Investment Multiplier and Income Change

1. What is the Investment Multiplier?

The investment multiplier (denoted by K) measures how many times the total income increases as a result of an increase in investment. For instance, if a ₹100 crore increase in investment leads to a ₹400 crore increase in total income, the multiplier is 4.

The core idea is that one person's expenditure becomes another person's income. When investment increases, it creates income. The recipients of this income spend a portion of it (determined by the MPC), which then becomes income for others, who in turn spend a portion, and so on. This chain reaction causes the final increase in income to be a multiple of the initial investment.

2. The Key Formulas for the Multiplier

To solve numerical problems, you need to be very comfortable with three key formulas for the investment multiplier (K). The following video will quickly review these essential formulas.

To summarize the video, the three formulas are:

1. In terms of Income and Investment:
   $K=\frac{\Delta Y}{\Delta I}$
   where $\Delta Y$ is the change in income and $\Delta I$ is the change in investment.

2. In terms of MPC (Marginal Propensity to Consume):
   $K=\frac{1}{1-MPC}$

3. In terms of MPS (Marginal Propensity to Save):
   $K=\frac{1}{MPS}$
   (Remember from our previous lesson that $1-MPC=MPS$).

A crucial takeaway is the relationship between these variables:

• There is a direct relationship between MPC and the multiplier. A higher MPC means a larger multiplier.
• There is an inverse relationship between MPS and the multiplier. A higher MPS means a smaller multiplier.

3. Solving Multiplier Numericals: Step-by-Step

Now, let's apply these formulas to solve the types of questions you will encounter in your board exam. We will use a series of short video clips showing solved examples from past papers.

Type 1: Find the Change in Income ($\Delta Y$)

This is the most direct application. You'll be given MPC or MPS and a change in investment ($\Delta I$).

Problem: In an economy, MPS is 0.25. If investment increases by ₹2,000 crore, calculate the total increase in income.

Solution Steps:

1. Calculate the multiplier (K) using the MPS formula: $K=\frac{1}{MPS}$.
2. Use the main multiplier formula, $K=\frac{\Delta Y}{\Delta I}$, to find $\Delta Y$.

Type 2: Find the Required Change in Investment ($\Delta I$)

This is a common variation where you know the desired income increase and need to find the investment required to achieve it.

Problem: In an economy, MPC is 75% (0.75). How much additional investment is needed to increase income by ₹2,000 crore?

Solution Steps:

1. First, find MPS: $MPS=1-MPC$.
2. Calculate the multiplier (K) using MPS: $K=\frac{1}{MPS}$.
3. Rearrange the main formula to solve for $\Delta I$: $\Delta I=\frac{\Delta Y}{K}$.

Type 3: Change in Income due to a Change in MPC

This is a slightly more complex, multi-step problem that has appeared in board exams. You are asked to find the change in income when MPC changes.

Problem: For a hypothetical economy, investment changes by ₹1,000 crore. Calculate the increase in income if MPC increases from 75% to 90%.

Solution Steps:

1. Scenario 1 (MPC = 0.75):
   • Calculate $K_1$ using the initial MPC.
   • Calculate the resulting income change, $\Delta Y_1=K_1\times \Delta I$.
2. Scenario 2 (MPC = 0.90):
   • Calculate $K_2$ using the new MPC.
   • Calculate the new income change, $\Delta Y_2=K_2\times \Delta I$.
3. Find the increase in income: Calculate the difference: $\Delta Y_2-\Delta Y_1$.

The solution to a similar 2023 board exam question is shown in the image below.

4. Your Turn: Practice with Past Board Questions

You've seen the methods, now it's time for you to practice. This is the most critical step for building speed and confidence.

Conclusion

In this lesson, we focused on the crucial concept of the investment multiplier and its application in numerical problems. You learned how a small change in investment can have a magnified effect on the economy's income.

Key Takeaways:

• The investment multiplier (K) is calculated using one of three formulas: $K=\frac{\Delta Y}{\Delta I}$, $K=\frac{1}{1-MPC}$, or $K=\frac{1}{MPS}$.
• A higher MPC (or lower MPS) leads to a larger multiplier effect.
• Solving multiplier problems is a systematic process: identify the given variables (like MPC, $\Delta I$, or $\Delta Y$), choose the right formula to find K, and then use the relationship $K=\Delta Y/\Delta I$ to find the unknown value.

In the next lesson, we will continue with numerical practice, focusing on problems where you need to derive missing values in income-consumption-saving schedules. This will combine what you've learned about propensities and equilibrium in a table format, another common question type in your exam. The multiplier concept will reappear later when we discuss how the government uses policy to manage the economy.