Determination of Equilibrium Income & Investment Multiplier

Explanation:

(i) AD = AS Method:
Aggregate Demand (AD) = $C+I$
AD = $(200+0.75Y)+150$
AD = $350+0.75Y$

At equilibrium, AD = AS (where AS = $Y$):
$350+0.75Y=Y$
$350=Y-0.75Y$
$350=0.25Y$
$Y^{\ast }=\text{₹}1,400\text{ crore}$

(ii) S = I Method:
Saving function $S=-a+(1-\text{MPC})Y$
$S=-200+0.25Y$

At equilibrium, $S=I$:
$-200+0.25Y=150$
$0.25Y=350$
$Y^{\ast }=\text{₹}1,400\text{ crore}$

Verification:
Calculate $C$ at equilibrium: $C^{\ast }=200+0.75(1400)=200+1050=1,250$
Calculate $S$ at equilibrium: $S^{\ast }=Y^{\ast }-C^{\ast }=1400-1250=150$ (This perfectly matches $I=150$ ✓)
Calculate AD at equilibrium: $\text{AD}=C^{\ast }+I=1250+150=1400$ (This perfectly matches $Y^{\ast }=1400$ ✓)

Explanation:

(i) Multiplier ($K$):
$K={\displaystyle \frac{1}{1-\text{MPC}}}={\displaystyle \frac{1}{1-0.8}}={\displaystyle \frac{1}{0.2}}=\mathbf{5}$

(ii) Increase in National Income ($\mathrm{\Delta }Y$):
$\mathrm{\Delta }Y=K\times \mathrm{\Delta }I=5\times 500=\text{₹}\mathbf{2}\mathbf{,}\mathbf{500}\mathbf{\text{ crore}}$

Explanation:

First, find the Multiplier ($K$):
$K={\displaystyle \frac{\mathrm{\Delta }Y}{\mathrm{\Delta }I}}={\displaystyle \frac{1,000}{250}}=4$

Now, use the multiplier formula to find MPC:
$K={\displaystyle \frac{1}{1-\text{MPC}}}$
$4={\displaystyle \frac{1}{1-\text{MPC}}}$
$1-\text{MPC}={\displaystyle \frac{1}{4}}=0.25$
$\text{MPC}=\mathbf{0.75}$

Answer: B) 1

Explanation:
$K={\displaystyle \frac{1}{1-\text{MPC}}}={\displaystyle \frac{1}{1-0}}=1$.
Economically, when MPC = 0, it means that every single rupee of additional income is entirely saved (MPS = 1) and absolutely none of it is re-spent on consumption. Therefore, the initial injection of ₹100 of investment raises the national income by exactly that initial ₹100, and the chain stops immediately. There is no multiplier amplification.

Explanation:

First, determine the Multiplier ($K$): $K={\displaystyle \frac{1}{1-0.6}}=2.5$.
Total increase in income ($\mathrm{\Delta }Y$) = $2.5\times 100=\text{₹}\mathbf{250}\mathbf{\text{ crore}}$.

The Multiplier Process:

• Round 1: Investment rises by ₹100 crore. This immediately becomes ₹100 crore of new income for workers and capital suppliers. Because MPC = 0.6, these income earners consume ₹60 crore and save ₹40 crore.
• Round 2: The ₹60 crore spent on consumption becomes new income for a second group of producers/sellers. They, in turn, consume 60% of it (₹36 crore) and save 40% (₹24 crore).
• Round 3 onwards: This chain reaction continues infinitely. Each round generates 60% of the previous round's income as new consumption expenditure, forming a geometric progression:
  $\mathrm{\Delta }Y=100+60+36+21.6+\dots$

Conclusion: The sum of this infinite geometric series is exactly ₹250 crore ($100/(1-0.6)$). Thus, the initial ₹100 crore injection creates ₹250 crore of total national income. Notice that the total new saving generated throughout the process (40 + 24 + 14.4 + ...) equals exactly ₹100 crore, ensuring the new equilibrium where $\mathrm{\Delta }S=\mathrm{\Delta }I$.

Answer: B) Unplanned increase in inventories — firms reduce output.

Explanation: When AD < AS, it means producers are manufacturing more goods than consumers are willing to buy. The unsold goods physically pile up in warehouses, resulting in an unintended/unplanned inventory accumulation. To clear this excess stock and avoid losses, firms will respond in the next production cycle by cutting back production (reducing employment and output) until Aggregate Supply falls back down to meet Aggregate Demand (where AD = AS). In the Keynesian framework, it is the quantity of output and employment that adjusts to clear the market, not prices.