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Savings Function: APC vs. MPC - Are You Saving Enough?

Now We're going to break down the savings function and compare Average Propensity to Consume (APC) with Marginal Propensity to Consume (MPC) to better understand how they all come together.

The Scenario: A Sneak Peek at the Problem

I recently stumbled upon this problem:

"Suppose savings function is S = -5 + 0.3y, then find the correct answer from below:
(1) APC < MPC
(2) APC = MPC
(3) APS > MPS
(4) APC > MPC"

Let's analyze it to understand what all of it really means.

First Things First: Understanding the Terms

Before we dive into the solution, let's define those acronyms:

• Savings Function (S): A mathematical relationship showing the level of saving at different levels of income. In our case, it's S = -5 + 0.3y (where 'y' represents income). That "-5" is critical – it means that even with zero income, there's still dissaving (borrowing or using past savings).

• APC (Average Propensity to Consume): The proportion of income spent on consumption. Think of it as "What percentage of your income are you spending?" It's calculated as:
  APC = Total Consumption / Total Income

• MPC (Marginal Propensity to Consume): The change in consumption resulting from a change in income. In simple terms, if you get an extra dollar, how much of it will you spend? It's calculated as:
  MPC = Change in Consumption / Change in Income

• APS (Average Propensity to Save): The proportion of income saved.
  APS = Total Savings / Total Income

• MPS (Marginal Propensity to Save): The change in saving resulting from a change in income.
  MPS = Change in Savings / Change in Income

Solving the Puzzle: Putting It All Together

Here's how we can solve this problem and determine the correct answer:

1. Extract MPC and MPS Directly from the Savings Function:

   • In the savings function S = -5 + 0.3y, the coefficient of 'y' (which is 0.3) represents the MPS (Marginal Propensity to Save). So, MPS = 0.3.

   • A fundamental rule in economics is that MPC + MPS = 1. Therefore, MPC = 1 - MPS = 1 - 0.3 = 0.7.

2. Relating to Consumption:

   • Consumption function, C = y - S = y - (-5 + 0.3y) = 5 + 0.7y

3. Comparing APC and MPC

   • APC = C/y = (5 + 0.7y) / y = 5/y + 0.7

   As y increases APC will become less, and it would converge toward MPC.
   Hence APC > MPC.

4. Comparing APS and MPS

   • APS = S/y = (-5 + 0.3y) / y = -5/y + 0.3

   As y increases APS will become more, and it would converge toward MPS.
   Hence APS < MPS.

The Answer

After a little calculation and reasoning, we can conclude that:

• (4) APC > MPC

Key Takeaway

Understanding the savings function and the relationship between APC and MPC gives you insights into economic behavior. It helps explain how changes in income can affect saving and spending habits, and these principles are critical to understanding how the economy as a whole works. This knowledge empowers you to make smarter decisions with your money. So keep saving, keep learning, and thanks for reading!

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