Session 4
9-1
The Government Sector
The government affects the level of equilibrium output in two
ways:
1. Government expenditures (component of AD)
2. Taxes and transfers
Fiscal policy:
the policy of the government with regard to G, TR, and TA
◦ Assume G and TR are autonomous, and that there is a
proportional income tax (t ):
G=G
◦
TR = T R
TA = tY
Where t is a proportional tax rate (a given fraction of income
is collected in the form of taxes)
The Government Sector
◦
As TA = tY the consumption function becomes:
C = C + c(Y + T R − TA)
C = C + c(Y + T R − tY)
= C + cT R + c(1 − t)Y
(19)
◦
TR: raises autonomous consumption spending by c x TR
(induced spending out of transfers)
◦
TA: lowers consumption spending at each level of income,
because income taxes reduces disposable income and
consumption related to disposable income, so:
◦ mpc out of disposable income = c, and
◦ mpc out of income = c(1 - t), where (1 – t) is the fraction of
Y left after taxes.
◦ Eg: c = 0.8 & t = 0.25, what is the mpc out of income?
The Government Sector
Combining
C + cT R + c(1 − t)Y
(19) with AD:
AD = C + I + G + NX
= [C + cT R + c(1 − t)Y ] + I + G + NX
= [C + cT R + I + G + NX ] + c(1 − t )Y
= A + c(1 − t )Y
Where A = C + cT R + I + G + NX
(20)
The slope of the AD curve is affected by the tax rate, h/holds
now pay part of every Rand of income in taxes and are left with
1 – t of that Rand.
Now MPC out of income = c(1 - t), instead of c.
The Government Sector
Using the equilibrium condition, Y=AD, and equation (20), the
equilibrium level of output is:
Y = A + c(1 − t )Y
Y − c(1 − t )Y = A
Y [1 − c(1 − t )] = A
A
Y0 =
1 − c(1 − t )
(21)
The Government Sector
The equilibrium income without a govt sector, adapting equation
1
(12):
Y0 =
A
(1 − c)
where A = C + I
The equilibrium income with a govt sector, adapting equation (21):
Y0 =
A
1 − c(1 − t)
whereA = C + I + G + cT R
The Government Sector
The presence of the government sector:
◦ Raises autonomous spending by 𝐺𝐺̅
◦ Raises autonomous spending by induced spending out of
transfers, c𝑇𝑇𝑇𝑇
◦ Effect of income taxes:
◦ flattens the AD curve to c(1 - t) from c
1
◦ reduces the multiplier to
from
(1 − c(1 − t ))
1
(1 − c)
9-7
EXAMPLE: The Government Sector
Given the following values: c=0.8 and t=0.25
1. What is the slope of the AD schedule with and without a govt
sector?
2. What is the multiplier with and without a govt sector?
3. If TR increased from 0 to R800m, all other things constant, what
would be the impact on the AD schedule?
[note: do these on your own and check your answers in the lecture
video]
Income Taxes as an Automatic Stabilizer
Automatic stabilizer:
any mechanism in the economy that automatically (without caseby-case government intervention) reduces the amount by which
output changes in response to a change in autonomous demand
◦ One explanation of the business cycle is that it is caused by shifts in
autonomous demand, especially investment.
◦ Investment affected by investors’ attitude – it is optimistic or
pessimistic? Swings in investment demand have a smaller effect on
output when automatic stabilizers are in place:
◦ Proportional income tax → reduces the multiplier
◦ Unemployment benefits → enables unemployed to continue
consuming even though they do not have a job
Effects of a Change in Fiscal Policy
◦ Suppose government purchases (G) increase: fig 10.4
◦ Change in govt exp results in a change in autonomous spending
and shifts the AD schedule upward by the amount of that change
◦ At the initial level of output, Y0, the demand for goods > output,
and firms increase production until reach new equilibrium (E’)
How much does income expand? The change in equilibrium income
is:
1
ΔG = αG ΔG
ΔY0 =
1 − c(1 − t)
αG =
1
1 − c(1 − t)
(22)
(23)
AD
AD=Y
AD= 𝐴𝐴1 +c(1−t)Y
E1
↑G
𝐴𝐴1
AD= 𝐴𝐴0 +c(1−t)Y
E0
𝐴𝐴0
Y0
Y1
Y
Effects of a Change in Fiscal Policy
A R1 increase in G will lead to an increase in income in
excess of ONE Rand
◦ If c = 0.80 and t = 0.2
◦ If there is a R1 increase in G, what will be the increase in
equilibrium income?
Effects of a Change in Fiscal Policy
Suppose government increases TR instead
◦ 𝐴𝐴̅ would increase by only c∆TR:
◦   output by αG c∆TR
◦  multiplier for transfer payments is smaller than
that for a change in govt purchases by a factor of c:
◦ This is because part of any increase in TR is saved
(since considered income)
Effects of a Change in Fiscal Policy
If the government  tax rate, two things happen:
◦ Direct effect is that AD is reduced since disposable
income decreases, so consumption falls
◦ Multiplier is reduced, and the shocks will have a
smaller effect on AD