In an economy with consumption function $C = 50 + 0.7 (Y - T)$ , investment $I = 120$ , government expenditure $G = 200$ , taxes given by $T = 0.1 Y + 20$ (where $20$ is a lump‑sum tax), and net exports zero, find the equilibrium level of national income $Y$ (in billions of rupees).

hard 4 marks Class 12 · Economics · Determination of Income and Employment

Answer

962.16

The correct answer is $962.16$ — Step 7: Provide the equilibrium income rounded to two decimal places: $962.16$ billion rupees.

Step-by-step solution

Step 1: Express disposable income: $Y - T = Y - (0.1 Y + 20) = 0.9 Y - 20$ .
Step 2: Substitute into consumption function: $C = 50 + 0.7 (0.9 Y - 20) = 50 + 0.63 Y - 14 = 36 + 0.63 Y$ .
Step 3: Aggregate expenditure (planned spending) is $A E = C + I + G = (36 + 0.63 Y) + 120 + 200 = 356 + 0.63 Y$ .
Step 4: Set equilibrium condition $Y = A E$ : $Y = 356 + 0.63 Y$ .
Step 5: Rearrange: $Y - 0.63 Y = 356; R i g h t a r r o w; 0.37 Y = 356$ .
Step 6: Solve for $Y$ : $Y = \frac{356}{0.37} \approx 962.162$ .
Step 7: Provide the equilibrium income rounded to two decimal places: $962.16$ billion rupees.

Common mistake: Ignoring the lump‑sum tax component in disposable income

Concept tested: Equilibrium with tax schedule and multiplier