Introduction to Income Determination

The fundamental objective of macroeconomics is to develop theoretical frameworks, or models, that can systematically explain how key aggregate economic variables are determined. These variables include the overall level of national income (output), the general price level, the rate of interest, and the level of employment.

These models are not merely academic exercises; they are essential tools for understanding and answering the crucial questions that affect the well-being of a nation's citizens:

• What are the underlying causes of business cycles, such as periods of slow growth or economic recessions?
• What forces lead to a sustained increase in the general price level, a phenomenon known as inflation?
• What are the root causes of a rise in unemployment, and what policies can be implemented to address it?

Given the immense complexity of an economy, analyzing all variables simultaneously is an impossible task. Therefore, macroeconomic modeling relies heavily on the assumption of ceteris paribus, a Latin phrase meaning 'other things remaining equal'. This powerful analytical technique allows us to isolate and study the relationship between a few key variables by assuming that all other influencing factors are held constant during the analysis.

This chapter will focus on the determination of the equilibrium level of National Income using the foundational framework developed by John Maynard Keynes. To build this model in a clear and step-by-step manner, we will begin with two critical simplifying assumptions:

1. The general price level of final goods is assumed to be fixed and constant. This is a reasonable starting assumption for an economy with unused resources, where output can be increased without raising costs and prices.
2. The market rate of interest is also assumed to be constant and given.

These assumptions will be relaxed in more advanced analyses, but they provide a clear and powerful framework for understanding the basic principles of how national income is determined in the short run.

Aggregate Demand and Its Components

To understand how the equilibrium level of income is determined, we must first distinguish between planned and actual values of key macroeconomic variables.

• Ex-post measures: This refers to the actual or accounting values of variables that have been recorded at the end of a given period. For example, ex-post investment is the actual investment that took place in an economy over a year. Ex-post values are always equal by accounting identity (e.g., actual output is always equal to actual expenditure).
• Ex-ante measures: This refers to the planned, intended, or desired values of variables at the beginning of a period. For example, ex-ante consumption is the amount that households plan to consume.

Ex-post and ex-ante values can differ. A producer might plan to add ₹100 to her inventory (ex-ante investment), but if sales are unexpectedly high, she might have to sell from her stock, causing her actual inventory to increase by only ₹70 (ex-post investment).

The theory of income determination is about the alignment of plans in the economy. Therefore, our analysis must focus on the ex-ante (planned) values of the components of aggregate demand.

1. Consumption (C)

The largest component of aggregate demand is the planned consumption expenditure by households. The primary determinant of consumption is disposable income. The functional relationship between planned consumption and income is described by the consumption function.

The simplest and most widely used form is a linear consumption function:

$C = \bar{C} + cY$

This function has two main components:

• $\bar{C}$ is Autonomous Consumption. This is the minimum level of consumption expenditure that households undertake even when their income (Y) is zero. This is the consumption necessary for survival and is financed by drawing down past savings or by borrowing. By definition, $\bar{C}$ is positive.
• $cY$ is Induced Consumption. This is the portion of consumption that varies directly with the level of income. As income rises, households are "induced" to consume more.
• $c$ is the Marginal Propensity to Consume (MPC).

Marginal Propensity to Consume (MPC)

The MPC is the rate of change of consumption as income changes. It represents the fraction of each additional unit of income that households plan to spend on consumption. It is the slope of the consumption function.

$MPC = c = \frac{\Delta C}{\Delta Y}$

The value of MPC is psychologically and logically assumed to lie between 0 and 1 (i.e., $0 \le c \le 1$). People are unlikely to spend more than their additional income ($c \le 1$) and are also unlikely to consume nothing out of their additional income ($c \ge 0$).

Savings (S) and Marginal Propensity to Save (MPS)

Savings is defined as that part of income that is not consumed. The planned savings function can be derived from the consumption function:

$S = Y - C = Y - (\bar{C} + cY) = -\bar{C} + (1-c)Y$

Here, $-\bar{C}$ represents dissaving when income is zero, and $(1-c)$ is the Marginal Propensity to Save.

The Marginal Propensity to Save (MPS), denoted by $s$, is the rate of change of savings as income changes. It is the fraction of each additional unit of income that is saved.

$MPS = s = \frac{\Delta S}{\Delta Y}$

Since any additional unit of income is either consumed or saved, there is a fundamental relationship between MPC and MPS:

MPC + MPS = 1 or $c + s = 1$

Therefore, $s = 1 - c$.

2. Investment (I)

In macroeconomics, investment is defined as the addition to the stock of physical capital (such as machines, buildings, and other productive equipment) and the change in the inventories of a firm. This is also known as capital formation. It's a component of final expenditure because capital goods are not used up in a single production cycle.

