Mastering Propensities: 2019-2024 Board Paper Numerical Analysis

1. The Toolkit: A Quick Formula Refresher

Before we dive into solving problems, let's quickly review the essential formulas that govern the relationship between income, consumption, and saving. These are the tools you'll use for every question in this lesson.

• The Fundamental Identity: Income is either consumed or saved.
  $Y=C+S$
• Average Propensities (The "what proportion" questions):
  • Average Propensity to Consume (APC) = $\frac{C}{Y}$
  • Average Propensity to Save (APS) = $\frac{S}{Y}$
  • Relationship: $APC+APS=1$
• Marginal Propensities (The "what happens to additional income" questions):
  • Marginal Propensity to Consume (MPC) = $\frac{\Delta C}{\Delta Y}$ (where $\Delta$ means "change in")
  • Marginal Propensity to Save (MPS) = $\frac{\Delta S}{\Delta Y}$
  • Relationship: $MPC+MPS=1$

To see how these formulas are derived and interconnected, let's watch a foundational video segment.

2. Category 1: Table-Based Numericals

This is the most frequent format for a 3 or 4-mark question. You'll be given a schedule (table) with some values for income, consumption, or saving, and asked to calculate the missing values, including the propensities.

Let's walk through a typical board exam question together.

Your Turn: Practice with a Board Question

Now it's your turn to apply these steps. The following image is a question from a past CBSE paper.

Your Task:

1. Calculate Savings (S): Use the formula $S=Y-C$. The consumption values are given.
2. Calculate Average Propensity to Consume (APC): Use the formula $APC=C/Y$.
3. Calculate Marginal Propensity to Save (MPS):
   • First, find the change in savings ($\Delta S$) and change in income ($\Delta Y$) between levels.
   • Then, use the formula $MPS=\frac{\Delta S}{\Delta Y}$.
   • (Hint: You might notice that MPC is constant. If you calculate MPC first, you can easily find MPS using $MPS=1-MPC$.)

Take a few minutes to solve this on paper. The final part, deriving the consumption function, is a preview of what we'll do more of later, but see if you can figure it out! The function is $C=\bar{C}+bY$, where $\bar{C}$ is autonomous consumption (consumption at zero income) and $b$ is MPC.

3. Category 2: Sentence-Based Word Problems

Sometimes, the data isn't given in a neat table. You have to read a paragraph and extract the relevant numbers yourself. This tests both your calculation and comprehension skills.

Let's see how to tackle this type of question.

4. Category 3: Conceptual & MCQ-Style Questions

These questions test your understanding of the properties of the propensities. They often appear as 1-mark MCQs. Let's tackle two questions from the CBSE 2024 Board Paper.

Question 1 (Table Interpretation)

From the given table, identify the level of income where Average Propensity to Save (APS) becomes zero.

Income (Rs. crore)	Consumption (Rs. crore)
0	50
50	75
100	100
200	150

(This is adapted from Q8, Set 1, 58/4/1, CBSE 2024)

Solution:

• We know that $APS=S/Y$. For APS to be zero, Savings (S) must be zero.
• We also know that $S=Y-C$.
• Looking at the table, when Income (Y) is 100, Consumption (C) is also 100.
• Therefore, Savings $S=100-100=0$.
• This level of income, where Y=C and S=0, is also known as the break-even point. The correct answer is 100.

Question 2 (Properties of Propensities)

If a straight-line consumption function makes a positive intercept on the Y-axis, it implies that the Marginal Propensity to Consume (MPC) _______ and the Average Propensity to Consume (APC) _______ as the level of income rises.

1. remains constant, rises
2. falls, falls
3. rises, rises
4. remains constant, falls

(This is Q4, Set 1, 58/4/1, CBSE 2024)

Solution:

• MPC: A straight-line consumption function has a constant slope. The slope of the consumption function is the MPC. Therefore, MPC remains constant.
• APC: The formula is $APC=C/Y$. The consumption function is $C=\bar{C}+bY$, where $\bar{C}$ is the positive intercept (autonomous consumption) and $b$ is MPC. So, $APC=(\bar{C}+bY)/Y=\frac{\bar{C}}{Y}+b$.
• As Income ($Y$) increases, the term $\frac{\bar{C}}{Y}$ (the proportion of autonomous consumption) gets smaller and smaller. Since $b$ (MPC) is constant, the whole expression for APC decreases. Therefore, APC falls.
• The correct option is (4).

Conclusion

Excellent work today. We've systematically tackled the key numerical problems related to propensities, a topic that is almost guaranteed to appear on your exam. By practicing these categorized questions, you are now better prepared to identify the question type and apply the correct formulas quickly and accurately.

Key Takeaways:

• There are three main types of numericals on propensities: table-based, sentence-based, and conceptual MCQs.
• For table problems, work systematically: calculate intermediate values first and use the relationships ($APC+APS=1$, $MPC+MPS=1$) as shortcuts.
• For word problems, the first step is always to extract the given information and list it clearly.
• Remember the properties: For a linear consumption function, MPC is constant, while APC falls as income rises.

In our next lesson, we will continue building on this chapter's numericals. We will focus on solving for equilibrium income, consumption, and savings when you are given a consumption/saving function and the level of investment. This is the next logical step in mastering the numericals from this unit. Keep practicing