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

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

The Government spends £100 million on improving roads in

Birmingham

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 Ballet

• 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………

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

Tax Rate 0.25£ Millions Savings Rate 0.2

Government Injection 101st round consumption 62nd round consumption 3.63rd round 2.164th round 1.2964th round 0.77764th round 0.466564th round 0.2799364th round 0.1679616

0.100776960.0604661760.036279706

Tax Rate 0.25

£ Millions Savings Rate 0.2

Government Injection 10

1st round consumption 6

2nd round consumption 3.6

3rd round 2.16

4th round 1.296

4th round 0.7776

4th round 0.46656

4th round 0.279936

4th round 0.1679616

0.10077696

0.060466176

0.036279706

0.021767823

0.013060694

0.007836416

0.00470185

TOTAL 24.99294723 close to £25 million

Tax Rate 0.25

£ Millions Savings Rate 0.2

Government Injection 10

1st round consumption 6

2nd round consumption 3.6

3rd round 2.16

4th round 1.296

4th round 0.7776

4th round 0.46656

4th round 0.279936

4th round 0.1679616

0.10077696

0.060466176

0.036279706

0.021767823

0.013060694

0.007836416

0.00470185

TOTAL 24.99294723 close to £25 million

Successive rounds of increase

0

2

4

6

8

10

12

1 3 5 7 9 11 13 15

Expenditure round

Fu

rth

er

inc

rea

se

in Y

Series1

• 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

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