In a two-sector economy, the aggregate demand line cuts the vertical axis at Rs 100 crore, and the economy is in equilibrium at an income of Rs 400 crore. If autonomous investment now rises by Rs 20 crore, what will the new equilibrium income be?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 480 crore
The vertical intercept of the AD line is autonomous expenditure, Ā. Equilibrium income is Ā ÷ (1 − c), so the old equilibrium tells us c, and c gives the multiplier.
Given:
Ā = Rs 100 crore
Y* = Rs 400 crore
ΔI = Rs 20 crore
\( \displaystyle 400 = \frac{100}{1 - c} \)
\( 1 - c = 0.25 \)
\( c = 0.75 \)
\( \displaystyle k = \frac{1}{0.25} = 4 \)
\( \displaystyle \Delta Y = 4 \times 20 = 80 \)
\( \displaystyle \text{New } Y^{*} = 400 + 80 = 480 \)
The new equilibrium income is Rs 480 crore.
Option (1) Rs 420 crore — this adds only the first rise in investment, without the multiplier.
NCERT (2026-27): “4.2 Determination of Income in Two-sector Model … This equation can be further simplified by adding up the two autonomous terms, C̄ and Ī, making it Y = Ā + c.Y where Ā = C̄ + Ī is the total autonomous expenditure in the economy. In reality, these two components of autonomous expenditure behave in different ways. C̄, representing subsistence consumption level of an economy, remains more or less stable over time. However, Ī has been observed to undergo periodic fluctuations. …” “4.3.3 The Multiplier Mechanism … The increment in equilibrium value of total output thus exceeds the initial increment in autonomous expenditure. The ratio of the total increment in equilibrium value of final goods output to the initial increment in autonomous expenditure is called the investment multiplier of the economy. Recalling that 10 and 0.8 represent the values of ΔI = ΔA and mpc, respectively, the expression for the multiplier can be explained as”
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