Wednesday, October 26, 2022

Some notes to my IB Economics students on the MULTIPLIER EFFECT


A (Keynesian) idea whereby an increase in government expenditures G will lead to a greater increase in national income (in real GDP)

i.e. ΔY > ΔG or, ΔY = κ ΔG

(where little κ is the multiplier)

Let the government increase government expenditures by $100mil. If national income increases by $300mil, the multiplier (little κ) is ‘3’: $300m/ = 3 x $100m

 Why should we expect this to be the case? Because:

  • Your spending is my income.
  • Economic activity takes place in successive rounds (as clearly illustrated by the ‘circular flow of income’ diagram; use in an essay if you consider it necessary)

If the government spends $100 to build a tiny road in my neighborhood and I’m the only worker / engineer, it means that my income increases by $100.

Part of this additional income earned, I will spend on domestic goods and services, say $80. For example, from the additional $100 I earned, I will spend $80 for a dancing company to come at my birthday party and dance for my guests. National income will have increased by $100 + $80 = $180 (and note that two ‘goods’ will have been produced: a tiny road and a dancing performance).

Generalizing: If out of each dollar earned as additional income people spend 80 cents then the so-called Marginal Propensity to Consume (MPC) is 0.80

MPC = ΔC / ΔY, equal to say ‘b’

Let the dancers now spend 0.8 of their additional income on violin lessons for their offspring.  They thus spend $64 (0.8x80) on the violin teachers.  Violin teachers now have additional income equal to $64 and national income has increased by a total of $100+$80+$64 = $244.  They in turn will spend part (0.8) of their additional income on feta cheese…and so on and so forth…

More generally (a geometric series; sum of; converges as 0 < b < 1):

ΔY = ΔG + bΔG + b^2ΔG + b^3ΔG + …

ΔY = (1+b+b^2 +b^3 +b^4 +…) x ΔG

ΔY = (1/(1-b)) x ΔG, so little κ:

κ = {1 / (1-MPCd)] = {1/(MPW)], where MPW = MPS + MPT + MPM

(as if I spend out of $100 of additional income on domestic goods, the rest (i.e. $20) I have either saved (S) or paid in taxes (T) or spent, but on imports M): all three (S,T, M are withdrawals / leakages from the circular flow)

(MPS is the marginal propensity to save, MPT is the marginal tax rate and MPM is the marginal propensity to spend on imports: their sum [MPS+MPT+MPM] is the marginal propensity to withdraw : So (1-MPCd) = MPW (remember the circular flow again)  


  • The multiplier effect holds if any of the 3 injections increases (remember that injections 'J' include government expenditures G, but also exports X and private investment I) (note that the export multiplier is responsible for the international transmission of the business cycle)
  • The importance of the Keynesian multiplier of government expenditures (G) is that it shows that expansionary fiscal policy in the form of increased government expenditures (G) is very powerful to help an economy grow - lift an economy out of a recession (but, remember the other side, the crowding-out effect)
  • Expansionary fiscal is not only a result of an increase in G but could also be a result of a decrease in direct taxes T.

But, the multiplier effect of an equal (to ΔG) decrease in taxes T is smaller. Why?

Because the first-round effect does not exist. When a government decreases my taxes by $100, my income does not rise by $100: it is my disposable income that rises by $100 so the multiplier process starts with the 2nd round effect of an equal increase in G (since I will spend $80 of this increase in my disposable income on the dancing company above). So, the tax multiplier will be [b/(1-b)]  (the first term of the geometric series is now ‘b’, not ‘1’) It follows that if b is 0.8, then the government expenditure multiplier will be 1 / 0.2 = 5 but the tax multiplier will be 0.8 / 0.2 = 4 (smaller)

  • The multiplier operates also in the opposite direction. A decrease in government expenditures (G) will lead to a greater decrease in national income (Y). When Greece was ‘forced’ to borrow to avoid default during the Greek debt crisis, it ‘agreed’ to decrease government expenditures (G) as part of the agreement.  The IMF had then estimated that the Greek government expenditure multiplier, was, say equal to  ‘2’, so that a decrease in Greek government expenditures (G) by, say, €200mil., was expected to lead to a decrease of Greece’s national income by €400mil. (2x200)

BUT the recession that ensued (the decrease in national income) proved much more severe than expected: Greece’s rGDP decreased by much more than estimated by the IMF, say, by €500 million, and consequently even more people lost their jobs and their income, forcing the IMF (and its then Chief Economist, Olivier Blanchard - now at PIIE), to issue what was referred to as a “mea culpa”: a new IMF paper re-estimated ‘correctly’ the Greek little ‘κ’.

[Please check the Study Guide for other Real World Examples of the multiplier for use in part (b) of a Paper 1 essay]


In Keynes' General Theory we read (p. 128, Palgrave 2007 edition):

"If the Treasury were to fill old bottles with banknotes, bury them at suitable depths in disused coal mines which are then filled up to the surface with town rubbish, and leave to the private dig the notes up again...there need be no more unemployment and, with the help of the repercussions, the real income of the community...would probably become a good deal greater than it is."

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