The Keynesian Multiplier (DP IB Economics)

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Steve Vorster

Written by: Steve Vorster

Reviewed by: Jenna Quinn

An Introduction to the Keynesian Multiplier

  • The multiplier is the ratio of change in real income to the injection that created the change

    • E.g. If the Brazilian government injected an additional 5bn Brazilian real (BZL) into the economy through government spending and it resulted in an increase in real income of 15bn BZL, the value of the multiplier would be 3

  • The multiplier process is based on the idea that one individual's spending is another individual's income

    • An increase in consumption immediately increases AD

      • Store owners who have benefitted from the extra consumption now have extra income

      • They spend some of that income on goods/services

      • Their expenditure on goods/services is now income for the next tier of individuals 

    • Due to the successive rounds of spending, the final increase in national income is much larger than the initial injection

    • The size of the multiplier is entirely dependent on the size of leakages that occur during the process

      • The higher the leakages the smaller the multiplier

  • The initial injection shifts AD to the right

    • The result of the multiplier process is that there is then a secondary movement of AD to the right which (if the multiplier were 2) may be double the initial movement

  • The multiplier can also work in reverse when injections are reduced (downward multiplier effect)

The Effects of Marginal Propensities on the Multiplier

  • The 'marginal propensities' refer to the proportion of the next $ earned that a consumer saves, consumes, is taxed, or purchases imports with

  • Marginal propensities are calculated for economies and provide insights into how each additional $ of income is allocated

    • Sweden has a higher tendency to save than the USA

      • Their marginal propensity to save is higher 

      • The USA, therefore, has a greater multiplier on any injections into the Circular Flow

An Explanation of the Marginal Propensities


Marginal Propensity


Explanation


Formula

Marginal Propensity to Consume (MPC)

  • The proportion of additional income that is spent on consumption (C)

MPC space equals fraction numerator increment straight C over denominator increment straight Y end fraction

Marginal Propensity to Save (MPS)

  • The proportion of additional income that is saved (S)

MPS space equals fraction numerator increment straight S over denominator increment straight Y end fraction

Marginal Propensity to Tax (MPT)

  • The proportion of additional income that is paid in tax (T) 

MPT space equals fraction numerator increment straight T over denominator increment straight Y end fraction

Marginal Propensity to Import (MPM)

  • The proportion of additional income that is spent on imports (M

MPM space equals fraction numerator increment straight M over denominator increment straight Y end fraction

Calculating the Multiplier

  • The value of the multiplier can be calculated one of two ways

    • By focusing on the marginal propensity to consume (MPC)

    • Or, by focusing on the withdrawals that occur on each additional $ of income (MPS + MPT + MPM)

  1. Focussing on the MPC
    Multiplier space equals space fraction numerator 1 over denominator left parenthesis 1 space minus MPC right parenthesis end fraction
     

  2. Focusing on the Withdrawals
    Multiplier space equals space fraction numerator 1 over denominator MPW space end fraction space equals space fraction numerator 1 over denominator left parenthesis MPM space plus space MPS space plus space MPT right parenthesis end fraction

Worked Example

An economy has the marginal propensity to save of 0.15, marginal propensity to tax of 0.20 and a marginal propensity to import of 0.15.

a) Calculate the size of the multiplier.

b) If the Government increases their infrastructure spending by £60m, calculate the total increase in GDP, assuming all other things remain equal.

 Answer:

Step 1: Insert the values into the withdrawal formula

size 14px Multiplier size 14px space size 14px equals size 14px space fraction numerator size 14px 1 over denominator size 14px left parenthesis size 14px MPM size 14px space size 14px plus size 14px space size 14px MPS size 14px space size 14px plus size 14px space size 14px MPT size 14px right parenthesis end fraction

size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px space fraction numerator size 14px 1 over denominator size 14px left parenthesis size 14px 0 size 14px. size 14px 15 size 14px space size 14px plus size 14px space size 14px 0 size 14px. size 14px 15 size 14px space size 14px plus size 14px space size 14px 0 size 14px. size 14px 20 size 14px right parenthesis end fraction size 14px space size 14px space size 14px equals size 14px space fraction numerator size 14px 1 over denominator size 14px 0 size 14px. size 14px 5 end fraction

size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px space size 14px 2

Step 2: Multiply the injection by the multiplier

Impact on GDP = Injection x multiplier

= £60m x 2

= £120m

Worked Example

Calculate the amount of government spending required to restore an economy's macroeconomic equilibrium if the economy faces a $22bn recessionary gap and its MPC is 0.6 [2]

Answer:

Step 1: Calculate the multiplier

 Multiplier space equals space fraction numerator 1 over denominator left parenthesis 1 space minus MPC right parenthesis end fraction

Multiplier space equals space fraction numerator 1 over denominator left parenthesis 1 space minus 0.6 right parenthesis end fraction

Multiplier space equals space 2.5 space bold space[1 mark]

Step 2: Calculate the value of government spending required

Government space spending space required space equals fraction numerator $ 22 bn over denominator 2.5 end fraction

Government space spending space required space equals $ 8.80 space bn space

[1 mark]

Significance of the Multiplier in Shifting Aggregate Demand (AD)

  • The greater the withdrawals, the smaller the value of the multiplier - and vice versa

  • The greater the MPC, the higher the value of the multiplier - and vice versa

  • Any change in one of the factors that impacts on disposable income, will change the multiplier

    • If taxes increase the value of the multiplier reduces

    • If interest rates increase, savings increase and consumption decreases and the multiplier reduces

    • If exchange rates appreciate the level of imports will increase and the multiplier decreases

    • If confidence in the economy increases consumption increases and the multiplier increases
       

  • It is extremely useful for the Government to know the value of the multiplier

    • They can use it to judge the likely economic growth caused by increased spending
       

  • There is a time lag as it takes time for the successive rounds of income to work through the economy

Examiner Tips and Tricks

The final bullet point above mentions time lags. This is an excellent point to include in any evaluation on the effectiveness of the multiplier. It may take up to 18 months for the full multiplier effect to be seen & any change to consumer confidence during this period will impact the final outcome.

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Steve Vorster

Author: Steve Vorster

Expertise: Economics & Business Subject Lead

Steve has taught A Level, GCSE, IGCSE Business and Economics - as well as IBDP Economics and Business Management. He is an IBDP Examiner and IGCSE textbook author. His students regularly achieve 90-100% in their final exams. Steve has been the Assistant Head of Sixth Form for a school in Devon, and Head of Economics at the world's largest International school in Singapore. He loves to create resources which speed up student learning and are easily accessible by all.

Jenna Quinn

Author: Jenna Quinn

Expertise: Head of New Subjects

Jenna studied at Cardiff University before training to become a science teacher at the University of Bath specialising in Biology (although she loves teaching all three sciences at GCSE level!). Teaching is her passion, and with 10 years experience teaching across a wide range of specifications – from GCSE and A Level Biology in the UK to IGCSE and IB Biology internationally – she knows what is required to pass those Biology exams.