Expenditure Multipliers and the Keynesian Model Notes

Expenditure Multipliers: The Keynesian Model

Introduction

• This chapter explores how the economy reacts to fluctuations in investment and exports, examining whether it smooths out these bumps or magnifies them.

Fixed Prices and Expenditure Plans

• The Keynesian model describes the economy in the very short run when prices are fixed.

• Key assumptions:

  • The price level is fixed.

  • Aggregate demand determines real GDP.

Expenditure Plans

• Components of aggregate expenditure sum to real GDP: Y = C + I + G + X – M

• Consumption (C) and Imports (M) are influenced by real GDP (Y), creating 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.

Consumption and Saving Plans

• Consumption expenditure is directly influenced by disposable income.

• Disposable income (YD) is real GDP (Y) minus net taxes (T): YD = Y – T

• Disposable income is either spent on consumption (C) or saved (S): YD = C + S

• Consumption Function: Relationship between consumption expenditure and disposable income.

• Saving Function: Relationship between saving and disposable income.

• When consumption expenditure exceeds disposable income, saving is negative (dissaving).

• When consumption expenditure is less than disposable income, there is saving.

Marginal Propensities to Consume and Save

• Marginal Propensity to Consume (MPC): Fraction of a change in disposable income spent on consumption.

  • MPC = \frac{C}{YD}

  • The MPC is the slope of the consumption function.

• Marginal Propensity to Save (MPS): Fraction of a change in disposable income that is saved.

  • MPS = \frac{S}{YD}

  • The MPS is the slope of the saving function.

• The sum of MPC and MPS equals 1: MPC + MPS = 1

Consumption as a Function of Real GDP

• If tax rates don’t change, real GDP is the primary influence on disposable income, making consumption expenditure a function of real GDP.

Import Function

• U.S. imports are primarily influenced by U.S. real GDP in the short run.

• The marginal propensity to import is the fraction of an increase in real GDP spent on imports.

Real GDP with a Fixed Price Level

• Aggregate demand is determined by aggregate expenditure plans when the price level is fixed.

• Aggregate planned expenditure: planned consumption + planned investment + planned government expenditure + planned exports - planned imports.

• Planned consumption and imports are influenced by real GDP.

• Planned investment, government expenditure, and exports are not directly influenced by real GDP.

Aggregate Planned Expenditure

• Aggregate Expenditure Schedule: Lists the level of aggregate expenditure planned at each level of real GDP.

• Aggregate Expenditure Curve: Graph of the aggregate expenditure schedule.

• Induced Expenditure: Consumption expenditure minus imports, which varies with real GDP.

• Autonomous Expenditure: Sum of investment, government expenditure, and exports, which does not vary with GDP (but consumption and imports can have an autonomous component).

Actual Expenditure, Planned Expenditure, and Real GDP

• Actual aggregate expenditure is always equal to real GDP.

• Aggregate planned expenditure may differ from actual aggregate expenditure due to unplanned changes in inventories.

• Equilibrium Expenditure: Level of aggregate expenditure when aggregate planned expenditure equals real GDP.

Convergence to Equilibrium

• From Below Equilibrium: If aggregate planned expenditure exceeds real GDP, there is an unplanned decrease in inventories, leading firms to increase production and real GDP.

• From Above Equilibrium: If real GDP exceeds aggregate planned expenditure, there is an unplanned increase in inventories, leading firms to decrease production and real GDP.

• At Equilibrium: If aggregate planned expenditure equals real GDP, there is no unplanned change in inventories, and real GDP remains constant.

The Multiplier

• A change in autonomous expenditure leads to a larger change in equilibrium expenditure and real GDP.

• Multiplier: The amount by which a change in autonomous expenditure is magnified to determine the change in equilibrium expenditure and real GDP.

Basic Idea of the Multiplier

• An increase in investment increases aggregate expenditure and real GDP.

• The increase in real GDP leads to an increase in induced expenditure.

• The 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.

Why Is the Multiplier Greater than 1?

• Because an increase in autonomous expenditure induces further increases in aggregate expenditure.

Size of the Multiplier

• The change in equilibrium expenditure divided by the change in autonomous expenditure.

