Equilibrium Income: Board Paper Numericals (2019–2024)

1. The Equilibrium Toolkit: Formulas and Concepts

An economy is in equilibrium when the total planned spending (Aggregate Demand, AD) equals the total planned output (Aggregate Supply, AS). In a simple two-sector economy (households and firms), this leads to our master equation.

Let's quickly review the essential formulas.

• Aggregate Demand (AD): The total planned spending.
  $AD=C+I$
  Where $C$ is Consumption Expenditure and $I$ is Investment Expenditure.
• Aggregate Supply (AS): The total value of output, which is equal to National Income ($Y$).
  $AS=Y$
• The Equilibrium Condition (AD-AS Approach):
  $Y=C+I$
• The Alternative Equilibrium Condition (Saving-Investment Approach): At equilibrium, planned savings must equal planned investment.
  $S=I$
• The Consumption Function: Remember this from our last lesson? It's crucial.
  $C=\bar{C}+bY$
  Where $\bar{C}$ is autonomous consumption (consumption at zero income) and $b$ is MPC.

To see how these all fit together for solving numericals, let's watch a quick refresher.

2. Category 1: Calculating Equilibrium Income (Y), C, and S

This is the most common question you'll encounter. You will be given a consumption function (or the data to find it) and a value for autonomous investment ($I$), and you'll be asked to find the equilibrium income ($Y$).

The steps are always the same:

1. Write down the equilibrium condition: $Y=C+I$.
2. Substitute the full consumption function $C=\bar{C}+bY$ and the given value of $I$ into the equation.
3. You will get an equation with $Y$ on both sides. Solve it algebraically.
4. Once you have the equilibrium $Y$, you can calculate the equilibrium consumption ($C$) by plugging $Y$ back into the consumption function.
5. You can then calculate equilibrium savings ($S$) using the identity $S=Y-C$.

Let's see this in action.

This table illustrates the concept. Equilibrium is the point where AD equals AS (which is Y).

3. Category 2: Finding a Missing Component

In this variation, you are given the equilibrium income ($Y$) and asked to find a missing piece of the puzzle, such as Autonomous Consumption ($\bar{C}$) or Investment ($I$). The process is reversed, but the formula is the same.

A common trick here is that the question might give you MPS instead of MPC. You must first calculate MPC using the relationship we learned: $MPC=1-MPS$.

Let's see how to solve for a missing investment value.

Your Turn: Practice Problem

Now, apply this logic to solve a typical board question.

4. An Alternative Method: The Saving-Investment Approach

Remember the second equilibrium condition, $S=I$? This provides a powerful and often faster way to find equilibrium income, especially if you are given the saving function directly.

The saving function is: $S=-\bar{C}+sY$, where 's' is the MPS.

Example:
An economy has a saving function $S=-250+0.25Y$. Planned investment is ₹2,000 crores. Find the equilibrium income.

Solution:

1. Start with the equilibrium condition: $S=I$
2. Substitute the given values: $-250+0.25Y=2000$
3. Solve for Y:
   $0.25Y=2000+250$
   $0.25Y=2250$
   $Y=\frac{2250}{0.25}=9000$
   The equilibrium income is ₹9,000 crores. This method is demonstrated in the problem found in the resource LINK under the title "The saving function of an economy is given as..." (section 4).

Conclusion

You've done an excellent job working through these numericals. Finding the equilibrium income is a foundational skill for this chapter, and mastering the algebraic manipulation is key.

Key Takeaways:

• Equilibrium income can be found using two main conditions: $Y=C+I$ or $S=I$.
• The AD-AS approach ($Y=C+I$) is the most versatile. It can be used to find Y, C, S, $\bar{C}$, or I.
• The S-I approach is a quick shortcut if you are given the saving function and investment.
• Always check if the question provides MPC or MPS. If MPS is given, your first step should be to calculate MPC ($MPC=1-MPS$) before using the consumption function.

In our next lesson, we will tackle the final numerical type from this unit: the investment multiplier. We will see how a change in investment causes a multiplied change in national income, and we will solve board questions related to it.