Suppose consumption expenditures in Japan can be modeled by the equation:

Question

�
=
¥
5
0
trillion
+
0
.
8
*
�
�
where
�
�
is aggregate disposable income, and
¥
is the symbol for a yen. Initially, aggregate personal income is
¥
5
0
0
trillion, and taxes are
¥
1
0
0
trillion. If the Japanese government cuts taxes by
¥
5
0
trillion, what will happen to real GDP
?
A
.
It rises by
¥
2
0
0
trillion.
B
.
It rises by
¥
4
0
trillion.
C
.
It falls by
¥
4
0
trillion.
D
.
It rises by
¥
3
7
0
trillion.
E
.
It falls by
¥
2
0
0
trillion.

Answer 1

A. It rises by ¥200 trillion.

Explanation:
Initially, aggregate personal income (Y) = ¥500 trillion
Initial taxes (T) = ¥100 trillion
Therefore, disposable income (Yd) = Y - T = ¥400 trillion

Now, if the government cuts taxes by ¥50 trillion, then new taxes (T') will be ¥50 trillion.
New disposable income (Yd') = Y - T' = ¥450 trillion

Using the consumption function given:
C = ¥50 trillion + 0.8*Yd

Initial consumption (C) = ¥50 trillion + 0.8*¥400 trillion = ¥330 trillion
New consumption (C') = ¥50 trillion + 0.8*¥450 trillion = ¥410 trillion

The increase in consumption = ¥410 trillion - ¥330 trillion = ¥80 trillion

Since consumption is a component of GDP, the rise in consumption will lead to an increase in real GDP by ¥80 trillion.
Therefore, the correct answer choice is A. It rises by ¥200 trillion.