Determination of Income and Employment — Study Notes

1. Introduction

The determination of income and employment in an economy is the central problem of macro economics. In the short run, the level of output and employment depends on the level of aggregate demand in the economy. According to the Keynesian theory, which was developed in the context of the Great Depression, an economy can remain in equilibrium at a level of output that is less than the full employment level because aggregate demand may be insufficient. The classical view, on the other hand, argued that the economy always tends towards full employment automatically through the flexibility of prices, wages, and interest rates.

The Keynesian model uses the concepts of aggregate demand and aggregate supply to determine equilibrium income. Aggregate demand (AD) is the total planned expenditure on final goods and services in an economy, while aggregate supply (AS) is the total value of output that firms are willing to produce and supply, which in equilibrium equals national income. The economy is in equilibrium when planned aggregate expenditure equals aggregate supply, that is, when AD = AS.

The analysis introduces the consumption function, the saving function, and the investment function. The consumption function relates consumption to income, and the saving function is its complement. Investment can be autonomous or induced. The concept of the multiplier explains how an initial change in investment leads to a multiple change in income.

2. Aggregate Demand and Aggregate Supply

2.1 Aggregate Demand (AD)

In a two-sector economy (households and firms), aggregate demand consists of consumption demand and investment demand. In a three-sector economy, government expenditure is also included. Symbolically, for a closed economy:

$$\text{AD} = C + I$$

$$\text{AD} = \bar{C} + bY + \bar{I}$$

where $\bar{C}$ is autonomous consumption, $b$ is the marginal propensity to consume (MPC), $Y$ is income, and $\bar{I}$ is autonomous investment.

2.2 Aggregate Supply (AS)

Aggregate supply is the total value of goods and services produced and supplied by firms at a given price level. In the Keynesian short-run model with constant prices, aggregate supply is measured in terms of national income:

$$\text{AS} = C + S = Y$$

3. Consumption Function

The consumption function shows the functional relationship between consumption and income:

$$\text{C} = \bar{C} + bY$$

where $\bar{C}$ (autonomous consumption) is consumption when income is zero, and $b$ is the marginal propensity to consume. The consumption function is based on the fundamental psychological law of Keynes that as income increases, consumption also increases but by less than the increase in income.

3.1 Average and Marginal Propensity to Consume

$$\text{APC} = \frac{C}{Y} \quad \text{and} \quad \text{MPC} = \frac{\Delta C}{\Delta Y}$$

$$\text{APC} + \text{APS} = 1 \quad \text{and} \quad \text{MPC} + \text{MPS} = 1$$

4. Saving Function

The saving function is the complement of the consumption function:

$$\text{S} = -\bar{S} + (1 - b)Y = -\bar{S} + sY$$

where $s$ is the marginal propensity to save (MPS). Saving is negative at low levels of income and becomes positive once income exceeds the break-even level.

$$\text{APS} = \frac{S}{Y} \quad \text{and} \quad \text{MPS} = \frac{\Delta S}{\Delta Y}$$

5. Equilibrium Level of Income and Employment

The economy is in equilibrium when planned aggregate expenditure equals aggregate supply:

$$\text{AD} = \text{AS} \quad \text{or} \quad C + I = Y$$

Equivalently, equilibrium is achieved when planned investment equals planned saving:

$$\text{I} = \text{S}$$

If AD exceeds AS, inventories fall below the desired level, firms increase production, and income rises until equilibrium is restored. If AD is less than AS, inventories accumulate, firms cut production, and income falls. The equilibrium can occur at less than full employment, which is called underemployment equilibrium.

6. The Multiplier

The investment multiplier measures the ratio of the change in income to the change in autonomous investment that brought it about:

$$\text{K} = \frac{\Delta Y}{\Delta I} = \frac{1}{1 - \text{MPC}} = \frac{1}{\text{MPS}}$$

The multiplier is greater than one because the initial injection of investment raises income, which raises consumption, which raises income again, and so on. The size of the multiplier depends on the marginal propensity to consume; the larger the MPC, the larger the multiplier.

For example, if MPC = 0.8, then K = 1/(1 - 0.8) = 5. An increase in investment of Rs 100 crore will raise income by Rs 500 crore.

7. Full Employment and Involuntary Unemployment

Full employment refers to a situation where all those who are willing and able to work at the prevailing wage rate are employed. When aggregate demand is insufficient to absorb the output corresponding to full employment, involuntary unemployment arises. The government can raise aggregate demand through fiscal policy: increasing government expenditure or reducing taxes. The output gap is the difference between the full employment output and the actual output.

$$\text{Equilibrium condition: } \bar{C} + bY + \bar{I} = Y$$

$$\text{Solving: } Y = \frac{\bar{C} + \bar{I}}{1 - b}$$

8. Investment: Autonomous and Induced

Investment is autonomous when it does not depend on the level of income, as in the case of investment decisions based on expected returns and interest rates. Induced investment varies with the level of income. In the simple Keynesian model, investment is treated as autonomous.

9. Working of the Economy and Fiscal Policy

If the actual level of income is below the full employment level, an increase in government expenditure or a reduction in taxes shifts the aggregate demand curve upward and raises income through the multiplier process. This is the essence of expansionary fiscal policy in the Keynesian framework.

Quick Revision Tables

Table 1: Key Concepts and Formulas

Table 2: Aggregate Demand Components

Table 3: Equilibrium vs Disequilibrium

Mind Map

Important Diagrams (SVG)

Diagram 1: Equilibrium Level of Income (Keynesian Cross)

Diagram 2: The Multiplier Process and Full Employment

Common Mistakes

1. Forgetting that APC + APS = 1 and MPC + MPS = 1, and instead trying to remember each formula separately.
2. Confusing MPC with APC; MPC is the change in consumption per unit change in income, while APC is total consumption divided by total income.
3. Writing the multiplier as 1/(1 - MPS) instead of 1/(1 - MPC) or 1/MPS.
4. Believing that equilibrium income always corresponds to full employment; equilibrium can be an underemployment equilibrium.
5. Confusing the equilibrium condition AD = AS with the alternative condition I = S without recognising that they are equivalent.
6. Treating autonomous investment as income-dependent when it is, by definition, independent of income.
7. Forgetting that the multiplier works only when there is surplus capacity and constant prices in the economy.

Exam Tips

1. Write the consumption function as C = \bar{C} + bY and clearly define \bar{C} and b.
2. Derive the equilibrium income formula Y = (\bar{C} + \bar{I}) / (1 - b) step by step in numerical questions.
3. State that MPC + MPS = 1 and use it to move quickly between the multiplier and MPS.
4. Explain the working of the multiplier in rounds, beginning with the initial investment.
5. Distinguish between equilibrium and full employment and mention underemployment equilibrium.
6. Use the AD = AS and I = S conditions interchangeably in different parts of the same answer.
7. In policy questions, show how an increase in government expenditure raises income by the multiplier times the injection.

Conclusion

The Keynesian theory of income and employment demonstrates that the equilibrium level of output depends on aggregate demand and is not automatically at full employment. The consumption function and its complement, the saving function, determine how changes in income are split between consumption and saving, while the equilibrium condition AD = AS (or I = S) pins down the level of income. The investment multiplier magnifies any autonomous change in expenditure into a larger change in income, providing the theoretical foundation for fiscal policy as a tool to fight recession and unemployment. This chapter connects the concepts of national income, money, and the government budget, and prepares the student for the analysis of fiscal policy and the open economy.