In reality, a firm's investment decisions are complex and depend on many factors, most notably the market rate of interest (which reflects the cost of borrowing) and their expectation of future profits. However, for the purpose of our simple Keynesian model, we make a crucial simplifying assumption that firms plan to invest a fixed amount every year, regardless of the level of national income. This is called autonomous investment.

The ex-ante investment demand function is therefore written as a constant:

$I = \bar{I}$

where $\bar{I}$ is a positive constant representing the given or exogenous level of planned investment in the economy.

Determination of Equilibrium Income in the Short Run

The Keynesian model of income determination focuses on how the equilibrium level of national income is established in the short run. This analysis is built upon the interaction between aggregate demand (planned spending) and aggregate supply (planned output) under the assumption of a fixed price level.

The Two-Sector Model and Aggregate Demand

To build the model, we start with the simplest possible economy: a two-sector model which includes only households and firms. In this model, there is no government intervention (no taxes or government spending) and no international trade (a closed economy).

In this simple economy, the ex-ante (planned) Aggregate Demand (AD) for final goods is the sum of the total planned consumption expenditure by households (C) and the total planned investment expenditure by firms (I).

$AD = C + I$

By substituting the behavioral equations for the consumption function ($ C = \bar{C} + cY $) and the autonomous investment function ($ I = \bar{I} $), we can express aggregate demand as a function of national income (Y):

$AD = (\bar{C} + cY) + \bar{I}$

We can group the autonomous (income-independent) components together. Let $\bar{A} = \bar{C} + \bar{I}$ represent the total autonomous expenditure in the economy. The aggregate demand function can then be simplified to:

$AD = \bar{A} + cY$

This equation shows that total planned demand in the economy has two parts: an autonomous part ($\bar{A}$) which does not depend on the current level of income, and an induced part ($cY$) which is directly proportional to the current level of income.

The Equilibrium Condition

The final goods market, and therefore the entire economy in this simple model, is in equilibrium when the total planned supply of final goods (which is the total output or income of the economy, Y) is exactly equal to the total planned demand for those goods (AD).

$Y = AD$

This is the central condition for macroeconomic equilibrium. It represents a state of rest where the production plans of firms are perfectly matched by the spending plans of households and firms.

Disequilibrium and the Role of Inventories

If the economy is not in equilibrium, an automatic adjustment process, driven by unplanned changes in inventories, will guide it back towards equilibrium.

• If $Y > AD$ (Planned Output > Planned Spending): Firms have produced more goods than consumers and investors plan to buy. The unsold goods will pile up in warehouses, leading to an unplanned accumulation of inventories. This signals to firms that they have overproduced. In the next production cycle, they will cut back on production, causing the national income (Y) to fall towards the equilibrium level.
• If $Y < AD$ (Planned Output < Planned Spending): The planned spending in the economy is greater than the current level of production. To meet this high demand, firms will have to sell from their existing stock of goods, leading to an unplanned decumulation (depletion) of inventories. This signals to firms that they have underproduced. In the next production cycle, they will increase production, causing the national income (Y) to rise towards the equilibrium level.

Macroeconomic Equilibrium with Price Level Fixed

The Keynesian analysis assumes an economy with unused resources (e.g., unemployed labour, idle machinery). In such a situation, firms can increase production to meet higher demand without needing to raise prices. This is the justification for taking the price level as fixed.

(A) Graphical Method

We can determine the equilibrium level of income by constructing the aggregate demand and aggregate supply curves on a diagram.

1. Consumption Function - Graphical Representation

The consumption function, $C = \bar{C} + cY$, is a straight line. It has a positive vertical intercept equal to $\bar{C}$ (autonomous consumption) and an upward slope equal to the MPC, $c$. Since $0 < c < 1$, the slope is less than 1, making the line flatter than a 45° line.

2. Investment Function - Graphical Representation

The investment function, $I = \bar{I}$, represents autonomous investment. Since it does not depend on income, it is graphed as a horizontal line at a height equal to $\bar{I}$.

3. Aggregate Demand - Graphical Representation

The Aggregate Demand function, $AD = C + I$, is obtained by the vertical summation of the consumption and investment functions. The resulting AD curve is a straight line that is parallel to the consumption curve (it has the same slope, $c$) but is shifted vertically upwards by the amount of autonomous investment, $\bar{I}$. The vertical intercept of the AD curve is $\bar{C} + \bar{I} = \bar{A}$.

