Q.Suppose for two imaginary economies A and B, the value of Marginal Propensity to Consume (MPC) stands at 0·8 and 0·6 respectively. For both the economies, Autonomous Consumption (c̄) = ₹ 400 crore and Investment Expenditure (I) = ₹ 2,000 crore. Calculate the following :

To calculate the break-even level of income and the equilibrium level of income, we use the fundamental relationships between consumption, income, and investment in a simple two-sector economy.

1. The break-even level of income is the point where total consumption equals total income, meaning saving is zero. The consumption function is given by $C = \bar{c} + bY$, where $\bar{c}$ is autonomous consumption and $b$ is the Marginal Propensity to Consume (MPC). At the break-even level, $Y = C$. For Economy A: Given $\bar{c} = \text{₹ } 400 \text{ crore}$ and $b = 0.8$.

   $Y = \bar{c} + bY$

   $Y = 400 + 0.8Y$

   $Y - 0.8Y = 400$

   $0.2Y = 400$

   $Y = \frac{400}{0.2}$

   $Y = \text{₹ } 2,000 \text{ crore}$

2. The equilibrium level of income in a two-sector economy is achieved when Aggregate Demand (AD) equals Aggregate Supply (AS), or equivalently, when planned Investment (I) equals planned Saving (S). The equilibrium condition is $Y = C + I$. Substituting the consumption function $C = \bar{c} + bY$:

   $Y = (\bar{c} + bY) + I$

   $Y - bY = \bar{c} + I$ …

In macroeconomics, understanding how income, consumption, and saving interact is fundamental. The consumption function describes the relationship between consumption expenditure and disposable income. It's a crucial component of aggregate demand. Similarly, the saving function shows the relationship between saving and disposable income. These functions, along with investment, help us determine key levels of economic activity, such as the break-even level of income and the equilibrium level of income.

The break-even level of income is the point where an economy's total income is exactly equal to its total consumption expenditure. At this income level, there is no saving, meaning saving is zero. If income is below the break-even level, households are dissaving (consuming more than their income); if income is above it, households are saving.

The equilibrium level of income in a simple two-sector economy (households and firms) is the level of income where aggregate demand ($AD$) equals aggregate supply ($AS$). Aggregate demand is the sum of consumption ($C$) and investment ($I$). Aggregate supply is essentially the national income ($Y$). So, equilibrium occurs when $Y = C + I$. Alternatively, equilibrium can also be defined as the point where planned saving ($S$) equals planned investment ($I$). Both conditions yield the same equilibrium income.

Let's apply these concepts to the given economies.

(a) Break-even level of income for Economy A

The break-even level of income occurs when total income ($Y$) is equal to total consumption ($C$). At this point, saving ($S$) is zero.

The consumption function is given by $C = \bar{c} + bY$, where $\bar{c}$ is autonomous consumption and $b$ is the Marginal Propensity to Consume (MPC).

For Economy A:

• Autonomous Consumption ($\bar{c}$) = ₹ 400 crore
• Marginal Propensity to Consume ($b$) = 0.8

1. State the formula for break-even income: $Y_{BE} = \frac{\bar{c}}{1-b}$
2. Substitute the given values for Economy A: $Y_{BE} = \frac{400}{1-0.8}$ $Y_{BE} = \frac{400}{0.2}$
3. Calculate the break-even level of income: $Y_{BE} = \frac{400}{\frac{2}{10}} = 400 \times \frac{10}{2} = 400 \times 5$ $Y_{BE} = \text{₹ } \mathbf{2,000 \text{ crore}}$ …