Answer to Question #178297 in Macroeconomics for SPENCER GYABENG

Question

Given the following macro-economics model :

Y = C+I+G

C = 20+0.07Y

I = 12+0.1Y

G = 10

a. Express the model in matrix form.

b. Using Cramer's Rule , calculate the equilibrium values of national income (Y) , consumption (C) and investment (I)

c. what is the income multiplier?

Answer 1

Y = C+I+G

C = 20+0.07Y

I = 12+0.1Y

G = 10

(a) In matrix form Itcan be represented as-

$\begin{pmatrix} 1 & -1&-1&0 \\ -0.07&1&0&0 \\ 0&0&1&-0.1\\ K&0&0&-l \end{pmatrix} \begin{pmatrix} Y \\C \\ I\\ i \end{pmatrix}=\begin{pmatrix} G_o\\20 \\ 12 \\ M_o \end{pmatrix}$

(b) As National Income

$Y=C+I+G\\ Y =20+0.07Y+12+0.1Y+10\\ Y =42+0.17Y$

$0.83Y=42\Rightarrow Y=50.60$

Consumption, $C=20+0.07(50.60)=23.542$

Investment, $I=12+0.1(50.60)=17.06$

(c) Income Multiplier $=\dfrac{C}{I}=\dfrac{23.542}{17.06}=1.38$