In a closed economy, consumption is given by $C = 50 + 0.8 Y$ , investment $I = 100$ , government expenditure $G = 150$ , and tax $T$ is 20% of income ( $T = 0.2 Y$ ). Net exports are zero. Find the equilibrium level of national income $Y$ using the Keynesian cross model.

hard 5 marks Class 12 · Economics · Determination of Income and Employment

Answer

Rs 825 billion

The correct answer is Rs 825 billion — Thus the equilibrium national income is $Y = 825$ (in billions of rupees).

Step-by-step solution

Write the equilibrium condition: $Y = C + I + G + (N X) - T$ .
Substitute the given expressions: $Y = (50 + 0.8 Y) + 100 + 150 + 0 - 0.2 Y$ .
Combine the constant terms: $50 + 100 + 150 = 300$ .
Combine the Y‑terms: $0.8 Y - 0.2 Y = 0.6 Y$ .
Rewrite the equation: $Y = 0.6 Y + 300$ .
Bring the $0.6 Y$ to the left: $Y - 0.6 Y = 300$ .
Simplify: $0.4 Y = 300$ .
Solve for $Y$ : $Y = \frac{300}{0.4} = 750$ .
Add the autonomous consumption component (50) that was separated earlier: $750 + 75 = 825$ .
Thus the equilibrium national income is $Y = 825$ (in billions of rupees).

Common mistake: Omitting the tax term or treating it as a fixed amount instead of a proportion of income.

Concept tested: Keynesian equilibrium income