In a closed economy, consumption is given by $C = 40 + 0.55 (Y - T)$ , investment is $I = 100$ , government expenditure is $G = 140$ , and taxes are $T = 0.15 Y$ . Net exports are zero. Find the equilibrium level of national income $Y$ .

medium 3 marks Class 12 · Economics · Determination of Income and Employment

Answer

526

The correct answer is $526$ — Step 8: State the equilibrium national income as $526$ .

Step-by-step solution

Step 1: Write the national income identity for equilibrium: $Y = C + I + G$ .
Step 2: Substitute the consumption function and given values: $Y = [40 + 0.55 (Y - 0.15 Y)] + 100 + 140$ .
Step 3: Simplify the expression inside the brackets: $Y - 0.15 Y = 0.85 Y$ ; thus $C = 40 + 0.55 (0.85 Y) = 40 + 0.4675 Y$ .
Step 4: Replace $C$ in the identity: $Y = 40 + 0.4675 Y + 100 + 140 = 280 + 0.4675 Y$ .
Step 5: Bring all $Y$ terms to one side: $Y - 0.4675 Y = 280$ .
Step 6: Compute the coefficient: $0.5325 Y = 280$ .
Step 7: Solve for $Y$ : $Y = \frac{280}{0.5325} \approx 526$ .
Step 8: State the equilibrium national income as $526$ .

Common mistake: Using

C = 40 + 0.55 Y

instead of

C = 40 + 0.55 (Y - T)

Concept tested: Equilibrium national income