Chapter 11 Expenditure Multipliers

Fixed Prices and Expenditure Plans

• The Keynesian model is used to describe the economy in the short run when prices are fixed.
• With fixed prices per firm, the economy sees a fixed price level and aggregate demand determining real GDP.

Expenditure Plans

• Components of aggregate expenditure sum up to the real GDP
• Y = C + I + G + X – M, where:
  • Y = Real GDP
  • C = Consumption expenditure
  • I = Investment
  • G = Government expenditure
  • X = Exports
  • M = Imports
• Consumption and imports are influenced by real GDP, creating a two-way link between aggregate expenditure and real GDP.
• An increase in real GDP will increase aggregate expenditure
• An increase in aggregate expenditure will increase real GDP

Planned Consumption Expenditure

• Consumption expenditure is mostly influenced by disposable income.
• Disposable income is aggregate income (real GDP, Y) minus net taxes (T).
• Disposable income is called YD and can be found using the equation YD = Y-T.
• Disposable income (YD) is either spent on consumption (C) or saved (S): YD = C + S.
• The relationship between consumption expenditure and disposable income is the consumption function.
• The saving function is the relationship between saving and disposable income.
• Consumption expenditure exceeding disposable income means saving is negative (dissaving)
• The consumption expenditure is less than disposable income, there is saving

Consumption Function

• As disposable income increases, consumption expenditure also increases.
• Consumption expenditure is positive even when disposable income is zero, which is called autonomous consumption.
• Consumption expenditure exceeding autonomous consumption is induced consumption and results from an increase in disposable income.

Other Influences on Consumption and Saving

• Factors that influence consumption and saving include the real interest rate, wealth, and expected future income.
• A change in those factors changes autonomous consumption and shifts the consumption and saving functions.

Marginal Propensities to Consume and Save

• The marginal propensity to consume (MPC) calculates the fraction of a change in disposable income spent on consumption: MPC = Change in Consumption (C) / Change in Disposable Income (YD).

• The MPC can be found as the slope of the consumption function

  • For example: Disposable income increases by $400 billion, consumption expenditure increases by $300 billion, the MPC is 0.75.

• The marginal propensity to save (MPS) calculates the change in savings (S) divided by the change in disposable income (YD) that brought it about: MPS = S/YD.

• The MPS can be found as the slope of the saving function

  • For example: Disposable income increases by $400 billion, saving increases by $100 billion, the MPS is 0.25.

• The MPC plus the MPS equals 1 and can be expressed as MPC + MPS = 1.

Consumption as a Function of Real GDP

• Disposable income changes when real GDP or net taxes change.
• Real GDP is the singular influence on disposable income if tax rates remain consistent, so consumption expenditure is a function of real GDP used to determine real GDP when the price level is fixed.

Import Function

• Canadian imports during the short run are influenced primarily Canadian real GDP.
• An increase in real GDP spent on imports is the marginal propensity to import.

Real GDP with a Fixed Price Level

• Aggregate demand is determined by aggregate expenditure plans when the price level is fixed.
• Aggregate planned expenditure is planned consumption expenditure plus planned investment, government expenditure, and exports, minus planned imports.
• Planned consumption expenditure and planned imports are influenced by real GDP.
• An increase in real GDP increases planned consumption expenditure and planned imports.
• Planned investment, government expenditure, and planned exports are not influenced by real GDP.

Aggregate Planned Expenditure

• An aggregate expenditure schedule describes the relationship between aggregate planned expenditure and real GDP.
• The schedule lists the quantity of aggregate expenditure planned at each quantity of real GDP.
• An aggregate expenditure curve can also describe the relationship
• The aggregate expenditure curve is a graph of the aggregate expenditure schedule.
• Consumption expenditure minus imports that varies with real GDP is considered induced expenditure.
• The sum of investment, government expenditure, and exports that do not vary with GDP is autonomous expenditure.

Actual Expenditure, Planned Expenditure, and Real GDP

• The actual aggregate expenditure is always the same as real GDP.
• Aggregate planned expenditure can differ from actual because firms can have unplanned changes in inventories.

Equilibrium Expenditure

• Equilibrium expenditure happens when the aggregate planned expenditure equals real GDP.
• Equilibrium occurs at the point where the AE curve crosses the 45° line.
• At this point, there are no unplanned changes in inventory investment.

Convergence to Equilibrium

• When aggregate planned expenditure exceeds real GDP, there's an unplanned decrease in inventories.
  • To restore inventories, firms hire workers and increases production meaning real GDP increases.
• When aggregate planned expenditure is less than real GDP, firms have an unplanned increase in inventories.
  • To reduce inventories, firms fire workers and decrease production meaning real GDP decreases.
• When aggregate planned expenditure equals real GDP, no unplanned changes in inventories occur
  • Firms maintain their current production meaning real GDP remains constant.

