Propensities to Consume and Save

1. The 'Average' Propensities: APC and APS

First, let's look at how we can describe the proportion of total income that is used for consumption or saving. This is measured by the Average Propensities.

• Average Propensity to Consume (APC): The ratio of total consumption to total income. It answers the question: "On average, what fraction of our income are we spending?" $$\text{APC}=\frac{\text{Consumption (C)}}{\text{Income (Y)}}$$
• Average Propensity to Save (APS): The ratio of total saving to total income. It answers the question: "On average, what fraction of our income are we saving?" $$\text{APS}=\frac{\text{Saving (S)}}{\text{Income (Y)}}$$

A clear understanding of the definitions, formulas, and possible values of APC and APS is essential. Let's watch a video that explains these concepts thoroughly.

The Relationship between APC and APS

Since your income (Y) can only be either consumed (C) or saved (S), it follows that Y = C + S. This simple identity leads to a crucial relationship between APC and APS. If we divide the entire equation by Y:

This means that the fraction of income consumed and the fraction of income saved must add up to 1. This relationship is very useful for solving numerical problems. If you know APC, you can easily find APS, and vice-versa.

Let's see the derivation and a few examples in the same video.

2. The 'Marginal' Propensities: MPC and MPS

While average propensities look at total income, Marginal Propensities focus on the effect of additional or extra income. This is a vital concept for understanding economic behavior and is represented by the Greek letter delta ($\Delta$), which signifies 'change'.

• Marginal Propensity to Consume (MPC): The ratio of the change in consumption to the change in income. It answers the question: "If we get one more rupee of income, how many paise of that rupee will we spend?" $$\text{MPC}=\frac{\text{Change in Consumption (}\Delta C\text{)}}{\text{Change in Income (}\Delta Y\text{)}}$$
• Marginal Propensity to Save (MPS): The ratio of the change in saving to the change in income. It answers the question: "If we get one more rupee of income, how many paise of that rupee will we save?" $$\text{MPS}=\frac{\text{Change in Saving (}\Delta S\text{)}}{\text{Change in Income (}\Delta Y\text{)}}$$

Let's turn back to our video resource for a clear explanation of MPC and MPS.

The Relationship between MPC and MPS

Just like with average propensities, any change in income ($\Delta Y$) must be split between a change in consumption ($\Delta C$) and a change in saving ($\Delta S$). Therefore, ΔY = ΔC + ΔS.

Dividing this equation by ΔY gives us another fundamental identity:

This means that the fraction of any additional income consumed and the fraction saved must always sum to 1. This is another essential shortcut for your numericals.

The final segment from this video explains this relationship.

3. Calculation and Practice

Now that we have the theory and formulas, let's focus on applying them—the part you want to master. The most common format for these questions in your exam is a table with missing values.

Let's watch a quick, fast-paced video that demonstrates exactly how to fill in these tables.

Guided Practice

Let's try a comprehensive problem. The image below shows a solved table from the Teachoo resource, which is a perfect template for how to approach these questions.

Now, let's apply this method to a typical exam-style question.

Problem: Complete the following table.

Solution Walkthrough:

1. Find Missing Values (like Savings): We need Savings (S) to calculate APS. Remember S = Y - C.
   • Row 1: S = 0 - 20 = -20
   • Row 2: S = 100 - 110 = -10
   • Row 3: S = 200 - 200 = 0
2. Calculate Changes (ΔY, ΔC): We need these for MPC.
   • For Row 2: ΔY = 100 - 0 = 100; ΔC = 110 - 20 = 90
   • For Row 3: ΔY = 200 - 100 = 100; ΔC = 200 - 110 = 90
3. Calculate MPC: MPC = ΔC / ΔY
   • Row 2: MPC = 90 / 100 = 0.9
   • Row 3: MPC = 90 / 100 = 0.9
4. Calculate APS: APS = S / Y
   • Row 1: APS = -20 / 0 = Undefined
   • Row 2: APS = -10 / 100 = -0.1
   • Row 3: APS = 0 / 200 = 0

Completed Table:

Your Turn: Practice Problem

Now it's your turn to practice. This is the best way to prepare for the exam. Use the methods we've just discussed to solve the following problem.

Problem (Question 1 from the image):
From the following schedule, compute APC, APS, MPC, and MPS.

Take a few minutes to create a full table with columns for Y, S, C, ΔY, ΔS, ΔC, APC, APS, MPC, and MPS. Calculate all the values.


...


Solution:
You can find the detailed, step-by-step solution in the resource below. Compare your answer with it.

Conclusion

Excellent work today. We have thoroughly covered the definitions and calculation methods for APC, APS, MPC, and MPS. Mastering these four concepts and their interrelationships is non-negotiable for scoring well in the Macroeconomics numerical section.

Key Takeaways:

• Average Propensities relate total consumption/saving to total income.
  • $\text{APC}=C/Y$
  • $\text{APS}=S/Y$
  • Key Identity: $\text{APC}+\text{APS}=1$
• Marginal Propensities relate the change in consumption/saving to the change in income.
  • $\text{MPC}=\Delta C/\Delta Y$
  • $\text{MPS}=\Delta S/\Delta Y$
  • Key Identity: $\text{MPC}+\text{MPS}=1$
• The first step in table-based problems is always to calculate the "change" columns ($\Delta Y$, $\Delta C$, $\Delta S$).

In our next lesson, we will use these concepts to build the complete algebraic equations for the Consumption Function (C = C̄ + bY) and the Saving Function (S = -C̄ + (1-b)Y). You will see that the MPC you learned to calculate today is the 'b' in the consumption function, a crucial parameter for determining equilibrium income.