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Government spends £10 million on improving roads in Birmingham. ALL of this money goes into road builders pockets.

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MPC = 0.8; tax rate 25% They pay 25% in tax, leaving them £7.5 million in increased disposable income They save 20% (£1.5 million) leaving them to spend £6 million. They spend all of this £6 million on watching Birmingham City Football Club

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The Government spends £100 million on improving roads in Birmingham

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MPC = 0.8; tax rate 25% ALL of this £6 million goes to the football players (this is a very simplified example). THEY pay 25% in tax leaving them £4.5 million in increased disposable income They save 20% (£0.9 million) leaving them to spend £3.4 million. They spend all of this £6 million on watching the Birmingham Birmingham Royal BalletBirmingham Royal Ballet

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ALL of this goes to the dancers……………….. You can see that the initial injection of £10m led to a first round increase in consumers expenditure of £6m and a second round increase of £3m And so on and so on and so on………

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Sum the increases and they come to almost £25m.

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Tax Rate0.25 £ MillionsSavings Rate0.2 Government Injection10 1st round consumption6 2nd round consumption3.6 3rd round2.16 4th round1.296 4th round0.7776 4th round0.46656 4th round0.279936 4th round0.1679616 0.10077696 0.060466176 0.036279706 0.021767823 0.013060694 0.007836416 0.00470185 TOTAL24.99294723close to £25 million

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Tax Rate0.25 £ MillionsSavings Rate0.2 Government Injection10 1st round consumption6 2nd round consumption3.6 3rd round2.16 4th round1.296 4th round0.7776 4th round0.46656 4th round0.279936 4th round0.1679616 0.10077696 0.060466176 0.036279706 0.021767823 0.013060694 0.007836416 0.00470185 TOTAL24.99294723close to £25 million

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Hence the multiplier is 2.5= £25m/£10m. Can we prove this? Y=C+I+G (Closed economy) C=b0+b1*YD YD=(1-t)Y: t = tax rate C=b0+b1*(1-t)Y Y=b0+b1*(1-t)Y+I+G

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MPC=0.8; t=0.25 Y=b0+b1*(1-t)Y+I+G Y-b1*(1-t)Y=b0+I+G Y(1-b1*(1-t))=b0+I+G Y=[b0+I+G]/(1-b1*(1-t)) Any increase in G (or I, but b0 is fixed) will increase Y by 1/(1-b1*(1-t)) = 1/(1-0.8*(1-0.25)) = 1/(1-0.8*0.75) = 1/(1-0.6) =1/0.4 =2.5

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