The Multiplier

• Autonomous expenditure changes, equilibrium expenditure and real GDP also change.
• The shift in equilibrium expenditure is larger than the shift in autonomous expenditure.
• The multiplier is the amount by which a change in autonomous expenditure is magnified to determine the change in equilibrium expenditure and real GDP.

The Basic Idea of the Multiplier

• An increase in investment increases aggregate expenditure and real GDP.
• The increase in real GDP also lead to an increase in induced expenditure
• That increase in induced expenditure leads to a further increase in aggregate expenditure and real GDP.
• Real GDP increases by more than the initial increase in autonomous expenditure.
• Investment increases by $50 billion, and firms increase production to restore inventories, increasing real GDP to $2,200 billion.

Why is the Multiplier Greater than One?

• If there is an increase in autonomous expenditure, further increases in aggregate expenditure are induced.

The Size of the Multiplier

• The size of the multiplier is the change in equilibrium expenditure divided by the change in autonomous expenditure.

The Multiplier and the Slope of the AE Curve

• The slope of the AE curve determines the magnitude of the multiplier.
• Multiplier = 1 / (1 – Slope of AE Curve).
• Change in real GDP is ΔY, change in autonomous expenditure is ΔA, and change in induced expenditure is ΔN, the multiplier is ΔY / ΔA.
• To find the equation of the multiplier:
  • ΔY = ΔN + ΔA, and Slope of AE curve = ΔN / ΔY:
    • ΔN = (Slope of AE curve × ΔY)
    • ΔY = (Slope of AE curve × ΔY) + ΔA
  • Rearrange it to (1 – Slope of AE curve) × ΔY = ΔA
  • ΔY = ΔA / (1 – Slope of AE curve)
  • Multiplier = ΔY / ΔA
  • Multiplier = 1 / (1 – Slope of AE curve)
• With numbers from Figure 11.5, the slope of the AE curve is 0.75, so the multiplier is: ΔY ÷ ΔA = 1 / (1 – 0.75) = 1 / (0.25) = 4.

Imports and Income Taxes

• The number of imports and payments of income tax reduces the size of the multiplier.
• In part (a) with no taxes or imports, the slope of the AE curve is 0.75 and the multiplier is 4.
• In part (b) with taxes and imports, the slope of the AE curve is 0.5 and the multiplier is 2.

The Multiplier Process

• The amount of induced expenditure at each round, represented by the green bar, determines how aggregate expenditure moves towards equilibrium expenditure.

Business Cycle Turning Points

• Turns in business cycles, peaks and troughs, happen when changes to autonomous expenditure occur.
• An increase in autonomous expenditure will triggers an expansion.
• A decrease in autonomous expenditure will trigger a recession.

The Multiplier and the Price Level

• The AS-AD model works to explain the consistent determination of real GDP and the price level.
• Real firms do not hold their prices consistent for long
• When firms have an unplanned change in inventories, they change production and prices to match.

Aggregate Expenditure and Aggregate Demand

• The relationship of aggregate planned expenditure and real GDP, with all other influences on aggregate planned expenditure remaining the same, is the aggregate expenditure curve.
• The aggregate demand curve is the relationship between the quantity of real GDP demanded and the price level, with all other influences on aggregate demand remaining the same.

Deriving the Aggregate Demand Curve

• Wealth and substitution effects change the aggregate planned expenditure and the quantity of real GDP demanded, when the price lever changes.
• A rise in price level shifts the AE curve downward decreases equilibrium expenditure shifts a movement up along the AD curve.
• For example, rises in price levels shifts the AE curve downward from AE0 to AE1 and decreases equilibrium expenditure from $2,000 billion to $1,900 billion, bringing a movement up along the AD curve from point B to point A.
• A fall in price level and increases equilibrium expenditure shifts a movement down along the AD curve
  • For example, falls in price level shifts the AE curve upward from AE0 to AE2 and increases equilibrium expenditure from $2,000 billion to $2,100 billion, brings a movement down along the AD curve from point B to point C.
• Points A, B, and C on the AD curve all correspond to the equilibrium expenditure points A, B and C at the joint point of the AE curve and the 45° line. Changes in Aggregate Expenditure and Aggregate Demand
  • An increase in investment can cause an upward shift of the AE curve.
  • An increase investment can cause a to shift rightward of the AD curve.
  • How far rightward is based on amount and its relationship to the multiplier.

Equilibrium Real GDP and the Price Level

• The AE curve upward and AD curve rightward when investment increases.
• With the level left alone, the real GDP would increase to $2,200 billion at point B.
• The price level rises, which leads to a downward shift of the curve.
• Equilibrium expenditure decreases to $2,130 billion.
• Real GDP increases along the SAS curve to $2,130 billion as the price level increases.
• The multiplier in the short run is smaller than when the price level is fixed.
• The money wage rate continues to rise, and the SAS curve will continue leftward
• Real GPD equals potential GDP.
• The multiplier is zero in the long run.