CBSE Class 12 Economics NCERT Solutions: National Income Determination and Multiplier

Solution:

Given:

• Autonomous Investment + Autonomous Consumption ($\backslash bar\{A\}$) = Rs 50 crores
• Marginal Propensity to Save (MPS) = 0.2
• Level of Income (Y) = Rs 4000 crores

First, we calculate the Marginal Propensity to Consume (MPC):

$MPC\; =\; 1\; -\; MPS$

$MPC\; =\; 1\; -\; 0.2\; =\; 0.8$

The formula for ex-ante aggregate demand (AD) in a two-sector economy is:

$$AD\; =\; C\; +\; I$$

Where C = $\backslash bar\{C\}\; +\; bY$ and I = $\backslash bar\{I\}$. Combining autonomous consumption and investment, we get $\backslash bar\{A\}\; =\; \backslash bar\{C\}\; +\; \backslash bar\{I\}$ and $b\; =\; MPC$.

So, the aggregate demand function is:

$$AD\; =\; \backslash bar\{A\}\; +\; bY$$

$$AD\; =\; 50\; +\; 0.8Y$$

Now, we calculate the level of ex-ante aggregate demand at the given income level (Y = Rs 4000 crores):

$$AD\; =\; 50\; +\; 0.8(4000)$$

$$AD\; =\; 50\; +\; 3200$$

$$AD\; =\; 3250$$

The ex-ante aggregate demand is Rs 3250 crores.

To determine if the economy is in equilibrium, we compare ex-ante aggregate demand (AD) with the national income (Y), which represents aggregate supply (AS) in this context. Equilibrium occurs where AD = Y.

At Y = Rs 4000 crores, AD = Rs 3250 crores.

Since $AD\; (3250)\; \backslash neq\; Y\; (4000)$, the economy is not in equilibrium.

Reason: Ex-ante aggregate demand (planned spending) is less than the aggregate supply (total output/income). This indicates that producers have produced more goods and services than are being demanded, leading to an unplanned accumulation of inventories. Consequently, output and income will tend to fall until equilibrium is reached.

Solution:

The 'Paradox of Thrift' is a concept in macroeconomics that describes a situation where an attempt by individuals or households in an economy to increase their savings can paradoxically lead to a decrease in the total savings of the economy, along with a fall in national income.

Explanation:

1. Individual vs. Aggregate Savings: For an individual, saving more means consuming less. This decision is generally seen as prudent and beneficial for personal financial security.
2. Impact on Aggregate Demand: However, when a large number of people in the economy simultaneously decide to save more, they reduce their consumption expenditure. Since one person's expenditure is another person's income, this widespread reduction in consumption leads to a fall in aggregate demand.
3. Fall in Income and Employment: A decrease in aggregate demand causes businesses to reduce their production and investment, leading to a fall in national income and employment.
4. Reduced Overall Savings: As national income falls, the total amount of money available to be saved also decreases. Even though the proportion of income saved (MPS) might remain the same or even increase, the lower income level results in a lower absolute amount of total savings for the economy.

Diagrammatic Representation:

In a standard AD-AS or Savings-Investment diagram, an increase in the propensity to save (or a shift towards saving more at every income level) leads to a downward shift in the aggregate demand curve or the savings curve. This results in a lower equilibrium level of national income and, consequently, lower total savings.

Conclusion: The paradox highlights that while individual thriftiness is good, collective attempts to save more can be detrimental to the overall economy by reducing demand, output, and ultimately, total savings.

Solution:

Effective Demand:

Effective demand refers to the level of aggregate demand (total planned spending) at which the aggregate demand for goods and services is equal to the aggregate supply (total planned output). It is the point where the decisions of consumers and producers to spend and produce align, leading to a stable equilibrium in the economy. In simpler terms, it is the level of income where the economy "clears" – the amount people want to buy matches the amount firms are willing to sell.

Derivation of the Autonomous Expenditure Multiplier:

The autonomous expenditure multiplier shows the change in equilibrium national income resulting from a unit change in autonomous expenditure (like autonomous consumption or investment). We assume fixed prices and interest rates for this derivation.

