x

A Change in Aggregate Demand Changes National Output, and the Multiplier Makes the Final Effect Larger Than the Initial Injection

Definition

The multiplier: the process by which an initial change in injections or spending leads to a larger eventual change in national income, equal to 1 divided by (1 minus the marginal propensity to consume).

How Aggregate Demand Drives Economic Activity

  1. Aggregate demand is total planned spending in the economy, AD=C+I+G+(X−M)AD=C+I+G+(X-M)AD=C+I+G+(X−M).
  2. A rise in AD raises the level of economic activity, increasing real output and employment; a fall in AD lowers it.
  3. An injection such as investment, government spending or exports sets off a multiplier process that adds to income over several rounds.
Note
  • Aggregate demand is C+I+G+(X−M)C+I+G+(X-M)C+I+G+(X−M).
  • A change in any component shifts AD and changes the level of economic activity.

The Multiplier Process

  1. The multiplier means an initial injection leads to a larger eventual rise in national income.
  2. Spending becomes income for others, who then re-spend part of it in the next round.
  3. Each round is smaller because saving, taxation and imports leak income out of the flow.
Example
  • Worked example: an injection of £10 billion with an MPC of 0.80.80.8, so 80%80\%80% of each extra pound is re-spent.
  • Round 1 adds £10 billion; round 2 adds 0.8×£10bn=£8bn0.8\times\pounds 10\text{bn}=\pounds 8\text{bn}0.8×£10bn=£8bn; round 3 adds 0.8×£8bn=£6.4bn0.8\times\pounds 8\text{bn}=\pounds 6.4\text{bn}0.8×£8bn=£6.4bn, and so on.
  • The shrinking series £10bn+£8bn+£6.4bn+…\pounds 10\text{bn}+\pounds 8\text{bn}+\pounds 6.4\text{bn}+\dots£10bn+£8bn+£6.4bn+… sums to £50 billion, exactly matching the formula answer of k=5k=5k=5.
Note
  • The multiplier is k=11−MPCk=\dfrac{1}{1-\text{MPC}}k=1−MPC1​.
  • Equivalently k=1MPWk=\dfrac{1}{\text{MPW}}k=MPW1​, where the MPW (marginal propensity to withdraw) equals MPS+MPT+MPM\text{MPS}+\text{MPT}+\text{MPM}MPS+MPT+MPM; for AQA you only need to calculate the multiplier from the MPC.
Example
  • With an MPC of 0.80.80.8, the multiplier is 11−0.8=10.2=5\dfrac{1}{1-0.8}=\dfrac{1}{0.2}=51−0.81​=0.21​=5.
  • So an injection of £10 billion raises national income by £10bn×5=£50bn\pounds 10\text{bn}\times 5=\pounds 50\text{bn}£10bn×5=£50bn.

Calculating the Multiplier From the Marginal Propensity to Consume

  1. The marginal propensity to consume (MPC) is the fraction of any extra income that households spend.
  2. From the MPC, the multiplier is 11−MPC\dfrac{1}{1-\text{MPC}}1−MPC1​; the larger the leakages, the smaller the multiplier.
  3. The leakages are saving, taxation and imports, which together make up the marginal propensity to withdraw (MPW).
Example
  • Suppose the MPC is 0.70.70.7, so households re-spend 70%70\%70% of each extra pound of income.
  • The multiplier is 11−0.7=10.3≈3.3\dfrac{1}{1-0.7}=\dfrac{1}{0.3}\approx 3.31−0.71​=0.31​≈3.3, so an injection of £10 billion raises national income by about £33 billion.

Why the Size of the MPC Determines the Size of the Multiplier

  1. A larger MPC means households re-spend more of each extra pound, so less income leaks out and the MPW is smaller.
  2. Because the multiplier is 11−MPC\dfrac{1}{1-\text{MPC}}1−MPC1​, a larger MPC (and smaller MPW) gives a larger multiplier and a bigger final change in national income.
  3. A smaller MPC (larger leakages) gives a smaller multiplier and a weaker effect on activity.
Example
  • If the MPC is 0.50.50.5, the multiplier is 11−0.5=10.5=2\dfrac{1}{1-0.5}=\dfrac{1}{0.5}=21−0.51​=0.51​=2, so £10 billion raises income by £10bn×2=£20bn\pounds 10\text{bn}\times 2=\pounds 20\text{bn}£10bn×2=£20bn.
  • A higher MPC would mean smaller leakages, giving a larger multiplier and a bigger effect.
Note
  • The full multiplier effect only appears when there is spare capacity, so extra spending raises real output rather than prices.
  • Near full capacity, extra AD feeds mainly into inflation, so the real multiplier is weaker; the effect also works in reverse, magnifying a fall in injections.
Exam technique
  • Find the multiplier as 11−MPC\dfrac{1}{1-\text{MPC}}1−MPC1​; do not divide by the MPC itself.
  • Multiply the injection by the multiplier to find the final change in national income.
Self review
  • What are the components of aggregate demand?
  • State the formula for the multiplier in terms of the MPC.
  • If the MPC is 0.80.80.8, what is the multiplier, and by how much would a £5 billion injection raise income?
  • Why does a larger MPC give a larger multiplier?
  • Why might the real multiplier be smaller when the economy is near full capacity?
PreviousNext

How was this guide?

2.2.4 Aggregate demand and the level of economic activity Revision Guide

  1. A Level
  2. /Economics
  3. /2.2.4 Aggregate demand and the level of economic activity