Find investment national income 500 autonomous consumption 100 mpc 0.75
Answers
a) Consumption (C) is the sum of autonomous consumption(AC) and after tax income multiplied by marginal propensity to consume.
C
=
A
C
+
M
P
C
×
(
Y
−
T
)
C
=
500
+
0.75
×
(
Y
−
T
)
We plug consumption function into output equation:
Y
=
500
+
0.75
×
(
Y
−
T
)
+
I
+
G
+
(
X
−
M
)
i, G, T, X, and I represents investment, government expenditure, taxes, exports and imports respectively. When I=$500, G=$1200, T=$400, X=$300, and I=$500, equilibrium output is:
Y
=
500
+
0.75
×
(
Y
−
400
)
+
500
+
1200
+
(
300
−
500
)
Y
=
2
,
000
+
0.75
Y
−
300
Y
−
0.75
Y
=
1
,
700
0.25
Y
=
1
,
700
Y
=
6
,
800
Equilibrium income is $6,800.
b) Equilibrium consumption is:
C
=
500
+
0.75
(
6
,
800
−
400
)
=
5
,
300
c) Saving(S) is the amount left after households pay for their consumption and taxes.
S
=
Y
−
T
−
C
S
=
6
,
800
−
5
,
300
−
400
=
1
,
100
d) Saving function is written as follows:
S
=
Y
−
T
−
C
S
=
Y
−
T
−
A
C
−
M
P
C
×
(
Y
−
T
)
S
=
(
1
−
M
P
C
)
(
Y
−
T
)
−
A
C
S
=
M
P
S
(
Y
−
T
)
−
A
C
where MPS is marginal propensity to save.
e) In this economy saving, imports and taxes are withdrawals, where as investment, government spending and exports are injections. At the equilibrium GDP, withdrawals equal to injections.
S
+
M
+
T
=
I
+
G
+
X
1
,
100
+
500
+
400
=
500
+
1
,
200
+
300
=
2
,
000