Identify the correct expression to calculate equilibrium level of inc…

The correct answer is Option (2) → $(\bar C+\bar I)/MPS$

The equilibrium level of income ($Y$) in a simple Keynesian model (two-sector economy) is determined where Aggregate Demand ($AD$) equals Aggregate Supply ($AS$, which is equal to $Y$).

The model is defined by:

1. Equilibrium Condition: $Y=AD=C+I$

2. Consumption Function: C= $\bar C$ + MPC ⋅ Y (where $\bar C$ is autonomous consumption)
3. Autonomous Investment: I=$\bar I$ (where $\bar I$ is autonomous investment)

$Substituting\; the\; consumption\; and\; investment\; functions\; into\; the\; equilibrium\; condition:$

Y= $\bar C$ + MPC ⋅ Y + $\bar I$

Y−MPC⋅Y = $\bar C$ + $\bar I$

Y(1−MPC) = $\bar C$ + $\bar I$

Y = $\bar C$ + $\bar I$ / (1 - MPC) 

We know that 1−MPC=MPS

$\text{Y = \$bar C\$ + \$bar I\$ / MPS}$