Question

Given $\text{C}=400+0.9\text{Y}$ and $\text{I}=4,000$, find:

(i) Y at equilibrium

(ii) S and C at equilibrium

Answer 1

Equilibrium Y is found when, $\text{Y=C+I}$

Substituting the values, we get:

$\text{Y}=400+0.9\text{Y}+4,000$

Or, $\text{Y-0.9 Y}=400+4,000\Rightarrow 0.1\text{Y}=4,400$

Thus, $\text{Y}=\frac{4,400}{0.1}=44,000$

C at equilibrium: $\text{C}=\overline{\text{C}}+\text{MPC. Y}$

$=400+0.9(44,000)$

$=400+39,600=40,000$

S at equilibrium: $\text{S}=-\overline{\text{S}}+\text{MPS. Y}$

$=-400+0.1(44,000)$

$=-400+4,400=4,000$

Alternatively, in equilibrium, $\text{S}=I$

Since $\text{I}=4,000$ (given), S must be equal to 4,000 at equilibrium.