Finding Equilibrium Consumption in a Two-Sector Economy

This question asks us to determine the equilibrium level of consumption given a saving function and autonomous investment. In a simple two-sector economy (Households and Firms), the equilibrium level of national income is reached when aggregate demand equals aggregate supply, or equivalently, when planned saving equals planned investment (S = I).

Given Information:

• Saving Function: \(S = -20 + 0.2Y\)
• Autonomous Investment (I): Rs. 100 million

Step 1: Determine the Equilibrium Level of National Income (Y)

Equilibrium occurs where Saving (S) equals Investment (I).

Set the given saving function equal to the autonomous investment:

\(S = I\)

\(-20 + 0.2Y = 100\)

Now, solve for Y:

\(0.2Y = 100 + 20\)

\(0.2Y = 120\)

\(Y = \frac{120}{0.2}\)

\(Y = \frac{1200}{2}\)

\(Y = 600\)

So, the equilibrium level of national income is Rs. 600 million.

Step 2: Determine the Consumption Function

In a two-sector economy, National Income (Y) is either consumed (C) or saved (S). Thus, \(Y = C + S\). This means \(C = Y - S\).

We are given the saving function \(S = -20 + 0.2Y\).

Substitute this into the equation for C:

\(C = Y - (-20 + 0.2Y)\)

\(C = Y + 20 - 0.2Y\)

\(C = 20 + (1 - 0.2)Y\)

\(C = 20 + 0.8Y\)

This is the consumption function. Here, autonomous consumption is 20, and the marginal propensity to consume (MPC) is 0.8.

Step 3: Calculate Equilibrium Consumption

Now that we have the equilibrium level of national income \(Y = 600\) and the consumption function \(C = 20 + 0.8Y\), we can find the equilibrium level of consumption by substituting the value of Y into the consumption function.

\(C = 20 + 0.8 \times 600\)

\(C = 20 + 480\)

\(C = 500\)

Therefore, the equilibrium level of consumption is Rs. 500 million.

At this equilibrium level, let's check Saving:

\(S = -20 + 0.2Y = -20 + 0.2 \times 600 = -20 + 120 = 100\)

Since Investment is also 100, the equilibrium condition \(S=I\) is satisfied.

Summary of Steps:

1. Used the equilibrium condition \(S=I\) to find the equilibrium National Income (Y).
2. Derived the Consumption Function (C) from the given Saving Function (S).
3. Substituted the equilibrium National Income (Y) into the Consumption Function (C) to find the equilibrium Consumption.

The equilibrium level of consumption is 500 million.

Revision Table: Key Concepts

Additional Information: Keynesian Equilibrium

The analysis used here is based on the simple Keynesian model of income determination in a two-sector economy. In this model:

• Aggregate Demand (AD): In a two-sector model, AD consists of Consumption (C) and Investment (I). \(AD = C + I\).
• Aggregate Supply (AS): Represents the total output of goods and services in the economy, which is equal to National Income (Y).
• Equilibrium: Achieved when \(AD = AS\), i.e., \(C + I = Y\). Since \(Y = C + S\) by definition, substituting this into the equilibrium condition gives \(C + I = C + S\), which simplifies to \(I = S\). This confirms that the saving-investment equality is equivalent to the aggregate demand-aggregate supply equality for equilibrium.
• Autonomous Expenditure: Components of AD that do not depend on the current level of income, such as autonomous consumption (\(C_a\)) and autonomous investment (I).
• Induced Expenditure: Components of AD that depend on the current level of income, primarily induced consumption (\(cY\)).

Understanding the relationship between the saving function and the consumption function is crucial. The negative constant in the saving function (\(-20\)) represents autonomous saving, which is the saving that occurs even at zero income. Autonomous saving is the negative of autonomous consumption. The coefficient of Y in the saving function (0.2) is the marginal propensity to save (MPS), which indicates the fraction of additional income that is saved. The marginal propensity to consume (MPC) is \(1 - MPS\).