Tax Function &
Government Expenditures
Tax Function
Tax function expresses the level of government spending
depending on three factors.
Y = national income
s = minimum tax which is independent of Y; minimum tax
when income is zero
t = marginal propensity to tax
MPT is the ratio of change in tax to change in national
income.
MPT is the slope of the Tax function.
Tax Function
Tax is a function of national income.
T = s + tY
where:
T = tax level
s
= minimum tax
Y = national income
t
= marginal propensity to tax
MPT(t) = Change in tax
Change in Y
Consumption Function
Y
T
Yd
C
I
C+I
C+I+G
50
250
50
90
0
160
200
280
30
230
310
290
370
450
500
700
130
140
180
320
360
520
360
390
460
390
420
490
450
480
550
Consumption Function
C = b + cYd
200= b + c (0)
MPC(c)=280-200/160-0=0.50
200=b + 0.50(0)
200=b +0
b=200
C= 200 +0 .50Yd
Investment Multiplier
INVESTMENT MULTIPLIER
-an income injection into the circular flow could
generate a much greater increase in income.
Investment Multiplier (K)
K = 1/1-MPC= 1/MPS
K=1/0.05
K=2
Tax Function
Tax is a function of national income.
T = s + tY
50= s + t (50)
MPT(t)=90-50/250-50=0.20
50=t + 0.20(50)
50=t +10
50-10=t
t=40
t = 40 +0 .20Y
Income Equilibrium
Ye= C + I + G
Ye= b-c(s)+ I + G/1-c+ct
Ye= 200-0.50(40) + 30 +60/1-.50+.50(.20)
Ye= 270/0.60=450
T=40+.20(450)=130
Yd=Ye-T=450-130=320
C=200+.50(320)=360
C + I + G=360 + 30 + 60=450
Ye=450; C+I+G=450
Hence, this is the 3rd Income Equilibrium
when Y = C+ I + G