• Multiplier = \frac{Change \,in \,equilibrium \,expenditure}{Change \,in \,autonomous \,expenditure}

• Example: If initial equilibrium expenditure is 13 trillion, autonomous expenditure increases by 0.5 trillion, and equilibrium expenditure increases by 2 trillion, the multiplier is 4.

The Multiplier and the Slope of the AE Curve

• Multiplier = \frac{1}{1 – Slope \,of \,AE \,curve}

• If the change in real GDP is DY, the change in autonomous expenditure is DA, and the change in induced expenditure is DN, then Multiplier = \frac{DY}{DA}

• Since DY = DN + DA and Slope \,of \,AE \,curve = \frac{DN}{DY}, then DN = Slope \,of \,AE \,curve * DY

• Substituting, DY = (Slope \,of \,AE \,curve * DY) + DA and rearranging, (1 - Slope \,of \,AE \,curve) * DY = DA

• Therefore, DY = \frac{DA}{(1 - Slope \,of \,AE \,curve)} and Multiplier = \frac{DY}{DA} = \frac{1}{(1 - Slope \,of \,AE \,curve)}

• With no income taxes and no imports, the slope of the AE curve equals the marginal propensity to consume, so the multiplier is Multiplier = \frac{1}{(1 - MPC)}. Since 1 – MPC = MPS, the multiplier is also Multiplier = \frac{1}{MPS}.

Imports and Income Taxes

• Both imports and income taxes reduce the size of the multiplier.

The Multiplier Process

• The MPC determines the magnitude of the amount of induced expenditure at each round as aggregate expenditure moves toward equilibrium expenditure.

• ∆Y = ∆I + b∆I + b^2∆I + b^3∆I + b^4∆I + b^5∆I + … (where b = slope of AE curve).

• Multiply by b: b∆Y = b∆I + b^2∆I + b^3∆I + b^4∆I + b^5∆I + …

• Subtract the second equation from the first: ∆Y – b∆Y = ∆I, or (1 – b) ∆Y = ∆I, so that ∆Y = \frac{∆I}{(1 – b)}$$.

Business Cycle Turning Points

• Turning points in the business cycle—peaks and troughs—occur when autonomous expenditure changes.

• An increase in autonomous expenditure brings an unplanned decrease in inventories, which triggers an expansion.

• A decrease in autonomous expenditure brings an unplanned increase in inventories, which triggers a recession.

The Multiplier and the Price Level

Adjusting Quantities and Prices

• Firms don’t hold their prices constant for long; they change production and prices when they have unplanned changes in inventories.

• The price level changes when firms change prices.

• The AS-AD model explains the simultaneous determination of real GDP and the price level.

Aggregate Expenditure and Aggregate Demand

• Aggregate Expenditure Curve: Relationship between aggregate planned expenditure and real GDP, holding all other influences constant.

• Aggregate Demand Curve: Relationship between the quantity of real GDP demanded and the price level, holding all other influences constant.

Deriving the Aggregate Demand Curve

• Changes in the price level cause wealth and substitution effects, changing aggregate planned expenditure and the quantity of real GDP demanded.

• A rise in the price level shifts the AE curve downward, decreasing equilibrium expenditure.

• A fall in the price level shifts the AE curve upward, increasing equilibrium expenditure.

• Points on the AD curve correspond to equilibrium expenditure points on the AE curve at the intersection of the AE curve and the 45° line.

Changes in Aggregate Expenditure and Aggregate Demand

• An increase in investment shifts the AE curve upward and the AD curve rightward by an amount equal to the change in investment multiplied by the multiplier.

Equilibrium Real GDP and the Price Level

• The increase in investment shifts the AE curve upward and shifts the AD curve rightward.

• With no change in the price level, real GDP would increase to a certain point.

• But the price level rises, shifting the AE curve downward, and equilibrium expenditure decreases.

• As the price level rises, real GDP increases along the SAS curve.

• The multiplier in the short run is smaller than when the price level is fixed.

• In the long run, there is an inflationary gap, and the money wage rate starts to rise, shifting the SAS curve leftward until real GDP equals potential real GDP.

• In the long run, the multiplier is zero.