPS = rac{ riangle S }{ riangle Y_D } = rac{0.5}{2} = 0.25
  • Note: MPC + MPS = 1 (assuming no other leaks) of the change in YD.
• Summary: the MPC is the slope of the consumption function; the MPS is the slope of the saving function.

Slopes and Marginal Propensities

• The slope of the consumption function = MPC.
• The slope of the saving function = MPS.
• These slopes determine how much of a change in income is spent vs saved when income changes.

Consumption as a Function of Real GDP

• Consumption expenditure changes when disposable income changes, and disposable income changes when real GDP changes.
• Therefore, C is indirectly a function of Y via YD, since YD depends on Y (and taxes, if any).

Import Function

• South Africa’s real GDP is the main influence on imports in the short run: an increase in real GDP increases imports.
• The relationship between imports and real GDP is determined by the marginal propensity to import (MPI):
  ext{MPI} = rac{ riangle M }{ riangle Y }
  
• Effect on GDP:
  • An increase in aggregate expenditure raises real GDP, but part of the increase is spent on imports, which does not contribute to domestic GDP.
  • The larger the MPI, the smaller is the increase in domestic real GDP.

Real GDP with a Fixed Price Level

• The relationship between aggregate planned expenditure and real GDP can be described by:
  • An aggregate expenditure (AE) schedule: AE is the level of aggregate planned expenditure at each level of real GDP.
  • An AE curve: Graph of the AE schedule.
• Induced vs Autonomous Expenditure (revisited)
  • Induced expenditure: C − M (consumption net of imports).
  • Autonomous expenditure: I + G + X (which does not vary with real GDP).
• Actual Expenditure, Planned Expenditure and Real GDP
  • Actual aggregate expenditure is always equal to real GDP (Y).
  • Aggregate planned expenditure need not equal actual expenditure because inventories may differ from their desired levels, causing discrepancies between AE and Y.

Equilibrium Expenditure

• Equilibrium expenditure is the level of aggregate expenditure that occurs when aggregate planned expenditure equals real GDP:
  ext{Equilibrium: } AE = Y \
  ext{or equivalently } Y = C(Y_D) + I + G + X - M(Y)
  
• Convergence to Equilibrium
  • If AE > Y, inventories fall, firms increase production, raising Y toward AE.
  • If AE < Y, inventories rise, firms cut production, lowering Y toward AE.

Real GDP with a Fixed Price Level: Equilibrium Expenditure (Figure 28.4)

• The intersection of the AE curve with the 45° line (Y = AE) determines the equilibrium level of real GDP.
• At equilibrium, planned expenditure equals real GDP; deviations lead to inventory adjustments until equilibrium is achieved.

The Multiplier

• The multiplier is the amount by which a change in autonomous expenditure is magnified to determine the change in equilibrium expenditure and real GDP:
  ext{Multiplier} = rac{ riangle Y }{ riangle A }
  
• Basic idea (illustrated by the standard AE model): a small autonomous change in expenditure induces a larger total change in equilibrium expenditure.
• Why the multiplier is greater than 1:
  • An increase in autonomous expenditure raises income, which raises consumption, which raises income further, and so on, creating a multiplied effect on Y.
• Size of the multiplier:
  • In the simple case with no leaks, the multiplier is:
    k = rac{1}{1 - MPC}
    
• In more realistic cases with leaks (e.g., imports and taxes), the multiplier is smaller:
  • The slope of the AE curve determines the multiplier’s size.
  • Imports and taxes reduce the effective marginal propensity to spend domestically.

The Multiplier and the Slope of the AE Curve

• The multiplier depends on the slope of the AE curve (the marginal responsiveness of AE to income).
• Larger leakage (imports and taxes) flattens the AE curve, reducing the multiplier.
• Imports and Income Taxes (two key leakage channels)
  • Imports:
  • An increase in investment raises real GDP and, in turn, increases consumption, but some of the increased spending goes to imported goods and services. Only the portion spent on domestically produced goods and services adds to domestic GDP.
  • Higher MPI => smaller change in domestic real GDP.
  • Income taxes:
  • Rising investment raises real GDP, but income taxes increase as well, reducing disposable income and thus consumption relative to the increase in GDP.
  • Higher tax rate reduces the size of the change in real GDP.

The Multiplier Process

• The multiplier effect unfolds as follows:
  • An initial autonomous increase in spending → higher real GDP → higher incomes → higher consumption (partial) → further increases in GDP → etc., until the economy approaches a new equilibrium.

