The Investment Multiplier: Mechanism and Formula

1. The Multiplier Effect: An Introduction

The core idea of the investment multiplier is that an initial increase in investment leads to a magnified or multiple increase in the final national income. For example, an initial investment of ₹100 crores might lead to a total increase in income of ₹500 crores. In this case, the multiplier is 5.

This happens because of a simple, powerful principle: one person's expenditure is another person's income. When new investment occurs, it creates income. That new income is then partially spent, creating income for someone else, who then spends part of their new income, and so on. This creates a chain reaction.

Let's watch a short video to formalize this concept.

As the video explains, the investment multiplier, $K$, is defined as:

Where:

• $\Delta Y$ = Change in National Income
• $\Delta I$ = Change in Investment

2. The Multiplier Mechanism: How It Works

To truly understand the multiplier, you need to see the "chain reaction" in action. The process unfolds in several rounds, with the size of the effect in each round depending on the Marginal Propensity to Consume (MPC).

Let's trace the process with a hypothetical example. Assume there is a new autonomous investment of ₹100 crores and the MPC of the economy is 0.8.

• Round 1: The initial investment of ₹100 crores (e.g., to build a new road) is paid to contractors, workers, and suppliers. So, national income ($Y$) rises by ₹100 crores.

  • $\Delta I=\text{₹}100\text{ crores}$
  • $\Delta Y\text{ in Round 1}=\text{₹}100\text{ crores}$

• Round 2: The people who received this ₹100 crores will spend a portion of it, based on their MPC. Since MPC is 0.8, they will spend $0.8\times 100=\text{₹}80$ crores on goods and services. This ₹80 crores becomes new income for the producers of those goods and services.

  • $\Delta C=0.8\times 100=\text{₹}80\text{ crores}$
  • $\Delta Y\text{ in Round 2}=\text{₹}80\text{ crores}$

• Round 3: The recipients of the ₹80 crores will, in turn, spend 80% of it. This creates an additional income of $0.8\times 80=\text{₹}64$ crores.

  • $\Delta C=0.8\times 80=\text{₹}64\text{ crores}$
  • $\Delta Y\text{ in Round 3}=\text{₹}64\text{ crores}$

This process continues, with the additional income in each round getting smaller and smaller, until it eventually approaches zero. The total increase in income is the sum of the increases from all rounds: ₹100 + ₹80 + ₹64 + ...

The following video provides an excellent, clear walk-through of this entire mechanism with a similar example.

The table below visualizes this process. Notice how the initial investment of ₹200 crores, with an MPC of 0.8, generates a total income of ₹1,000 crores.

3. Derivation of the Multiplier Formula

While the round-by-round analysis is great for intuition, we need a direct formula. Your learning outcome requires you to derive this formula algebraically.

We start from the equilibrium condition in a two-sector economy:

Any change in income ($\Delta Y$) must come from a change in consumption ($\Delta C$) or a change in investment ($\Delta I$):

Now, we know from our previous lessons that the change in consumption ($\Delta C$) is determined by the MPC and the change in income ($\Delta Y$):

Let's substitute this into our equation:

Now, we need to solve this equation for $\frac{\Delta Y}{\Delta I}$.

As you saw in the reading, by rearranging the equation $\Delta Y=(\text{MPC}\times \Delta Y)+\Delta I$, we get:

Factoring out $\Delta Y$:

Finally, dividing both sides by $\Delta I$ and by $(1-\text{MPC})$, we get the formula for the multiplier $K$:

Since we also know that $1-\text{MPC}=\text{MPS}$ (Marginal Propensity to Save), we can also express the multiplier as:

These two formulas are extremely important for solving numericals.

4. Relationship between Multiplier, MPC, and MPS

The formulas reveal a clear relationship:

• Multiplier and MPC: There is a direct or positive relationship between $K$ and MPC. A higher MPC means a larger portion of income is re-spent in each round, leading to a larger multiplier effect. If people spend more, the chain reaction is stronger.
• Multiplier and MPS: There is an inverse or negative relationship between $K$ and MPS. A higher MPS means a larger portion of income is saved (leaked from the circular flow) in each round, dampening the chain reaction and leading to a smaller multiplier.

Range of the Multiplier:

• Minimum Value: If MPC = 0, then MPS = 1. The multiplier $K=1/1=1$. This means the total increase in income is exactly equal to the initial investment (the chain reaction dies after Round 1).
• Maximum Value: If MPC = 1, then MPS = 0. The multiplier $K=1/0=\infty$ (infinity). This is a theoretical case where no income is ever saved, and the chain reaction continues forever.

In reality, the value of the multiplier lies between 1 and infinity. Let's watch a final clip that summarizes these relationships.

Conclusion

In this lesson, you've learned about the powerful concept of the investment multiplier, which explains how an initial change in investment can have a much larger impact on the economy's total income.

Key Takeaways:

• Multiplier Mechanism: An initial investment increases income, which leads to a series of subsequent rounds of consumption spending and income creation. The size of this effect is governed by the MPC.
• Key Formulas: The investment multiplier ($K$) can be calculated in three ways:
  • $K=\frac{\Delta Y}{\Delta I}$
  • $K=\frac{1}{1-\text{MPC}}$
  • $K=\frac{1}{\text{MPS}}$
• Relationships:
  • The multiplier has a direct relationship with MPC.
  • The multiplier has an inverse relationship with MPS.
• Range: The value of $K$ ranges from 1 (when MPC=0) to infinity (when MPC=1).

You now have all the theoretical tools related to equilibrium and the multiplier. In our next lesson, we will shift our focus entirely to practice. We will tackle a series of categorized numerical problems from past CBSE board papers, focusing on calculating equilibrium income, propensities to consume/save, and using the investment multiplier. This will be crucial for building your confidence and speed for the exam.