chapter 11

The Multiplier: an informal intro

• How much extra income and spending are created from an initial change in spending

• 4 simplifying assumptions

  • Producers are willing to supply additional output at fixed price (price doesn’t increase)

  • Interest rate given

  • No govt. Spending or taxes

  • Exports and imports are zero

• An increase in consumer spending leads to increased incomes and increased savings and in turn, increased spending

• Marginal propensity to consume (MPC)

  • Increase in consumer spending when disposable income rises by $1

  • = Change in consumer spending / change in disposable income

  • Usually a number between 0 and 1

  • Marginal propensity to save (MPS)

    • Fraction of an additional dollar of disposable income saved

    • = 1 - MPC

    • MPS + MPC = 1

• Total increase in real GDP from some X rise in investment

  • = 1 / ( 1 - MPC ) * X

• Autonomous change in aggregate expenditure (AE)

  • Initial rise or fall in aggregate expenditure at a given level of real GDP

  • Cause (not result) of chain reaction

• Multiplier

  • Ratio of total change in real GDP caused by an autonomous change in aggregate expenditure to the size of that autonomous change

  • Change in real GDP = 1 / (1 - MPC) * AE

  • Multiplier = (change in  real GDP / AE) = 1 / (1 - MPC)

Consumer spending

• Current disposable income and consumer spending

  • Current disposable income

    • Income after taxes paid and govt. Transfers received

    • If higher people spend more

  • Individual consumption function

    • Shows how an individual household's consumer spending varies with households current disposable income

    • Simplest version is a linear equation

      • c = ac + mpc * yd

        • c = individual household consumer spending

          • Y axis

        • yd = individual household current disp income

          • X axis

        • mpc = marginal propensity to consume

          • slope

        • ac = individual household autonomous consumer spending

          • Spending if 0 disp income

          • Y intercept

    • Another equation for MPC

      • MPC = change in c / change in yd

      • Change in c = MPC * change in yd

  • Aggregate consumption function

    • Individual consumption function for the entire economy

    • Relationship between disp income and consumer spending for economy as a whole

    • C = AC + MPC * YD

      • C = aggregate consumer spending (consumer spending)

      • YD = aggregate current disp income (disp income)

      • AC = aggregate autonomous consumer spending

• Causes of Shifts of aggregate consumption function

  • Changes in expected future disp income

    • If consumers think higher disp income is coming

      • They will spend more at any level of current disp income

      • Increases AC and shifts aggregate consumption function up

    • Opposite happens if they think lower disp income is coming

    • Permanent income hypothesis

      • Consumer spending (C) depends mainly on expected income over the long term rather that current income

  • Changes in aggregate wealth

    • Wealth has an effect on consumer spending

    • Life-cycle hypothesis

      • Consumers plan their spending over a lifetime, not just in response to their current disp income

      • People with more wealth will spend more than those without

      • Smooths out consumption because it means we don’t make sudden changes in consumption

        • Good years we save, bad years we use savings

    • Increase in aggregate wealth

      • Increases AC and shifts aggregate consumption function up

    • Opposite happens with decrease in aggregate wealth

Investment spending

• Less than consumer spending

• Investment spending tends to drive business cycle

  • Very volatile compared to consumer spending

• Planned investment spending

  • Investment spending firms intent to undertake during a time period

• Planned investment spending depends on 3 principal factors

  • Interest rate

    • Spending on residential construction

      • People will only build homes if they can sell them

      • If interest rates lower, homes more affordable so more investment spending

    • Firms with investment spending projects only go ahead with project if expected rate of return higher than cost of funds needed to be borrowed

      • If interest rate higher, less projects profitable

    • Retained earnings

      • Past profits used to finance investment spending

      • They can lend out funds with interest instead of investing

    • Lower interest rate leads to more profit and more investing

  • Expected future real GDP and production capacity 

    • Firms will do more investment spending when they expect sales to grow

    • The higher the current capacity, the lower the investment spending

      • For given level of expected future real GDP

    • High expected future growth rate of real GDP is indicator of high growth of future sales