4. Supply Side of Macroeconomic Equilibrium (The 45° Line)

In the Keynesian framework, aggregate supply is assumed to be perfectly elastic at a fixed price level. Firms will supply whatever is demanded. The equilibrium condition, $Y = AD$, is therefore represented graphically by a 45° line starting from the origin. This line is a line of reference where every point on it has the same horizontal and vertical coordinates, signifying that aggregate spending (measured on the vertical axis) equals aggregate income/output (measured on the horizontal axis).

5. Equilibrium

The equilibrium level of income is found where planned aggregate demand equals planned aggregate supply. Graphically, this is the point where the AD curve intersects the 45° line. At this point of intersection (E), the economy is in equilibrium. The corresponding level of income on the horizontal axis, OY₁, is the equilibrium level of national income.

(B) Algebraic Method

We can also solve for the equilibrium income algebraically using the equilibrium condition, $Y = AD$, and substituting the aggregate demand function.

Equilibrium Condition: $Y = AD$

Substitute AD function: $Y = (\bar{C} + \bar{I}) + cY$

Let $\bar{A} = \bar{C} + \bar{I}$ (Total Autonomous Expenditure):

$Y = \bar{A} + cY$

Now, we solve for Y:

$Y - cY = \bar{A}$

$Y(1 - c) = \bar{A}$

The equilibrium level of income ($Y$) is:

$Y = \frac{\bar{A}}{1 - c}$

This equation shows that the equilibrium level of income is a multiple of the total autonomous expenditure, where the multiplier is $1/(1-c)$.

Effect of an Autonomous Change in Aggregate Demand on Income and Output

The equilibrium level of income is dependent on the level of aggregate demand. If there is an autonomous change in any component of AD (like a change in autonomous investment $\bar{I}$), the equilibrium level of income will also change.

Suppose there is an increase in autonomous investment by an amount $\Delta\bar{I}$. This will cause the AD curve to shift vertically upwards in a parallel manner by the amount $\Delta\bar{I}$.

As shown in the graph, the initial equilibrium is at point E1, with income Y*₁. The autonomous increase in investment shifts the AD curve up from AD₁ to AD₂. At the original income level Y*₁, there is now an excess demand equal to the vertical distance E₁F. This excess demand prompts firms to increase production.

The economy moves to a new equilibrium at point E₂, where the new aggregate demand curve AD₂ intersects the 45° line. The new equilibrium income is Y*₂.

A crucial observation is that the increase in income ($\Delta Y = Y_2^* - Y_1^*$) is greater than the initial increase in autonomous investment ($\Delta\bar{I}$). This magnified effect on income is due to the multiplier mechanism.

The Multiplier Mechanism

A central insight of Keynesian economics is that an initial change in autonomous expenditure ($\Delta\bar{A}$)—such as a change in autonomous investment or government spending—will lead to a much larger, or magnified, final change in the equilibrium level of national income ($\Delta Y$). This powerful phenomenon is known as the multiplier mechanism.

How the Multiplier Works: A Chain Reaction of Spending and Income

The multiplier process is driven by a simple but profound fact: in an economy, one person's expenditure is another person's income. This creates a continuous chain reaction of income generation and induced consumption spending. When there is an initial injection of new autonomous spending, it becomes income for the first group of recipients. They, in turn, spend a portion of this new income, which then becomes income for a second group, who then spend a portion of what they receive, and so on.

Let's trace this process with a concrete example. Suppose there is an autonomous increase in investment ($\Delta\bar{I}$) of ₹10 crore, and the Marginal Propensity to Consume (MPC or $c$) in the economy is 0.8.

1. Round 1: A firm makes a new investment of ₹10 crore (e.g., by building a new factory). This amount is paid out as income to factors of production (wages to workers, payments to suppliers, etc.).

   Initial increase in Aggregate Demand and Income: $\Delta Y_1 = \text{₹}10$ crore.

2. Round 2: The households who have received this additional ₹10 crore of income will spend 80% of it, as determined by the MPC. This creates new, induced consumption.

   Increase in Consumption: $\Delta C_1 = 0.8 \times \text{₹}10 = \text{₹}8$ crore.

   This new spending becomes income for another group of people (e.g., shopkeepers, service providers). So, the income in the second round increases by $\Delta Y_2 = \text{₹}8$ crore.

3. Round 3: The recipients of the ₹8 crore will, in turn, spend 80% of it.

   Increase in Consumption: $\Delta C_2 = 0.8 \times \text{₹}8 = \text{₹}6.4$ crore.

   This creates a third round of new income: $\Delta Y_3 = \text{₹}6.4$ crore.

