186
PART III
The Core of Macroeconomic Theory
This equation contains two parts. First, we note that net
taxes (
T
) will be equal to an amount
T
0
if income (
Y
) is zero.
Second, the tax rate (
t
) indicates how much net taxes change as
income changes. Suppose
T
0
is equal to
-
200 and
t
is 1/3. The
resulting tax function is
T
=
-
200 + 1/3
Y
, which is graphed in
Figure 9B.1. Note that when income is zero, the government
collects “negative net taxes,” which simply means that it makes
transfer payments of 200. As income rises, tax collections
increase because every extra dollar of income generates $0.33
in extra revenues for the government.
How do we incorporate this new tax function into our dis-
cussion? All we do is replace the old value of
T
(in the example
in the chapter,
T
was set equal to 100) with the new value,
-
200
+ 1/3
Y
. Look first at the consumption equation. Consumption
(
C
) still depends on disposable income, as it did before. Also,
disposable income is still
Y
-
T
, or income minus taxes. Instead
of disposable income equaling
Y
-
100, however, the new equa-
tion for disposable income is
Because consumption still depends on after-tax income,
exactly as it did before, we have
Nothing else needs to be changed. We solve for equilibrium
income exactly as before, by setting planned aggregate expen-
diture equal to aggregate output. Recall that planned aggregate
C
=
100
+
.75(
Y
+
200
-
1
>
3
Y
)
C
=
100
+
.75
Y
d
Y
d
K
Y
+
200
-
1
>
3
Y
Y
d
K
Y
-
(
-
200
+
1
>
3
Y
)