Equilibrium Income: The S-I Approach

1. The Saving-Investment Equilibrium Condition

The foundation of this approach is a direct consequence of the AD=AS equilibrium. Let's start by revisiting the equilibrium condition from our last lesson in a two-sector economy:

We know that Aggregate Demand (AD) is the sum of Consumption (C) and Investment (I), while Aggregate Supply (AS) is the sum of Consumption (C) and Saving (S), as it represents national income.

If we cancel out Consumption (C) from both sides of the equation, we are left with:

This simple equation is the heart of the Saving-Investment approach. It states that the economy is in equilibrium at the level of income where planned investment (I) is equal to planned saving (S).

It's crucial to remember that we are talking about planned (or ex-ante) saving and investment.

• Ex-ante Saving: The amount of saving that households plan or intend to make at different levels of income.
• Ex-ante Investment: The amount of investment that firms plan or intend to make.

Let's see a quick video that clearly explains how this S=I condition is derived.

2. Graphical and Tabular Representation

Just like with the AD-AS approach, we can illustrate the S-I equilibrium using a schedule (table) and a diagram.

The Components:

• Investment (I): In this model, we assume investment is autonomous, meaning it is a fixed amount (e.g., ₹100 crores) regardless of the income level. Graphically, this is a horizontal line parallel to the income (X) axis.
• Saving (S): As we learned previously, the saving function is $S=-\bar{C}+(1-b)Y$. The saving curve starts from a negative value (representing dissaving when income is zero) and slopes upward because saving increases as income increases.

Equilibrium is achieved where the saving curve intersects the investment curve.

The image below provides a powerful visual summary, showing the AD-AS equilibrium on top and the corresponding S-I equilibrium at the bottom. Notice how both approaches yield the exact same equilibrium level of income.

3. The Adjustment Mechanism: What if S ≠ I?

What happens if planned saving is not equal to planned investment? The economy will adjust to restore equilibrium. This process is driven by the same force we saw in the last lesson: unplanned changes in inventories.

Case 1: When Saving > Investment (S > I)

• What it means: Households are planning to save more than firms are planning to invest. If people are saving more, it directly implies they are consuming less.
• Effect on Demand: Lower consumption means that Aggregate Demand (AD) is now less than Aggregate Supply (AS).
• Impact on Inventories: Since total spending is less than total output, some goods will remain unsold. This leads to an unplanned increase in inventories (stock). Given your accounting background, you can think of this as the closing stock being higher than the firm desired.
• Producers' Response: To clear these unwanted inventories, firms will cut back on production.
• Result: A reduction in output leads to a fall in employment and income (Y). As income falls, saving also falls. This process continues until saving decreases enough to become equal to investment again (S=I).

Case 2: When Saving < Investment (S < I)

• What it means: Households are planning to save less than firms are planning to invest. If people are saving less, it means they are consuming more.
• Effect on Demand: Higher consumption means that Aggregate Demand (AD) is now greater than Aggregate Supply (AS).
• Impact on Inventories: Since total spending is greater than total output, firms will sell more than they produced by running down their existing stocks. This leads to an unplanned decrease in inventories.
• Producers' Response: To rebuild their inventories to the desired level and meet the higher demand, firms will increase production.
• Result: An increase in output leads to a rise in employment and income (Y). As income rises, saving also rises. This process continues until saving increases enough to become equal to investment (S=I).

This adjustment mechanism is a critical part of the theory. Let's watch a clear explanation.

Your Turn: Apply the Concept

Now it's time to put this into practice, which is the best way to prepare for your exam. Let's solve a typical numerical question using the S=I equilibrium condition.

Problem:
The saving function of an economy is given as: $S=-25+0.25Y$. If the planned investment is ₹ 200 crores, calculate the equilibrium level of income.

Think through the steps:

1. State the equilibrium condition for the S-I approach.
2. Substitute the given saving function and investment value into the equation.
3. Solve the equation for Y.

Once you have your answer, you can check your work against the solved example in the resource below.

(You should find that equilibrium income Y = ₹ 900 crores)

Conclusion

In this lesson, we have explored the Saving-Investment approach to determining equilibrium income. You should now see that it is not a separate theory but an alternative perspective on the AD=AS equilibrium we covered previously.

Key Takeaways:

• The equilibrium condition is Planned Saving (S) = Planned Investment (I).
• This condition is derived directly from the AD=AS equilibrium.
• Graphically, equilibrium is found where the upward-sloping saving curve intersects the horizontal autonomous investment curve.
• If S > I, it implies AD < AS. Unplanned inventory build-up causes firms to reduce output, lowering income until S=I.
• If S < I, it implies AD > AS. Unplanned inventory depletion causes firms to increase output, raising income until S=I.

Having mastered both the AD-AS and S-I approaches, you are now fully equipped with the theoretical foundation of income determination. In our next lesson, we will dive deep into solving various numerical problems based on these concepts, including finding equilibrium income, consumption, savings, and tackling questions involving the investment multiplier.