4. Subsequent Rounds: This process of spending creating income, which in turn creates more spending, continues in successive rounds. However, each subsequent increase is smaller than the last because a portion of the income (20% in this case, the MPS) "leaks out" into savings in each round.

The total increase in income is the sum of the increases from all these infinite rounds.

$\Delta Y = \Delta Y_1 + \Delta Y_2 + \Delta Y_3 + \dots$

$\Delta Y = 10 + (0.8 \times 10) + (0.8^2 \times 10) + (0.8^3 \times 10) + \dots$

This is an infinite geometric series. The sum of such a series is given by the formula $a / (1-r)$, where $a$ is the first term and $r$ is the common ratio. In our case, $a = 10$ and $r = 0.8$.

$ \Delta Y = 10 \times \left( \frac{1}{1 - 0.8} \right) = 10 \times \left( \frac{1}{0.2} \right) = 10 \times 5 = \text{₹}50 \text{ crore} $

Thus, an initial investment of ₹10 crore has led to a total increase in national income of ₹50 crore.

The Investment Multiplier Formula

The ratio of the total change in equilibrium income ($\Delta Y$) to the initial change in autonomous expenditure ($\Delta \bar{A}$) is called the investment multiplier (or autonomous expenditure multiplier), denoted by $k$.

$ \text{Multiplier (k)} = \frac{\text{Total Change in Income}}{\text{Initial Change in Autonomous Expenditure}} = \frac{\Delta Y}{\Delta \bar{A}} $

Derivation of the Formula

We know the equilibrium condition is $Y = \bar{A} + cY$.

If autonomous expenditure changes by $\Delta \bar{A}$, income will change by $\Delta Y$. The new equilibrium will be:

$Y + \Delta Y = (\bar{A} + \Delta\bar{A}) + c(Y + \Delta Y)$

$Y + \Delta Y = \bar{A} + \Delta\bar{A} + cY + c\Delta Y$

Subtracting the original equilibrium equation ($Y = \bar{A} + cY$) from this new equation, we get:

$\Delta Y = \Delta\bar{A} + c\Delta Y$

Rearranging to solve for $\Delta Y$:

$\Delta Y - c\Delta Y = \Delta\bar{A}$

$\Delta Y(1 - c) = \Delta\bar{A}$

$\frac{\Delta Y}{\Delta \bar{A}} = \frac{1}{1 - c}$

Since MPC = $c$ and MPS = $s = 1-c$, the formula for the multiplier is:

$ \text{Multiplier (k)} = \frac{1}{1 - MPC} = \frac{1}{MPS} $

The size of the multiplier depends entirely on the value of the MPC. A higher MPC means less leakage into savings per round, leading to a stronger chain reaction and a larger multiplier. Conversely, a higher MPS means more leakage per round, leading to a weaker chain reaction and a smaller multiplier.

The Paradox of Thrift

The Paradox of Thrift is a classic counter-intuitive conclusion drawn from the multiplier model. It states that if all the people in an economy collectively decide to become more thrifty—that is, they increase their marginal propensity to save (MPS) and decrease their marginal propensity to consume (MPC)—the total value of savings in the economy will not increase; in this simple model, it will remain unchanged, while the national income falls.

Explanation of the Paradox

While it is virtuous for an individual to save more, when everyone in society attempts to do so simultaneously, the aggregate result can be detrimental. The paradox arises from the fallacy of composition: what is true for an individual is not necessarily true for the whole.

The mechanism works as follows:

1. An increased desire to save means an autonomous decrease in the desire to consume. The MPC ($c$) falls, and the MPS ($s$) rises.
2. This causes the aggregate demand curve ($AD = \bar{A} + cY$) to pivot downwards, becoming flatter.
3. At the original equilibrium level of income, planned spending (AD) is now less than planned output (Y). This leads to an unplanned accumulation of inventories.
4. Firms respond to the unsold stock by cutting production, which leads to a fall in national income (Y).
5. This fall in income is amplified by the multiplier, which is now smaller due to the lower MPC. The economy settles at a new, lower equilibrium level of income.

The Outcome for Total Savings:

In the two-sector model, the equilibrium condition can also be stated as Planned Savings = Planned Investment ($S=I$). Since we assumed planned investment ($I = \bar{I}$) is autonomous and has not changed, the new equilibrium level of total savings must be equal to the same, unchanged level of investment. Therefore, even though every household is trying to save a larger proportion of their income, their total income has fallen by such a large amount that their total savings remain the same. The attempt to save more has failed in aggregate and has only succeeded in pushing the economy into a recession.

Answer:

Answer:

Answer:

Answer:

Answer:

Answer:

Multiple Choice Questions

Short Answer Type Questions

Long Answer Type Questions