1. Aggregate Demand (AD) Function: In a simple two-sector economy, aggregate demand is the sum of consumption (C) and investment (I).

$$AD\; =\; C\; +\; I$$

Consumption depends on income (Y) and the Marginal Propensity to Consume (MPC), denoted by 'b'. Autonomous consumption ($\backslash bar\{C\}$) and autonomous investment ($\backslash bar\{I\}$) are independent of income.

$$C\; =\; \backslash bar\{C\}\; +\; bY$$

$$I\; =\; \backslash bar\{I\}$$ (assuming investment is autonomous)

Combining these, the aggregate demand function becomes:

$$AD\; =\; \backslash bar\{C\}\; +\; bY\; +\; \backslash bar\{I\}$$

Let $\backslash bar\{A\}\; =\; \backslash bar\{C\}\; +\; \backslash bar\{I\}$ (total autonomous expenditure). Then:

$$AD\; =\; \backslash bar\{A\}\; +\; bY$$

2. Equilibrium Condition: The economy is in equilibrium where aggregate demand equals aggregate supply (AS). In this model, aggregate supply is often represented by national income (Y), assuming prices are fixed.

$$AS\; =\; Y$$

Equilibrium occurs when:

$$Y\; =\; AD$$

$$Y\; =\; \backslash bar\{A\}\; +\; bY$$

3. Solving for Equilibrium Income (Y): To find the equilibrium level of income, we rearrange the equation:

$$Y\; -\; bY\; =\; \backslash bar\{A\}$$

$$Y(1\; -\; b)\; =\; \backslash bar\{A\}$$

$$Y\; =\; \backslash frac\{\backslash bar\{A\}\}\{1\; -\; b\}$$

4. Deriving the Multiplier: The multiplier (k) is the ratio of the change in equilibrium income ($\backslash Delta\; Y$) to the initial change in autonomous expenditure ($\backslash Delta\; \backslash bar\{A\}$).

If autonomous expenditure changes by $\backslash Delta\; \backslash bar\{A\}$, the new equilibrium income will be:

$$Y\; +\; \backslash Delta\; Y\; =\; \backslash frac\{(\backslash bar\{A\}\; +\; \backslash Delta\; \backslash bar\{A\})\}\{1\; -\; b\}$$

Subtracting the initial equilibrium income equation ($Y\; =\; \backslash frac\{\backslash bar\{A\}\}\{1\; -\; b\}$) from this:

$$\backslash Delta\; Y\; =\; \backslash frac\{(\backslash bar\{A\}\; +\; \backslash Delta\; \backslash bar\{A\})\}\{1\; -\; b\}\; -\; \backslash frac\{\backslash bar\{A\}\}\{1\; -\; b\}$$

$$\backslash Delta\; Y\; =\; \backslash frac\{\backslash Delta\; \backslash bar\{A\}\}\{1\; -\; b\}$$

The multiplier (k) is therefore:

$$k\; =\; \backslash frac\{\backslash Delta\; Y\}\{\backslash Delta\; \backslash bar\{A\}\}\; =\; \backslash frac\{1\}\{1\; -\; b\}$$

Since $b\; =\; MPC$, and $MPC\; +\; MPS\; =\; 1$, we have $1\; -\; b\; =\; MPS$.

Thus, the multiplier can also be expressed as:

$$k\; =\; \backslash frac\{1\}\{MPS\}$$

Diagrammatic Representation:

The diagram shows the Aggregate Demand (AD) curve ($AD\; =\; \backslash bar\{A\}\; +\; bY$) and the 45-degree line representing Aggregate Supply (AS = Y). The initial equilibrium (E) is at the intersection of AD and the 45-degree line, determining income $Y$. An increase in autonomous expenditure from $\backslash bar\{A\}$ to $\backslash bar\{A\}\_1$ shifts the AD curve upwards to $AD\_1$. The new equilibrium (E1) occurs at a higher income level $Y\_1$. The increase in income ($Y\_1\; -\; Y$) is greater than the increase in autonomous expenditure ($\backslash bar\{A\}\_1\; -\; \backslash bar\{A\}$), illustrating the multiplier effect.