Business Cycle Turning Points

• At turning points, the economy shifts from expansion to recession or from recession to expansion.
• Adjusting Quantities and Prices
  • If firms cannot meet rising sales, inventories fall below target; they raise production, and may raise prices later.
  • If unwanted inventories accumulate, firms cut production and eventually reduce prices.
• Aggregate Expenditure vs Aggregate Demand
  • The aggregate expenditure curve shows planned expenditure as a function of real GDP.
  • The aggregate demand curve shows the relationship between the quantity of goods/services demanded and the price level.
• Deriving the Aggregate Demand Curve
  • When the price level changes, aggregate planned expenditure changes, and the quantity of real GDP demanded changes accordingly.

The Multiplier: Why the AD Curve Slopes Downward

• The aggregate demand curve slopes downward for two main reasons:
  • Wealth Effect: Higher price level reduces the real value of wealth, decreasing consumption.
  • Substitution Effects (Intertemporal): A higher price level today makes current goods relatively more expensive than future goods, delaying purchases (intertemporal substitution).

Changes in Aggregate Expenditure and Aggregate Demand

• When any influence on aggregate planned expenditure other than the price level changes, both the aggregate expenditure curve and the aggregate demand curve shift.
• Examples of such influences include changes in fiscal policy (G, T), investment incentives, consumer confidence, and net exports due to exchange rates or foreign income.

Equilibrium Real GDP and the Price Level

• Short-run vs long-run considerations:
  • Short Run: With prices fixed, shifts in AE affect real GDP directly through the multiplier.
  • Long Run: Prices adjust; the aggregate supply side moves; the real GDP may move toward potential output, and the price level adjusts to equilibrate aggregate demand and supply.
• An Increase in Aggregate Demand in the Short Run and in the Long Run
  • Short Run: Real GDP rises; the price level may rise as well, depending on the slope of the AS curve.
  • Long Run: Output tends to return to potential (if the economy has flexible prices), with higher price level reflecting higher overall demand.

Key Formulas and Concepts to Remember

• Aggregate planned expenditure:
  AE = C{planned} + I{planned} + G{planned} + (X{planned} - M_{planned})
• Real GDP equals aggregate expenditure at equilibrium:
  Y = AE \
  ext{(in equilibrium with fixed prices)}
• Consumption and saving functions (conceptual definitions):
  C = C(YD) \ S = S(YD)
• Disposable income:
  YD = Y - T \ ext{or, with a proportional tax } T = tY, \, YD = (1 - t)Y
• MPC and MPS (slopes):
  ext{MPC} = rac{ riangle C }{ riangle YD } \ ext{MPS} = rac{ riangle S }{ riangle YD } \ ext{and } ext{MPC} + ext{MPS} = 1 ext{ (in the simple model)}
• Import function:
  ext{MPI} = rac{ riangle M }{ riangle Y }
  
• Aggregate Expenditure (AE) slope with taxes and imports:
  • In a model with taxes t and imports MPI, the slope of AE with respect to Y is:
    rac{ riangle AE }{ riangle Y } = ext{MPC} imes (1 - t) \ ext{and} \ rac{ riangle AE }{ riangle Y } = ext{MPC}(1 - t) - ext{MPI}
    
• Multiplier with leaks (autonomous expenditure A):
  k = rac{ riangle Y }{ riangle A } = rac{1}{1 - rac{ riangle AE }{ riangle Y }} = rac{1}{1 - [ ext{MPC}(1 - t) - ext{MPI}]} = rac{1}{1 - ext{MPC}(1 - t) + ext{MPI}} \ ext{(for a simple model with } A = I + G + X ext{ and a tax–import channel)}
• Simple case (no taxes, no imports):
  k = rac{1}{1 - ext{MPC}}
  
• Example numbers (from the figure): MPC = 0.75; MPS = 0.25;
  • If \Delta YD = 2, \Delta C = 1.5 \text{ and } \Delta S = 0.5, \Delta C/ \Delta YD = 0.75, \Delta S/ \Delta Y_D = 0.25.
  • This confirms the slope values and the identity MPC + MPS = 1 under the given illustration.

Use these notes to organize your study around the main ideas:

• How planned expenditure is determined at fixed prices.
• How AE and Y are linked (two-way interaction).
• How C and S respond to YD and how imports affect domestic GDP.
• What the multiplier is, what factors shrink or expand it (imports, taxes), and how AD shifts vs. price changes.
• How the AD curve is derived from the AE framework via price-level changes and the wealth/substitution effects.