Mastering the Investment Multiplier: Board Exam Numericals (2019-2024)

1. The Multiplier Effect: Core Concepts and Formulas

In the last lesson, we found the economy's equilibrium income. But what happens if, for example, a company decides to build a new factory, increasing investment by ₹100 crores? Will the national income increase by just ₹100 crores? The answer is no; it will increase by a multiple of that amount. This phenomenon is called the investment multiplier effect.

The investment multiplier ($K$) is the ratio of the change in national income ($\Delta Y$) to the change in investment ($\Delta I$).

This chain reaction happens because one person's expenditure is another person's income. The initial investment of ₹100 crores becomes income for those who supplied materials and labour. They will spend a portion of this new income (determined by their MPC), which then becomes income for others, who in turn spend a portion of it, and so on.

To solve numericals, you need to be fluent with three key formulas for the multiplier ($K$):

1. In terms of Income and Investment:
   $K=\frac{\Delta Y}{\Delta I}$
2. In terms of MPC (b):
   $K=\frac{1}{1-\text{MPC}}$
3. In terms of MPS (s):
   $K=\frac{1}{\text{MPS}}$

Notice that because $MPC+MPS=1$, the formulas are equivalent. A higher MPC means a larger multiplier, as more of the new income is passed on in each round. The value of the multiplier $K$ will always be between 1 and infinity ($1\le K\le \infty$).

2. Solving Multiplier Numericals: A Step-by-Step Guide

Let's watch a video that breaks down the most common types of multiplier questions you will see on the exam. This will equip us with the methods to tackle the board paper questions that follow.

3. Practice with CBSE Board Paper Questions

Now it's your turn to apply these methods. We'll solve questions directly from the 2023 and 2024 board papers. This is the most effective practice you can do.

Question 1 (CBSE 2024 Board Paper)

Let's start with a conceptual check.

Solution Breakdown:

• "Entire additional income is consumed" means that $\Delta C=\Delta Y$.
• This implies MPC ($\frac{\Delta C}{\Delta Y}$) is 1.
• Plugging this into the formula: $K=\frac{1}{1-1}=\frac{1}{0}$, which is Infinity ($\infty$).
• Therefore, the correct option is (D).

Question 2 (CBSE 2023 Board Paper)

This is a classic calculation problem.

Question 3 (CBSE 2023 Board Paper - Advanced)

This question is slightly more complex and involves comparing outcomes. This is a high-value question type.

Conclusion

Excellent work today. You have successfully covered all the main numerical types related to the investment multiplier, using real board paper questions as your guide. This completes the numerical portion of the 'Income and Employment' unit.

Key Takeaways:

• The investment multiplier ($K$) shows how an initial change in investment ($\Delta I$) leads to a larger final change in income ($\Delta Y$).
• You must be proficient with all three formulas:
  • $K=\frac{\Delta Y}{\Delta I}$
  • $K=\frac{1}{1-MPC}$
  • $K=\frac{1}{MPS}$
• Board questions can ask you to find any variable ($K,\Delta Y,\Delta I,MPC,MPS$) when others are given. The key is to select the right formula and solve it algebraically.
• Be prepared for multi-step problems, such as calculating the impact of a change in MPC on the final income.

In our next lesson, we will move to the next major unit in Macroeconomics: Government Budget and the Economy. We will begin by understanding the components of a government budget and then focus on another important area for numericals: calculating revenue, fiscal, and primary deficits.