In an economy with a government, C = 20 + 0.8Yd, where Yd = Y – T is disposable income. Investment is 30, government expenditure G is 50 and taxes T are 50. What is the equilibrium income?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 300
Given:
C = 20 + 0.8Yd
I = 30
G = 50
T = 50
With a government, Y = C̄ + I + G + c(Y − T). Taxes cut consumption by cT, so A = C̄ + I + G − cT.
\( A = 20 + 30 + 50 - 0.8 \times 50 = 60 \)
\( \displaystyle Y = \frac{A}{1 - c} = \frac{60}{0.2} = 300 \)
Option (1) 300 — Correct. Equilibrium income is 300.
Option (2) 500 — Incorrect. 500 = (20 + 30 + 50) / 0.2 leaves out the tax.
Option (3) 250 — Incorrect. 250 subtracts the whole tax of 50. Households cut consumption by only cT = 40.
Option (4) 700 — Incorrect. 700 adds cT instead of subtracting it.
NCERT (2026-27): “4.2 Determination of Income in Two-sector Model … At this point, we can introduce a government in this economy. The major economic activities of the government that affect the aggregate demand for final goods and services can be summarized by the fiscal variables Tax (T) and Government Expenditure (G), both autonomous to our analysis. Government, through its expenditure G on final goods and services, adds to the aggregate demand like other firms and households. On the other hand, taxes imposed by the government take a part of the income away from the household, whose disposable income, therefore, becomes Yd = Y – T. Households spend only a fraction of this disposable income for consumption purpose. Hence, equation (4.3) has to be modified in the following way to incorporate the government Y = C̄ + Ī + G + c (Y – T ) Note that G – c.T , like C̄ or Ī , just adds to the autonomous term A . It does not significantly change the analysis in any qualitative way.” |