      • Accelerator principle

        • Lower expected sales lead to lower planned investment which accelerates a recession

        • Investment spending slumps

  • Inventories and unplanned investment spending

    • Inventories

      • Stocks of goods held to satisfy future sales

      • Firms hold inventories of goods and inputs

    • Increasing inventories is form of investment spending

    • Inventory investment

      • Value of change in total inventories held in economy during time period

      • Can be negative

    • Unplanned inventory investment

      • Inventory investment spending that occurred but was unplanned

    • Decrease in inventories is a sign of future expansion

      • Increase in inventories sign of future contraction

    • Actual investment spending = planned investment spending + unplanned inventory investment

      • I = Iunplanned + Iplanned

      • Iunplanned = unplanned inventory investment

The income-expenditure model

• Multiplier process assumptions

  • Changes in overall spending lead to changes in aggregate output

    • Fixed aggregate price level

  • Interest rate fixed

  • Taxes, govt. Transfers and govt. Purchases zero (G = T = TR = 0)

  • Exports and imports zero

• Planned aggregate expenditure and real GDP

  • GDP = C + I and (Total spending)

  • YD = GDP (Disposable income)

    • These two equations work because assumptions

  • Assume aggregate consumption function:

    • C = AC + MPC * YD

  • AEplanned = C + Iplanned

    • Planned aggregate spending

    • At equilibrium: AEplanned = GDP (when Iunplanned = 0)

  • For brief periods of time, planned aggregate expenditure can differ from real GDP because of the role of unplanned aggregate expenditure

    • Iunplanned (unplanned inventory investment)

    • Economy moves toward situation with no Iunplanned

• Income-expenditure equilibrium

  • Situation where there is no unplanned inventory investment

    • Where A planned = aggregate output (GDP)

  • Planned aggregate expenditure can be different from real GDP only if there's Iunplanned in the economy

  • Iunplanned = real GDP - AEplanned

    • If positive, firms producing more than consumers demand leading to unintended increase in inventories

    • GDP = C + I

    • = C + Iplanned + Iunplanned

    • = AEplanned + Iunplanned

  • Firms will change output if they have negative or positive Iunplanned

  • Firms wont change output if aggregate output (real GDP) equals planned aggregate expenditure

    • Income expenditure equilibrium

    • Iunplanned = 0

    • Keynesian cross

      • Point where planned aggregate expenditure line crosses 45 degree line

  • When Iunplanned < 0

    • Real GDP will rise

    • Opposite for > 0

  • Y* = Income-expenditure equilibrium GDP

• Multiplier process and inventory adjustment

  • Shift of planned aggregate expenditure line

    • Two sources of shift

      • Change in planned investment spending (Iplanned)

      • Shift of aggregate consumption function (CF)

        • There is autonomous change in planned aggregate expenditure

        • Multiplier process makes shift in planned aggregate expenditure much larger than autonomous change

        • Change in income-expenditure equilibrium GDP 

          • = multiplier * change in AE

          • = 1 / (1 - MPC) * change in AE

  • Declines in planned investment spending usually the major factor causing recessions

    • Most common source of autonomous reductions in aggregate expenditure

• What about exports and imports

  • Exports are like an increase in autonomous spending 

    • (intercept shift) of AEplanned

  • Govt expenditure also an intercept shift

  • Basic multiplier works with two modifications

    • Income earned from exports is a source of spending on domestically produced goods (like consumption and investment)

      • Changes in exports act like autonomous changes in spending

    • Multiplier made weaker thanks to foreign trade

      • When consumer spending rises or falls, part of that change reflected in changes in spending on imports, which don’t affect nations own income

        • Leakage from domestic economy

        • Makes slope of AEplanned less

      • Marginal propensity to import

        • Number between 0 and 1

        • Percentage of new income spent on imports

  • Trade creates interdependence among national economies

    • Each countries exports are anothers imports

    • Many countries have recessions and recoveries at the same time