In-Depth Notes on Expenditure Multipliers

Expenditure Multipliers

• Expenditure Plans and Real GDP Determination
  • In the short run, with fixed prices, the Keynesian model implies:
  • The overall price level remains fixed.
  • Aggregate demand influences the real GDP.
  • Key Components of Aggregate Expenditure:
  • $Y = C + I + G + X - M$
    • Where:
    • $Y$ = Real GDP
    • $C$ = Consumption
    • $I$ = Investment
    • $G$ = Government Spending
    • $X$ = Exports
    • $M$ = Imports
  • Increases in real GDP lead to increased aggregate expenditure and vice versa.

Planned Consumption Expenditure

• Disposable Income (YD)
  • $Y_D = Y - T$
  • Where $T$ is net taxes.
• Consumption Function:
  • Relationship between consumption expenditure ($C$) and disposable income ($Y_D$) is fundamental.
  • When $YD$ exceeds consumption, savings (S) occur; when consumption exceeds $YD$, negative savings (dissaving) occur.
• Autonomous vs Induced Consumption:
  • Autonomous consumption exists even when income is zero.
  • Induced consumption occurs from a rise in disposable income.

Factors Influencing Consumption and Saving

1. Real Interest Rates
2. Wealth Levels
3. Expected Future Income
   • Changes in these factors shift both the consumption and saving functions.

Marginal Propensities

• Marginal Propensity to Consume (MPC):
  • $MPC = \frac{∆C}{∆Y_D}$
  • Example from Figure 11.2(a):
    • If income increases by $400 billion$, and consumption increases by $300 billion$, then $MPC = 0.75$.
• Marginal Propensity to Save (MPS):
  • $MPS = \frac{∆S}{∆Y_D}$
  • Example from Figure 11.2(b):
    • Income increase of $400 billion$ leads to $100 billion$ in savings, providing $MPS = 0.25$.
• Relationship between MPC and MPS:
  • $MPC + MPS = 1$

Import Function

• In the short run, imports are largely driven by Canadian real GDP.
• The Marginal Propensity to Import (MPM) indicates how much imports increase with an increase in real GDP.
  • For instance, if a $100 billion$ increase in GDP leads to a $25 billion$ increase in imports, then $MPM = 0.25$.

Equilibrium Expenditure

• Aggregate Planned Expenditure:
  • Summation of planned consumption, investment, government expenditure, and net exports.
• Equilibrium occurs when:
  • Aggregate planned expenditure equals real GDP, leading to no unplanned changes in inventories.
• Adjustment to Equilibrium:
  • If planned expenditure exceeds real GDP, production increases to restore inventories.
  • If it is less, production decreases.

The Multiplier Effect

• Definition:
  • The multiplier reflects how a change in autonomous expenditure affects equilibrium expenditure and real GDP.
  • More specifically, an increase in autonomous expenditure can lead to a proportionally larger increase in GDP.
• Calculation of Multiplier:
  • $Multiplier = \frac{∆Y}{∆A}$
  • Where $∆Y$ is the change in GDP, and $∆A$ is the change in autonomous expenditure.
• MPC Impact:
  • Higher MPC results in a larger multiplier, and $Multiplier = \frac{1}{1 - MPC}$.
  • Conversely, the presence of taxes or imports dampens the multiplier effect.

Aggregate Demand Relationship

• The aggregate demand curve relates the quantity of real GDP demanded at different price levels and reflects the shifts in aggregate planned expenditure.
• Effects of Price Changes:
  • A rise in price level typically shifts the aggregate expenditure curve downward, leading to a lower equilibrium expenditure.
  • Conversely, a decrease in the price level shifts the expenditure curve upward, increasing equilibrium expenditure.

Long Run Considerations

• In the long run, adjustments in wages and prices generally lead to normalization of output at potential GDP, causing the multiplier effect to diminish to zero as full employment is reached.

• Overall, understanding these concepts is foundational in macroeconomics relating to expenditure, real GDP, and their broader implications on the economy.