The Multiplier Effect

Multiplier Effect

• “the impact on real GDP of a change in any of the components of aggregate spending (C, I , G , X-M).”

• The multiplier effect results in a larger change in real GDP than the initial change in any of the four components of aggregate spending

Mathematically speaking….

Multiplier = change in real GDP/initial change in expenditure

Or…

Initial change in expenditure X multiplier = change in real GDP

So you’re saying….

• That a $1 increase in spending by C, or I, or G, or X-M might lead to a greater than $1

increase in real GDP? How does that work?

It’s like a chain reaction!

The Chain Reaction Explained

• Suppose I increases by $8,000,000 (autonomous expenditure) . Real GDP goes up

by the same amount, but that’s not all that happens. Induced expenditures follow, because the $8,000,000 is also income

received by the factors of production, which in turn makes possible increased consumption

spending (C)

It’s kinda like dominoes…

What about leakages?

• As we know, increased income that flows to the owners of factors of production isn’t

always entirely spent. • A portion of the additional income will be

spent (these are injections to the circular flow), but the other portion will be saved

(leakages to the circular flow)

Marginal Propensity to Consume

• MPC is the fraction of additional income that households spend on consumption of

domestically produced goods and services. • So if MPC =3/4, and real income increases by

$8,000,000….• how much new consumption will result? • how much will leak out as savings?

Marginal propensity to save and friends

• MPS (marginal propensity to save) is one of the ways new income can leak from the circular flow.

• MPT (marginal propensity to tax) represents how much of new income must be paid in taxes

• MPI (marginal propensity to import) represents how much of new income will be spent on imports

So if you add ‘em all up….

• MPC + MPS + MPT + MPI = 1

• Makes sense because every $1 of additional income is either consumed, saved, taxed or

spent on imports.

So let’s do some math

• Let’s assume I has increased by $8,000,000. • So the initial increase to income is

$8,000,000. Then what happens? Let’s assume the MPC is .75…..

Calculating the value of the Multipler

Change in income Induced change in consumption

Initial increase in investment expenditure of

$8,000,0001st round $8,000,000 ¾ X 8 = 6

2nd round $6,000,000 ¾ X 6 = 4.5

3rd round $4,500,000 ¾ X 4.5 = 3.38

4th round $3,380,000 ¾ X 3.38 = 2.5

And on and on And on And on…..

Total $32,000,000 ¾ X 32 = 24

The answer is…..

• An increase of $8,000,000 in I will lead to an increase in income (real GDP) of $32,000,000

when MPC = .75.

• $8,000,000 of that is from the initial increase in I, the other $24,000,000 comes from the increase in induced consumption spending

So the value of the Multipier is….

• Multiplier = Change in real GDP/initial change in expenditure

$32,000,000/$8,000,000 = 4

More relationships…

• Multiplier = 1/1-MPC• Multiplier = 1/1-.75• Multiplier = 1/.25• Multiplier = 4

• So in order to calculate the multiplier, all we need to know is the marginal propensity to

consume

Moral of the story….

• The larger the marginal propensity to consume, the larger the value of the multiplier

will be. • Increases to any of the components of AD will

have the same effect• It works in the opposite way too, decreases in

spending will lead to a larger decrease in total income

Multiplier effect on AD

The multiplier and fiscal policy

• Obviously, the value of the multiplier plays an important role in the effect of expansionary or

contractionary fiscal policy. If government pursues expansionary fiscal policy, knowing

the value of the multiplier will give us a better idea of how much real GDP will actually

increase.

Tax cuts vs. government spending

• Remember that increased government spending will have a greater effect on real GDP than tax cuts. Does anybody remember why

this happens?

• If the multiplier = 4 (MPC= .75), a $1 increase in government spending leads to $4 in

increased AD• If the multiplier = 4 (MPC= .75), a $1 tax cut

will lead to $3 in increased AD and $1 in increased savings

• Increases in government spending have a greater effect on AD than tax cuts but are less

popular

Tax cuts vs. government spending

Final thoughts on the multiplier

• The multiplier is difficult to calculate because:

• It takes months for spending to cycle through the economy

• Changes to MPS, MPI, and MPT can cause the size of the multiplier to fluctuate

• Beware the effect of the price level! When in the horizontal portion of the Keynesian AS curve, increases in AD will increase output

without increasing the price level. However, as we move towards the upwards sloping

portion of the Keynesian AS curve, increases in AD will lead to rising price levels and less or no

increase in output!

Final thought on the multiplier

• In the neoclassical short run, increases in AD will lead to both increased output and an increasing price level. In the long run, the

vertical AS curve suggests that there will be no multiplier effect, only increases in the average

price level

Final thought on the multiplier

Keynes on the multiplier effect“I like it”