• 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
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